# Baroque "chord progressions"



## sealep

I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. They seems to rise or fall on the diatonic scale by a step, repeating the same motif. Does that make sense? For example, Bach seems to like repeating downward scales on successively incrementing steps; building tension upward with the key, while descending melodically.


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## sealep

In addition to that, how does Bach's music generate such an emotional response? It can't be me just me. Is there a music-theorical explanation?


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## EdwardBast

sealep said:


> I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. They seems to rise or fall on the diatonic scale by a step, repeating the same motif. Does that make sense? For example, Bach seems to like repeating downward scales on successively incrementing steps; building tension upward with the key, while descending melodically.


It makes perfect sense to analyze chord progressions in Baroque music! And yes, what you are observing, the sequential repetition of motives on different scale steps, is a mainstay of the style. The underlying progressions supporting these sequences tend to use lots of root motion by fifths, as in, for example, the progression:

iii - vi - ii - V - I - IV

Each root is a fifth above the next. Now if each repetition of a motive covers two chords in the sequence, the motive will sound like it is moving by step, as in *iii*-vi, *ii*-V, *I*-IV. The process of spinning out repeated motives in sequences is called _Fortspinnung_. Part of the reason it is so common in Baroque music is because of the _Doctrine of Affections_, which held, among other things, that each movement should have a single theme that expresses different shades of the same affect (feeling). So finding ways to extend and elaborate the same material was important. And circles of fifths always sound like they are driven as if by a natural force, like a kind of musical gravity.



sealep said:


> In addition to that, how does Bach's music generate such an emotional response? It can't be me just me. Is there a music-theorical explanation?


There isn't going to be a simple explanation for any complex aesthetic effect such as this. But Baroque music theory was heavily influenced by classical rhetorical theory, and under this way of thinking, the composer's role was often compared to that of an orator, whose job was to move an audience to feel one overriding emotion. This is where the Doctrine of Affections comes from. More specifically, there were whole inventories of musical figures based on rhetorical figures that added emotional inflection.


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## millionrainbows

sealep said:


> I know the concept of chord progression is not applicable in the period of the Baroque.


That's correct. If it was applicable, we'd have Bach using what could be called major seventh chords. You said "chord progression," not "CP chord progression."


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## EdwardBast

millionrainbows said:


> That's correct. If it was applicable, we'd have Bach using what could be called major seventh chords. You said "chord progression," not "CP chord progression."


No, it's not correct. Of course the concept of chord progression applies to the Baroque Era. It's just that certain dissonant tones, as in MRs example of a major 7th, weren't considered harmonic tones at the time. They were understood as linear phenomena. Later on such dissonant tones came to be interpreted as chord tones.


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## millionrainbows

EdwardBast said:


> No, it's not correct. Of course the concept of chord progression applies to the Baroque Era. It's just that certain dissonant tones, as in MRs example of a major 7th, weren't considered harmonic tones at the time. They were understood as linear phenomena. Later on such dissonant tones came to be interpreted as chord tones.


It would have been much clearer to say "The concept of chord progression applies to the Baroque, except in certain cases."

To say that the concept of chord progression applies to the Baroque is rather misleading. Besides, the dissonant tones which weren't considered harmonic tones at the time would apply past the Baroque era, into CP classical.

So really, the whole concept of chord progression in Baroque as well as CP tonality is riddled with exceptions like this, which are exceptions to a _modern_ or _jazz_ concept of what qualifies as a "chord," much less a "chord progression."

It sounds like you're trying to "stuff a horse into a suitcase." :lol:


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## Woodduck

sealep said:


> I know the concept of chord progression is not applicable in the period of the Baroque.


I'm a bit baffled by this. Does anyone actually think that composers before the Classical period did not hear and conceive music in terms of harmonic progression? To think that they didn't, wouldn't we have to believe that they achieved a satisfactory succession of harmonies not consciously and intentionally but incidentally, solely through the application of rules governing the movement of contrapuntal melodic lines?

I can't see how anyone able to perceive the precisely articulated tonal plan of a Bach prelude or a Handel aria could think that that plan was a sort of lucky accident, and that it can't be analyzed in terms of chord progression. Nothing in the potential movement of melodic lines will tell a composer how to return to the A section of a da capo aria after he's written a B section in the relative minor, or - crucially - give him a reason for doing so. If a composer wants to create a piece that coheres in time - that has shape and meaning as an entity - he needs a sense of harmonic movement, as well as a grasp of the principles of counterpoint, to tell him where his melodic lines need to go.

Is there a tradition of theoretical analysis that dichotomizes harmonic and contrapuntal thinking to the degree suggested by the OP's query?


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## millionrainbows

Woodduck said:


> I'm a bit baffled by this. Does anyone actually think that composers before the Classical period did not hear and conceive music in terms of harmonic progression?


No, except in certain cases of non-harmonic tones such as a major seventh chord, which was not considered to be a chord.


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## EdwardBast

millionrainbows said:


> It would have been much clearer to say "The concept of chord progression applies to the Baroque, except in certain cases."


This has no clarity whatever and it wasn't what I was saying.



millionrainbows said:


> To say that the concept of chord progression applies to the Baroque is rather misleading. Besides, the dissonant tones which weren't considered harmonic tones at the time would apply past the Baroque era, into CP classical.


Baroque harmonic practice _is_ part of CP. Please learn what the terms you are using mean. There is enough confusion in the world without sowing more.



millionrainbows said:


> So really, the whole concept of chord progression in Baroque as well as CP tonality is riddled with exceptions like this, which are exceptions to a _modern_ or _jazz_ concept of what qualifies as a "chord," much less a "chord progression."


Jazz and modern conceptions aren't relevant here.



millionrainbows said:


> It sounds like you're trying to "stuff a horse into a suitcase."


It sounds like you have trouble identifying both horses and luggage.



millionrainbows said:


> No, except in certain cases of non-harmonic tones such as a major seventh chord, which was not considered to be a chord.


Non-harmonic tones include passing tones, neighbor tones, appoggiaturas, suspensions, etc.-notes understood to be non-chord tones. Therefore what you wrote: "non-harmonic tones such as a major seventh chord" makes no sense. In your terms:

Non-harmonic tones = suitcase
Major seventh chord = horse


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## Woodduck

Is this what's called flogging a dead horse in a suitcase?


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## drmdjones

EdwardBast is correct in every point he makes.


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## drmdjones

In fact, Bach 4-part chorales are used in elementary harmony texts as the very model of CP harmony and voice leading.


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## millionrainbows

drmdjones said:


> EdwardBast is correct in every point he makes.


Yes, academically, but I question this CP concept:
"notes understood to be non-chord tones"

For instance, in the key of C major, the notes B and F, precisely the culprits I pointed out earlier.

In CP, there is no C major seventh chord. It's not recognized as a chord by convention; yet, we all know it exists as a chord. This shows how inflexible orthodox CP theory is. It also exposes the "non-harmonic" aspects of the C major scale. I'm interested in what is possible musically, not conventions.


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## Roger Knox

sealep said:


> I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. They seems to rise or fall on the diatonic scale by a step, repeating the same motif. Does that make sense? For example, Bach seems to like repeating downward scales on successively incrementing steps; building tension upward with the key, while descending melodically.


Here is my reply to the OP. _Disclaimer: I'm of "senior age." My studies and teaching in the relevant fields were in the "70's and '80's, before moving to a different area of music. The material below is also taught to students younger than university age, at conservatories or privately)_.

I'm glad you mentioned things you've identified accurately through _listening_. Especially "building tension upward with the key, while descending melodically," because that is a feeling response coupled with a valid insight. It implies principles of gradual change and of contrast that have practical and artistic implications.

And now to music theory and history, _pedagogical application_: the applicability to the Baroque period of the concept of chord progression. For my undergraduate theory teaching as a neophyte T.A., the very general rule of thumb was to use Roman numerals (e.g. I, IV, V) from 1680 CE onward. These Roman numerals are used in functional harmony. They specify the relation of a chord to a key and are used to name chord progressions. If the above is followed, we see that the identified change happens within the Baroque period. But historically, Roman numerals came along much later than 1680. (Figured bass, that specifies the relation of upper notes to the bass note, was used in practice throughout the Baroque.) 
IMO, TalkClassical needs musicians with your ears and insight and I hope you'll continue to post!


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## isorhythm

millionrainbows said:


> Yes, academically, but I question this CP concept:
> "notes understood to be non-chord tones"
> 
> For instance, in the key of C major, the notes B and F, precisely the culprits I pointed out earlier.
> 
> In CP, there is no C major seventh chord. It's not recognized as a chord by convention; yet, we all know it exists as a chord. This shows how inflexible orthodox CP theory is. It also exposes the "non-harmonic" aspects of the C major scale. I'm interested in what is possible musically, not conventions.


The concept of major seventh chords was definitely introduced into music theory some time during the common practice period.

Also, I think you're conflating theory and practice a little. There are plenty of major seventh chords in Bach, whether he would have called them that or not.


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## EdwardBast

isorhythm said:


> The concept of major seventh chords was definitely introduced into music theory some time during the common practice period.
> 
> Also, I think you're conflating theory and practice a little. *There are plenty of major seventh chords in Bach, whether he would have called them that or not.*


You mean where they is treated as a chord tone rather than a contrapuntal dissonance (suspension, passing tone etc.)? Have any handy examples?


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## Roger Knox

millionrainbows said:


> In CP, there is no C major seventh chord.


That is not true according to any harmony textbook I know, or any harmony course I've taken or taught. Regarding Common Practice Harmony (CP): it is a compilation, systematic but not rigidly consistent, of classical harmonic practice at least in the later 18th and earlier 19th centuries, if not more. Piston's Harmony is a well-known example. We can find exceptions in other harmony books and still more in the actual practice of composers. In common-practice harmony the seventh of a chord usually resolves by step, and is sometimes prepared with the same note in the preceding chord, like the treatment of a suspension in species counterpoint. That does not mean it isn't a chord; to be sure this chord is found within phrases and is not the final chord of a cadence (close), as it is in jazz or pop or sometimes modern classical music.

The idea that I7 (C7 in your example) is not a chord suggests Schenkerian analysis to me, where chords are mostly seen to be derived by linear motion. Only at the opening, the cadence, and certain other points of significance are chords labelled as such with Roman numerals; otherwise figured bass is used. So you might see a I7 chord shown as "7" (shorthand for "7/5/3") in a Schenkerian analysis. For me anyway, it is a problem when Schenkerian or Schenker-related concepts are introduced without identification.


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## millionrainbows

EdwardBast said:


> You mean where they is treated as a chord tone rather than a contrapuntal dissonance (suspension, passing tone etc.)? Have any handy examples?


I'm glad you mentioned things you've identified accurately through _listening. 
IMO, TalkClassical needs musicians with your ears and insight and I hope you'll continue to post!_


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## millionrainbows

MR: "In CP, there is no major seventh chord."



Roger Knox said:


> That is not true according to any harmony textbook I know, or any harmony course I've taken or taught. Regarding Common Practice Harmony (CP): it is a compilation, systematic but not rigidly consistent, of classical harmonic practice at least in the later 18th and earlier 19th centuries, if not more. Piston's Harmony is a well-known example.


"The seventh degree, leading-tone, for all its importance a an indicator of the tonic through its melodic tendency, has not been treated as a basic structural factor in tonality. It remains a significant melodic tone, common to both modes. It is seldom regarded as a generator of harmony, but is usually absorbed into the dominant chord. The progression, leading-tone to tonic, may be described as melodically VII-I and harmonically V-I." -Walter Piston, Harmony, p. 33

This treatment of the seventh degree supports what I am saying, as well as it weakens what you are saying.

"It follows that the tonal structure of music consists mainly of harmonies with tonal degrees as roots (I,IV,V, and II), with the modal degree chords (III and VI) used for variety." -Piston, p. 34

If the seventh degree cannot be used except melodically, as a leading-tone, or harmonically, as part of a V-I, this also supports my position that a C major seventh is not considered to be a chord unto itself.


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## Woodduck

The second act of _Tristan und Isolde_ (1859) begins on a major 7th. It's the earliest example I can think of in which the 7th is neither prepared nor resolved in the usual way. The motif and progression are also heard in that form elsewhere in the opera.


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## drmdjones

There are no major 7th chords in Bach (or Mozart, Beethoven, Mendelssohn, Schubert, Brahms). 7th above the root is a non-chord tone that always resolves to a chord tone. Those of you who think otherwise do not understand dissonance and its treatment, in theory or practice. Others in this thread have tried to explain it to you but apparently some of you still don't get it.

If you can show me one instance of a major 7th in Bach that is not treated as a dissonance, that is to say that it doesn't resolve to a consonance, I will fully repent.

Now that I mention it, I think this thread has gone about as far as it can without examples. Show me some. I double dog dare you


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## Woodduck

drmdjones said:


> There are no major 7th chords in Bach (or Mozart, Beethoven, Mendelssohn, Schubert, Brahms). *7th above the root is a non-chord tone that always resolves to a chord tone. *Those of you who think otherwise do not understand dissonance and its treatment, in theory or practice. Others in this thread have tried to explain it to you but apparently some of you still don't get it.
> 
> If you can show me one instance of a major 7th in Bach that is not treated as a dissonance, that is to say that it doesn't resolve to a consonance, I will fully repent.
> 
> Now that I mention it, I think this thread has gone about as far as it can without examples. Show me some. I double dog dare you


A major 7th need _not_ always resolve to a consonance in CP. If the note which is the seventh is held through the chord that follows, it may instead become a dissonant note in that chord as well. To illustrate: in the key of C, hold E in the top voice as a melody note over the tonic chord (l). Progress to lV (producing a major 7th), then to V7, still keeping the E in the melody, then resolve it to D and cadence on l. A similar case: over the tonic chord in C, let the melody descend from C to B or leap up from G to B (producing a major 7th), change the chord under it to iV, then resolve the dissonant B to A before cadencing on l, either directly or through V. In both cases the dissonant melody note producing the major seventh becomes the dissonant note in another chord.

What can probably be said is that a major 7th is never perceived as a consonance, and is never (to my knowledge) introduced except as a function of melodic movement, before the later 19th century. But as I pointed out in post #20, Wagner used an unprepared major 7th in 1859, and for all I know Liszt may have done so before him.
_
EDIT: See post #24 below._


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## drmdjones

Yes, thank you, I was aware of this type of dissonance treatment but was not inclined to go into such detail. I thought it might give the "pro-major 7ers" a reason to say that the chord with extended dissonance is a major 7, 11, or 13b9#5 chord.


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## Woodduck

drmdjones said:


> There are no major 7th chords in Bach (or Mozart, Beethoven, Mendelssohn, Schubert, Brahms). 7th above the root is a non-chord tone that always resolves to a chord tone. Those of you who think otherwise do not understand dissonance and its treatment, in theory or practice. Others in this thread have tried to explain it to you but apparently some of you still don't get it.
> 
> *If you can show me one instance of a major 7th in Bach that is not treated as a dissonance, that is to say that it doesn't resolve to a consonance, I will fully repent.
> *
> Now that I mention it, I think this thread has gone about as far as it can without examples. *Show me some. I double dog dare you*


I hope your dogs like the taste of crow.

Measure 21 in the Prelude #1 in C Major of the _Wohltemperirte Clavier_ consists entirely of a Major 7th that doesn't resolve to a consonance. Specifically, it's an F 7th in root position, F-F-A-C-E, that resolves to a diminished seventh, F#-C-A-C-Eb. Unusual in baroque music? I suppose so. But there you are.

Woof woof.


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## millionrainbows

Woodduck said:


> I hope your dogs like the taste of crow.
> 
> Measure 21 in the Prelude #1 in C Major of the _Wohltemperirte Clavier_ consists entirely of a Major 7th that doesn't resolve to a consonance. Specifically, it's an F 7th in root position, F-F-A-C-E, that resolves to a diminished seventh, F#-C-A-C-Eb. Unusual in baroque music? I suppose so. But there you are.
> 
> Woof woof.


If it resolves melodically, it's not a chord. Poor example choice anyway.


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## EdwardBast

Woodduck said:


> I hope your dogs like the taste of crow.
> 
> Measure 21 in the Prelude #1 in C Major of the _Wohltemperirte Clavier_ consists entirely of a Major 7th that doesn't resolve to a consonance. Specifically, it's an F 7th in root position, F-F-A-C-E, that resolves to a diminished seventh, F#-C-A-C-Eb. Unusual in baroque music? I suppose so. But there you are.
> 
> Woof woof.


The passage is a layering of linear motions. It's nearly all linear, making Roman numeral, or any other kind of straight harmonic analysis, of limited value. In the whole last half of the piece, measures 19-36, there are only four real root motions, as follows:

19-20 - I
21-22 - IV
23-32 - V
33-36 - I

The E in measure 21 is a suspension from the tonic chord in 19-20, not a chord tone. It eventually resolves via a chromatic passing tone to the D in 24-25.


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## millionrainbows

_He dares to disagree?_ Yep, I have to agree with EdwardBast on this.

As an added note, I find Walter Piston's view of (in C major) the seventh degree as either melodic (VII-I) or harmonic (V-I) as very revealing;

"The seventh degree, leading-tone, for all its importance a an indicator of the tonic through its melodic tendency, _has not been treated as a basic structural factor in tonality._ It remains a significant _melodic_ tone, common to both modes. _It is seldom regarded as a generator of harmony, but is usually absorbed into the dominant chord._ The progression, leading-tone to tonic, may be described as melodically VII-I and harmonically V-I."

"It follows that _the tonal structure of music consists mainly of harmonies with tonal degrees as roots (I,IV,V, and II), with the modal degree chords (III and VI) used for variety."_ -Walter Piston, Harmony, p. 33-34

So if VII can't be used as a tonic root, as a generator of harmony, it reinforces the view of B-D-F-A as in incomplete dominant ninth with its (assumed) root on G.

For me, this brings in to question whether _any _diminished seventh chord can be considered as a tonic-root generator of tonality, unless it is assumed to be an incomplete V7 or dominant ninth chord.


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## Anna Strobl

I'm just going to pop in here to say, Zelenka's favored expressive chord was the diminished seventh. 

I'm on a Zelenka tear today.


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## Woodduck

EdwardBast said:


> The passage is a layering of linear motions. It's nearly all linear, making Roman numeral, or any other kind of straight harmonic analysis, of limited value. In the whole last half of the piece, measures 19-36, there are only four real root motions, as follows:
> 
> 19-20 - I
> 21-22 - IV
> 23-32 - V
> 33-36 - I
> 
> The E in measure 21 is a suspension from the tonic chord in 19-20, not a chord tone. It eventually resolves via a chromatic passing tone to the D in 24-25.


All of that is obvious. Drmdjones was looking for a major 7th chord that doesn't resolve to a consonance. The _underlying_ harmony in measure 21 is lV, but the _audible chord_ is a lV major 7th, whether it results from the interaction of voices or not. Maybe he should have added more requirements: the 7th of the chord can't be suspended from the previous bar, resolution to a consonance need not happen in the next chord but may be delayed through passing chords, etc.

If there's a misunderstanding here, it seems to be a matter of terminology - of a certain way of talking theory. It doesn't make sense to me to say that a clearly audible 7th chord is not "really" a 7th chord merely because the 7th in it is a component of a melodic line moving through the measure. In this case hardly even a melodic line; the piece is a succession of chords broken into arpeggios, in which "melodic lines" and "counterpoint" are bound to result.


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## millionrainbows

"Maybe he should have added more requirements: the 7th of the chord can't be suspended from the previous bar, resolution to a consonance need not happen in the next chord but may be delayed through passing chords, etc."

In the case of the Bach Prelude, it's a non-harmonic tone, not a component of a chord.

"It doesn't make sense to me to say that a clearly audible 7th chord is not "really" a 7th chord merely because the 7th in it is a component of a melodic line moving through the measure."

If the seventh is not considered and treated as a component of the chord, it's a non-harmonic tone. Major seventh chords do not exist in CP tonality. In CP tonal thinking, the note on vii must be resolved to I, or be considered as a component of a V chord in a V-I.

You haven't been listening to jazz, have you? :lol:


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## Guest

millionrainbows said:


> That's correct. If it was applicable, *we'd have Bach using what could be called major seventh chords*. You said "chord progression," not "CP chord progression."


In Bach's chorales (see the "bible" known as the *Riemenschneider 371*) we see many examples of *IV7* (in major keys).


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## Guest

EdwardBast said:


> No, it's not correct. Of course the concept of chord progression applies to the Baroque Era. It's just that certain dissonant tones, as in MRs example of a major 7th, weren't considered harmonic tones at the time. They were understood as linear phenomena. Later on such dissonant tones came to be interpreted as chord tones.


See my post just above to MR.


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## Guest

EdwardBast said:


> You mean where they is treated as a chord tone rather than a contrapuntal dissonance (suspension, passing tone etc.)? Have any handy examples?


I do, mainly IV7 (in the major) and VI7 (in the minor). Do you want the precise bar numbers or will just the title of the chorales suffice?


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## EdwardBast

TalkingHead said:


> I do, mainly IV7 (in the major) and VI7 (in the minor). Do you want the precise bar numbers or will just the title of the chorales suffice?


Titles are fine. Thanks! Although multiple chorales often have the same title, so, the more information the better.

Actually, you don't have to. I got out my Riemenschneider and have been playing some!


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## EdwardBast

Woodduck said:


> All of that is obvious. Drmdjones was looking for a major 7th chord that doesn't resolve to a consonance. The _underlying_ harmony in measure 21 is lV, but the _audible chord_ is a lV major 7th, whether it results from the interaction of voices or not. Maybe he should have added more requirements: the 7th of the chord can't be suspended from the previous bar, resolution to a consonance need not happen in the next chord but may be delayed through passing chords, etc.
> 
> If there's a misunderstanding here, it seems to be a matter of terminology - of a certain way of talking theory. It doesn't make sense to me to say that a clearly audible 7th chord is not "really" a 7th chord merely because the 7th in it is a component of a melodic line moving through the measure. In this case hardly even a melodic line; the piece is a succession of chords broken into arpeggios, in which "melodic lines" and "counterpoint" are bound to result.


You're right. I think I let my discomfort with using harmonic explanations when linear explanations are available get the better of me.


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## Woodduck

EdwardBast said:


> You're right. I think I let my discomfort with using harmonic explanations when linear explanations are available get the better of me.


You had me sweating, Dr. Bast. I like debates where everyone is right.


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## Woodduck

TalkingHead said:


> I do, mainly IV7 (in the major) and VI7 (in the minor). Do you want the precise bar numbers or will just the title of the chorales suffice?


I have an old Kalmus edition. Can you cite a few titles?


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## isorhythm

I'm late responding, but I was in fact thinking of that very part of the first prelude in WTC Book 1.

I agree fully with Woodduck's take on the role of music theory here.

Perhaps more controversially, I think the same idea is applicable to Wagner and the dissolution of tonality. I've started to write a post about that a couple times and may yet finish it in the future.


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## millionrainbows

"I think I let my discomfort with using harmonic explanations when linear explanations are available get the better of me."

Yes, your arms must be sore from trying to stuff that horse into a suitcase.

I've got the Kalmus, the light blue one.


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## Woodduck

isorhythm said:


> I'm late responding, but I was in fact thinking of that very part of the first prelude in WTC Book 1.
> 
> I agree fully with Woodduck's take on the role of music theory here.
> 
> Perhaps more controversially, I think the same idea is applicable to Wagner and the dissolution of tonality. I've started to write a post about that a couple times and may yet finish it in the future.


You've piqued my interest. You can't back out now.


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## millionrainbows

In the Bach Prelude No. 1, there's a B-C-E-G-C which occurs early on, before the F chord.


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## drmdjones

In measure 8 of prelude 1 of WTC1 the B in the bass is a suspension that resolves down to A with the change of harmony from C major in m.8 to Am7 in m.9. Dissonances resolving at the change of harmony is common in CP music.

The B in the bass is treated as a dissonance, a suspension, a purely linear event, not as a chord tone. It also sounds, quite obviously, like a suspension.

Any more examples?

P.S. Bach never wrote a maj7 chord. Ever.


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## tdc

Well it has all the notes of a maj7, it sounds like a maj7, it has all the harmonic flavor of a maj7. Call it what you want.


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## millionrainbows

tdc said:


> Well it has all the notes of a maj7, it sounds like a maj7, it has all the harmonic flavor of a maj7. Call it what you want.


Ok, go ahead and think what you want to, instead of what's right.


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## Woodduck

I don't think there's any disagreement among us about the harmonic and contrapuntal origin and function of these maj7 chords in Bach. We'd can all see what's happening in the music (can't we?). The disagreement is in the use of the term "chord," which has more than one usage. This strikes me as a meaningless dispute.

It's obvious that Bach doesn't land on seventh chords out of the blue, just for the "color" of it, as happened in the 19th and 20th centuries. But it's interesting to observe what he does with them when they occur. In measure 21 of the WTC first prelude, where the melodic element is more implied than defined, the color of the chord really takes center stage, all the more so because it resolves into a dim7. Of course Bach was not averse to interesting harmonic effects, as heard in some of the extraordinary, expressive chromatic passages in many of his works (the _Goldberg Variations_ and the "Crucifixus" from the _B minor Mass_ come to mind).


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## Guest

Woodduck said:


> I have an old Kalmus edition. Can you cite a few titles?


Sure. 
For use of *IV7*:
a) Jesu, joy of man's desiring;
b) Nun ruhen alle Wälder;
c) Ich dank' dir, lieber Herre.


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## Roger Knox

millionrainbows said:


> MR: "In CP, there is no major seventh chord."
> 
> "The seventh degree, leading-tone, for all its importance a an indicator of the tonic through its melodic tendency, has not been treated as a basic structural factor in tonality. It remains a significant melodic tone, common to both modes. It is seldom regarded as a generator of harmony, but is usually absorbed into the dominant chord. The progression, leading-tone to tonic, may be described as melodically VII-I and harmonically V-I." -Walter Piston, Harmony, p. 33
> 
> This treatment of the seventh degree supports what I am saying, as well as it weakens what you are saying.
> 
> "It follows that the tonal structure of music consists mainly of harmonies with tonal degrees as roots (I,IV,V, and II), with the modal degree chords (III and VI) used for variety." -Piston, p. 34
> 
> If the seventh degree cannot be used except melodically, as a leading-tone, or harmonically, as part of a V-I, this also supports my position that a C major seventh is not considered to be a chord unto itself.


Here I am responding to the first line of your post only. I made a mistake in post #19 when I referred to harmony textbooks. Comparing common-practice harmony, Piston version (_Harmony_), and then Schenkerian analysis, I neglected to consider another important source: Schenker-influenced harmony textbooks such as Aldwell and Schachter's influential _Harmony and Voice Leading_; note the difference in title compared to Piston. Aldwell and Schachter acknowledge diatonic seventh chords of the dominant type and chords leading to the dominant (e.g. II7 and IV7) as _functional_ with Roman numerals. But -- unlike Piston -- not I7 (a _major seventh_ if in a major key) so I was wrong there. They don't acknowledge III7 or VI7 either, the 7th being considered a non-harmonic tone indicated by a figured bass numeral.

None of my comments here or earlier concern the practice of particular composers; rather, they refer to common-practice and my question is: what is considered common-practice (CP) harmony in 2019?


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## mikeh375

Roger Knox said:


> ......and my question is: what is considered common-practice (CP) harmony in 2019?


Hi Roger,

I'd suggest that if you are an untrained composer, CP involves chords (often simple common chords) without any concern for voice leading. The chord often becomes a digital audio block in DAW composing, to be shunted around as one sees fit. One could say that the chord in this instance exists in aural isolation if it is sampled.

If one is trained (as I am) then for concert/art music the old principles of voice leading and good part writing still apply in tonal and expanded tonal practice if only for practical reasons. CP for me involves scale/mode invention (sometimes over more than one octave) and the creation of harmonic/melodic material from them using traditional principles, albeit modified. I often apply enharmonic practice and do take liberties depending on where the music, along with my proclivities and aesthetics take me. CP in my case is also a search tool to find material - the workman aspect of composing.

CP as used by many untrained composers has yielded some very interesting and worthwhile musical results imv and the paradigm of sampled/block movement could be compared to French parallelism in the early 20thC. (Ades has exploited the concept of 'sampled' chords). The ubiquity of the DAW has also actually lessened the musical efficacy of such harmonic procedures imv, because of the ease with which music can be created digitally and the fact that everyone follows trends. However, one positive to come out of DAW dumbing down (DDD) so far as actual composition is concerned might well be more openness to unusual harmonic sequences as far as the composer is concerned, although the music created is still limited in scope because of genre limitations and perhaps ability.

CP today has to include atonality too. For me I see that as another resource and one I have also taken advantage of. Whatever the definition of CP, control is obviously essential, along with a sense of adventure and open ears (and the odd serendipitous moment).

The maj7th chord (or any other) can be defined as either a shape, an audio snippet, a sample (even fully scored!) and in someone like Ravel, more often than not, a beautiful moment. (I'm especially partial to his minor 9ths, especially if the 7th is in there too...aaahhh Chloe....


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## millionrainbows

Here's an example of a modern-day usage of a major seventh chord, as a chord, to counter Bach's use of it. A simple, ubiquitous example which I'm sure everyone has heard.


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## BabyGiraffe

Roger Knox said:


> ... my question is: what is considered common-practice (CP) harmony in 2019?


In art music - you are free to use any sonority available (including microtonal techniques). There is no such thing as common practice.

If you are after top 100 pop music, stick to major and minor chords, natural major and aeolian scales, tonics - G, F#/Gb, F , because they allow good, low bass that translates both to stadium rock or EDM festivals and streaming/radio/TV...


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## Roger Knox

*A Misunderstanding*

Popular music, jazz harmony, composition, 20th-21st century developments, music technology and many other aspects of music are fascinating to me, and I appreciate the responses and the variety of interests and accomplishments they represent.

I taught music theory and composition at the undergraduate university level, up to the end of the 1980's. My question should have been much more specific: "What is understood in 2019 music teaching as the _common-practice harmony_ of western classical music that was composed in _c._ the 18th-19th centuries?" That is what the term meant when I was studying harmony in the late 1960's-1970's. (We didn't use the abbreviation CP then.)

I'm referring to harmony textbooks (they do contain examples of great classical composers' music), and not specific composers or works, in order to make a broad comparison. In 2019, do we still take _common-practice harmony_ to be harmony of the 18th and 19th centuries? If so, which harmony are we referring to, taking as reference points these two books extensively used in North America, or their equivalents and successors?

1. Piston's French-derived _Harmony_ *or*,
2. Aldwell and Schachter's Schenker-influenced _Harmony and Voice-Leading_.

I know there are other approaches, but I haven't kept with post-1990 developments, textbooks or teaching in music theory. Here, my purpose is to identify the source of conflicts that came up in this particular thread (that now seem to have abated, to be sure).

My hunch is that they come from differences in when and where people posting here studied music theory, and especially whether they used French-derived books like Piston's, or Schenker-influenced ones like Aldwell and Schachter's.

Whether or not we agree on this I feel we can learn from each other. Everyone has different areas of knowledge, and I do not want my above comments to imply rancor against anyone, or assumed superiority, or anything else, except that I feel some clarity has been lacking in this thread.


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## EdwardBast

mikeh375 said:


> Hi Roger,
> I'd suggest that if you are an untrained composer, CP involves chords (often simple common chords) without any concern for voice leading. The chord often becomes a digital audio block in DAW composing, to be shunted around as one sees fit. One could say that the chord in this instance exists in aural isolation if it is sampled.


It depends on what part of the CP era, 250 years at least(!), is under discussion. In the Baroque Era and early Classical voice-leading is extremely important, with some configurations looking like diatonic 7th chords only occurring as the result of linear phenomena. Later the same "chords" occur with less strict, if any, linear justification.


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## Larkenfield

millionrainbows said:


> That's correct. If it was applicable, we'd have Bach using what could be called major seventh chords. You said "chord progression," not "CP chord progression."


I question what major seventh chords have anything to do with whether Baroque music has chord progressions or not. I find it hard to understand how someone could reach that conclusion when it's possible to hear the chord sequences and harmonic cadences.


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## BabyGiraffe

Roger Knox said:


> *A Misunderstanding*
> 
> Popular music, jazz harmony, composition, 20th-21st century developments, music technology and many other aspects of music are fascinating to me, and I appreciate the responses and the variety of interests and accomplishments they represent.
> 
> I taught music theory and composition at the undergraduate university level, up to the end of the 1980's. My question should have been much more specific: "What is understood in 2019 music teaching as the _common-practice harmony_ of western classical music that was composed in _c._ the 18th-19th centuries?" That is what the term meant when I was studying harmony in the late 1960's-1970's. (We didn't use the abbreviation CP then.)
> 
> I'm referring to harmony textbooks (they do contain examples of great classical composers' music), and not specific composers or works, in order to make a broad comparison. In 2019, do we still take _common-practice harmony_ to be harmony of the 18th and 19th centuries? If so, which harmony are we referring to, taking as reference points these two books extensively used in North America, or their equivalents and successors?
> 
> 1. Piston's French-derived _Harmony_ *or*,
> 2. Aldwell and Schachter's Schenker-influenced _Harmony and Voice-Leading_.
> 
> I know there are other approaches, but I haven't kept with post-1990 developments, textbooks or teaching in music theory. Here, my purpose is to identify the source of conflicts that came up in this particular thread (that now seem to have abated, to be sure).
> 
> My hunch is that they come from differences in when and where people posting here studied music theory, and especially whether they used French-derived books like Piston's, or Schenker-influenced ones like Aldwell and Schachter's.
> 
> Whether or not we agree on this I feel we can learn from each other. Everyone has different areas of knowledge, and I do not want my above comments to imply rancor against anyone, or assumed superiority, or anything else, except that I feel some clarity has been lacking in this thread.


Hm, what you teach in schools and early university courses is simplifications, distortions and anachronisms. The main point of music theory education is to develop practical skills ( and musicianship), not to teach some idealised theories.

We may do a statistical analysis on forgotten, but mediocre (not too original) composer styles in a chosen age and get an idea what the common practice was. Famous composers are not that good models, because many of them have too individual style. (We can see such analysis done usually on Bach and Mozart works - search academic university papers databases - and there are discrepancies between theory and practice in resolutions of dissonances and voice leading, which, of course, can be expected, because music is art form, not something that can be reduced to set of rules. Following blindly music theory book instructions will always lead to boring and mechanical end product.)

It is also disappointing that almost (I have seen only in English that doesn't do this and it's out of print, translation from German) every music theory book that is useful for teaching - not just advanced, dry theory- omits details on historical tunings. I'm pretty sure that many composers from the past would have experimented with more "progressive or radical" modulations and chords, if they weren't out of tune in the optimized for meantone gamuts (basically diatonic scale; meantone extensions have commas that make romantic chord progression - think Liszt - to require enharmonic shifts and splitted keys on keyboards, so you need more advanced keyboards or unfretted string instruments) in the historical tunings.

The best books on common practice are these that basically teach historical methods. These are very good, imo:

"The Art of Accompaniment from a Thorough-Bass: As Practiced in the XVII and XVIII Centuries" (2 volumes) - Arnold (Bach, Vivaldi etc lovers may find this one interesting,)

"Music in the Galant Style" - Gjerdingen (Mozart fans will love this)


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## millionrainbows

...but there are certain ways of thinking which are codified into rules, and do not change, such as parallel fifths, resolving dissonance, what dissonance is, and NO MAJOR SEVENTH CHORDS!

It sounds like there is a resistance to seeing academic theory as old-fashioned, outdated, and inflexible. Perhaps this is because it has been institutionalized into the dominant ideology. 

I urge all theorists to escape from the fold and explore new methods of music theory, which dare to go outside the box into more chromatic, less diatonic territory.


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## mikeh375

The point about learning theory (especially the old fashioned stuff) as a composer has not really been touched on and might be worth mentioning. When one learns from species counterpoint all the way through to atonality, the experience of handling notes via exercises is also giving a composer insight into his own aesthetics. A composer will find natural affinities with certain ways of doing things and will also probably discard techniques deemed unappealing. This process of exposure to, practice of (especially) and finding (developing) an instinctive affinity when choosing preferred techniques is of paramount importance during formative years and in this regard, the value of academic theory and earlier esoteric theory/practice can't be overstated imv. Academic learning for a composer is akin to an instrumentalist learning scales and arpeggios - once mastered, one can then concentrate on the music.

Obviously one also needs to balance the insights gleaned from tradition with newer techniques too for a fully rounded and informed approach to finding one's own voice, but in my opinion newer techniques are best sought out after one has a good grasp of tradition. The reason I say this is because a chromatic field used without any control could be construed as charlatanism - anybody can create a cacophony. To create a cogent expression is to know yourself and to know yourself requires knowledge of what is possible and that is what theory can give you.


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## BabyGiraffe

millionrainbows said:


> NO MAJOR SEVENTH CHORDS!


There is a whole chapter on them in the "Art of ..." If you don't believe in this book (which is basically compilation), check C.P.E. Bach talking about major sevenths ( I can't understand why do you think there was no such thing as theoretical concept back then):

free download:
https://imslp.org/wiki/Versuch_über...elen,_H.868,_870_(Bach,_Carl_Philipp_Emanuel)

English translation:
https://www.amazon.com/Essay-True-Playing-Keyboard-Instruments/dp/0393097161

Any practice is just a style: if you follow certain rules, you will sound in a particular way. I don't think that there is right and wrong in music.


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## mikeh375

BabyGiraffe said:


> in
> Any practice is just a style: if you follow certain rules, you will sound in a particular way. I don't think that there is right and wrong in music.


I agree BG. Theory (technique) does enable you to find yourself though because even practising (say) triple counterpoint in a Bachian way, you are exercising your creative muscle and training yourself to seek out perhaps motivic development and any music hidden or implied in an idea. This clearly has major benefits further on when ideas come at a later stage and whilst at first the exercises will sound like pastiche, once the principle is learnt, then one applies invention and imagination to the technique - imagination and invention which has been informed by the experience of learning.
All said though I absolutely agree that anything should and very often does go, unless you are about to take an exam, or have no idea how to express yourself in a succinct and artful manner - it might be advisable to try some learning in the latter case.


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## millionrainbows

mikeh375 said:


> ...Obviously one also needs to balance the insights gleaned from tradition with newer techniques too for a fully rounded and informed approach to finding one's own voice, but in my opinion newer techniques are best sought out after one has a good grasp of tradition. The reason I say this is because a chromatic field used without any control could be construed as *charlatanism - anybody can create a cacophony.* To create a cogent expression is to know yourself and to know yourself requires knowledge of what is possible and that is what theory can give you.


I understand the old ways well enough to know an archaic concept of harmony when I see it. In CP theory, there are many chords which don't exist, and I use them as chord changes to solo over. Such as E minor 9 to Eb Maj 13 b5 (or as a polychord F Major over Eb Maj) to D Maj 13 b5 etc. This is modern harmonic thinking which has no need to "resolve" any of these chord tones contrapuntally. It's a whole different way of thinking.
It's touching that you pay homage to the past (while dissing me as a possible charlatan), but I've moved on, and have bigger fish to fry.


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## mikeh375

millionrainbows said:


> I understand the old ways well enough to know an archaic concept of harmony when I see it. In CP theory, there are many chords which don't exist, and I use them as chord changes to solo over. Such as E minor 9 to Eb Maj 13 b5 (or as a polychord F Major over Eb Maj) to D Maj 13 b5 etc. This is modern harmonic thinking which has no need to "resolve" any of these chord tones contrapuntally. It's a whole different way of thinking.
> It's touching that you pay homage to the past (while dissing me as a possible charlatan), but I've moved on, and have bigger fish to fry.


MillionR, you completely and utterly misunderstood me - I'm not dissing you, I don't know you, let alone your compositional competence or what you do in music. 
I also agree with you about modern compound/bitonal etc. harmony as I often think in those terms (I used to play jazz guitar and all those chord designations are still with me and yes I too soloed over many a complicated sequence. There is no need to resolve anything academically and hasn't been for a long time. The old ways are a good foundation though in order to develop from, this I know to be true, even if it is not for everyone. Boil the fish, it's healthier.


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## millionrainbows

mikeh375 said:


> MillionR, you completely and utterly misunderstood me - I'm not dissing you, I don't know you, let alone your compositional competence or what you do in music.
> I also agree with you about modern compound/bitonal etc. harmony as I often think in those terms (I used to play jazz guitar and all those chord designations are still with me and yes I too soloed over many a complicated sequence. There is no need to resolve anything academically and hasn't been for a long time. *The old ways are a good foundation though in order to develop from, this I know to be true,* even if it is not for everyone. Boil the fish, it's healthier.


I disagree, and Pat Martino has spoken about the unspoken dominance of diatonic thinking and the tyranny of the keyboard: all the note names, notational system, and the very language of music itself, are derived from this diatonic key-system-based way of thinking. Chromatic thinking (in the truest sense) is an approach which clears the playing field.

By necessity, we all use this language to communicate our musical ideas to other musicians; but there is no need to "pay homage" to it or its ideologues.


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## mikeh375

MR, It's not about paying homage for me, it is about what learning technique inculcates into you as a developing creative artist. The polemics mean nothing to one who has the wits to assimilate the essence of technique and adapt it to their own proclivities. But getting to that stage is only achieved by learning in the first place. Those who have a voice will find themselves regardless as it is a natural bent. Keeping it simple in order for one to find their way at first is highly recommended, rather than giving them all 12 tones to dick around in without knowing how to make a statement cohere, write an extended phrase, develop motifs, score a passage effectively, acquire a sense of musicianship from which to spring forth, or achieve a sense of inevitability in the work. Giving an _inexperienced_ composer an open atonal field to play in will inevitably result in unsatisfying, wandering, uncertain nonsense with no sense of purpose unless the composer knows themselves and how to achieve their ideas or has a wonderful talent. Remember too that Schoenberg's innovation was long considered by him and not decided upon lightly, he was after all a composer with a considerable (traditional) technical arsenal.

The polemics you are engaging in don't actually mean much to a mature composer on a day to day basis as far as I'm concerned. What really matters is finding and presenting the idea and the more you know, the more options you have to support your fantasy. There are clearly many ways to learning composition (all valid imv by the way), but some come with more of a guarantee of good execution and lucid expression than others.

We will therefore have to disagree on the point about training and I for one don't care at all for distinctions being made about a diatonic or chromatic paradigm, having left those concerns behind years ago. I'm not saying they are not without significance and I am enjoying the thread and the theoretical prowess on display is wondeful. It's just that on a day to day basis, they are of no concern and the distinctions do not impact practically nor aesthetically on a young mind that needs to learn imv, that mind will transcend any diatonic 'hedging in' if it is able to.

I would like to ask you if you are a composer and if so, what are your credentials and what music do you write? (any links?, I'd love to hear some as you do make many valid points). This would give me a better understanding of you and help keep any antagonism in check. You can see my signature below if you want to know about me....if you want atonality, check out the preludes and fugues or the clarinet concerto, for expanded tonality, the violin sonata, or for more obvious diatonicism, the Partita Concordia. (page 3 on the site has scrolling scores).

I also have to say that this would've been a more pleasant conversation for me if you would have at least acknowledged your misunderstanding seeing that I was at pains to correct it, but never mind, this is the internet after all eh?


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## millionrainbows

mikeh375 said:


> MR, It's not about paying homage for me, it is about what learning technique inculcates into you as a developing creative artist. The polemics mean nothing to one who has the wits to assimilate the essence of technique and adapt it to their own proclivities. But getting to that stage is only achieved by learning in the first place. Those who have a voice will find themselves regardless as it is a natural bent. Keeping it simple in order for one to find their way at first is highly recommended, rather than giving them all 12 tones to dick around in without knowing how to make a statement cohere, write an extended phrase, develop motifs, score a passage effectively, acquire a sense of musicianship from which to spring forth, or achieve a sense of inevitability in the work. Giving an _inexperienced_ composer an open atonal field to play in will inevitably result in unsatisfying, wandering, uncertain nonsense with no sense of purpose unless the composer knows themselves and how to achieve their ideas or has a wonderful talent. Remember too that Schoenberg's innovation was long considered by him and not decided upon lightly, he was after all a composer with a considerable (traditional) technical arsenal.
> 
> The polemics you are engaging in don't actually mean much to a mature composer on a day to day basis as far as I'm concerned. What really matters is finding and presenting the idea and the more you know, the more options you have to support your fantasy. There are clearly many ways to learning composition (all valid imv by the way), but some come with more of a guarantee of good execution and lucid expression than others.
> 
> We will therefore have to disagree on the point about training and I for one don't care at all for distinctions being made about a diatonic or chromatic paradigm, having left those concerns behind years ago. I'm not saying they are not without significance and I am enjoying the thread and the theoretical prowess on display is wondeful. It's just that on a day to day basis, they are of no concern and the distinctions do not impact practically nor aesthetically on a young mind that needs to learn imv, that mind will transcend any diatonic 'hedging in' if it is able to.
> 
> I would like to ask you if you are a composer and if so, what are your credentials and what music do you write? (any links?, I'd love to hear some as you do make many valid points). This would give me a better understanding of you and help keep any antagonism in check. You can see my signature below if you want to know about me....if you want atonality, check out the preludes and fugues or the clarinet concerto, for expanded tonality, the violin sonata, or for more obvious diatonicism, the Partita Concordia. (page 3 on the site has scrolling scores).
> 
> I also have to say that this would've been a more pleasant conversation for me if you would have at least acknowledged your misunderstanding seeing that I was at pains to correct it, but never mind, this is the internet after all eh?


Edit: This is the internet after all, eh?


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## Roger Knox

EdwardBast said:


> It depends on what part of the CP era, 250 years at least(!), is under discussion. In the Baroque Era and early Classical voice-leading is extremely important, with some configurations looking like diatonic 7th chords only occurring as the result of linear phenomena. Later the same "chords" occur with less strict, if any, linear justification.


_Yes_, Edward, this post answers my question. The phrase we used in the 1960's-70's, "common practice _harmony_," is no longer valid. We see that for harmony it covered too broad a time period, approximately the 250 years of the CP era you mention. It ignored the distinction you have explained between Baroque/early Classical harmony and later, and was criticized by historical musicologists for ignoring the way Baroque/early Classical music was conceived, played, and heard at the time. As for more recent popular music and other musics, I'll get to that later.


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## Roger Knox

Re popular music, to what does the acronym "CP" apply? Does it refer to the 20th-21st-century continuation, of course with modifications, of harmony or other practices from the "Common-Practice Era" of classical music referred to above (c. 1650-1900)?


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## mikeh375

millionrainbows said:


> Edit: This is the internet after all, eh?


Sigh..ah well.

Roger,

I was using the acronym CP literally when referring to popular music, with no implications other than what the kids do as a matter of course, ie a common way of doing things - lazy of me I suppose, sorry for any confusion.


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## EdwardBast

Roger Knox said:


> _Yes_, Edward, this post answers my question. The phrase we used in the 1960's-70's, "common practice _harmony_," is no longer valid. We see that for harmony it covered too broad a time period, approximately the 250 years of the CP era you mention. It ignored the distinction you have explained between Baroque/early Classical harmony and later, and was criticized by historical musicologists for ignoring the way Baroque/early Classical music was conceived, played, and heard at the time. As for more recent popular music and other musics, I'll get to that later.


While you and Mikeh are here: I seem to remember reading (or hearing) that inversional equivalence was not part of Bach's thinking - that each inversion of a common triad or 7th chord was understood by him and many of his contemporaries as a separate entity from the others with a different function and requiring different treatment. Is this idea on your radar? Do you know the provenance of this idea, if it really is a thing?


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## millionrainbows

EdwardBast said:


> While you and Mikeh are here: I seem to remember reading (or hearing) that inversional equivalence was not part of Bach's thinking - that each inversion of a common triad or 7th chord was understood by him and many of his contemporaries as a separate entity from the others with a different function and requiring different treatment. Is this idea on your radar? Do you know the provenance of this idea, if it really is a thing?


Is this a test?

A chord in all its inversions has the same root function (not bass note), and the same quality (major/minor).

Maybe in earlier times, it is treated differently...

In some _convoluted sense,_ it could be said that since figured bass notation recognizes each inversion separately from a bass note (not a root function), that they are not "equivalent" in that sense. Is this what is being gotten at, as some sort of test? Is this one of the academic hurdles one is expected to deal with?

WIK: Figured-bass numerals express distinct intervals in a chord *only as they relate to the bass note *(not a root function)*. They make no reference to the key of the progression (unlike Roman-numeral harmonic analysis).

*Because that would be "harmonic thinking." Right? Is this the trick?


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## Roger Knox

EdwardBast said:


> While you and Mikeh are here: I seem to remember reading (or hearing) that inversional equivalence was not part of Bach's thinking - that each inversion of a common triad or 7th chord was understood by him and many of his contemporaries as a separate entity from the others with a different function and requiring different treatment. Is this idea on your radar? Do you know the provenance of this idea, if it really is a thing?


Interesting question, it is on my radar. I don't remember if Jean-Philiippe Rameau (1683-1764) was the first to think of chord "roots," but he was the one who systematically developed the idea, including the equivalence of chord inversions to root position chords, in his _Treatise on Harmony_ published in 1722. This book is beyond me! It is very complicated for modern readers, but there are explanations elsewhere, and the ideas themselves are not that difficult.

As for J. S. Bach, being of the German school he wouldn't have thought in terms of chord roots or inversional equivalence. Nor did his son C. P. E. Bach (1714-88), whose _Essay on the True Art of Playing Keyboard Instruments_ was cited in my learning years as the German opposite to Rameau's French treatise. (It is also much easier to read). Its translator into English, William Mitchell, was one of the early Schenkerian analysis promoters in the U.S.A.


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## millionrainbows

Roger Knox said:


> Interesting question, it is on my radar. I don't remember if Jean-Philiippe Rameau (1683-1764) was the first to think of chord "roots," but he was the one who systematically developed the idea, including the equivalence of chord inversions to root position chords, in his _Treatise on Harmony_ published in 1722. This book is beyond me! It is very complicated for modern readers, but there are explanations elsewhere, and the ideas themselves are not that difficult.
> 
> As for J. S. Bach, being of the German school he wouldn't have thought in terms of chord roots or inversional equivalence. Nor did his son C. P. E. Bach (1714-88), whose _Essay on the True Art of Playing Keyboard Instruments_ was cited in my learning years as the German opposite to Rameau's French treatise. (It is also much easier to read). Its translator into English, William Mitchell, was one of the early Schenkerian analysis promoters in the U.S.A.


This was posted while I was composing mine; and it confirms what I suspected, that there are differences of approach in harmonic/root thinking and "figured bass thinking."

I think these descriptions are rather misleading, and unclear (as I said above, _convoluted_). And if Rameau was thinking in roots, that's good enough for me. I've got the Rameau book, and I'm getting it out.

I think figured bass is rather archaic unless one has an overview, and I think it's limited to that older style of music, and is really more of a "technique" which was used in lieu of harmonic/root thinking, which was not developed or accepted or used, whatever.


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## EdwardBast

Roger Knox said:


> Interesting question, it is on my radar. I don't remember if Jean-Philiippe Rameau (1683-1764) was the first to think of chord "roots," but he was the one who systematically developed the idea, including the equivalence of chord inversions to root position chords, in his _Treatise on Harmony_ published in 1722. This book is beyond me! It is very complicated for modern readers, but there are explanations elsewhere, and the ideas themselves are not that difficult.
> 
> As for J. S. Bach, being of the German school he wouldn't have thought in terms of chord roots or inversional equivalence. Nor did his son C. P. E. Bach (1714-88), whose _Essay on the True Art of Playing Keyboard Instruments_ was cited in my learning years as the German opposite to Rameau's French treatise. (It is also much easier to read). Its translator into English, William Mitchell, was one of the early Schenkerian analysis promoters in the U.S.A.


Yeah, that's what I figured. The Bachs would likely have found Rameau out to lunch had they read him. I was thinking particularly of cases like the ii6/5 chord, which is an entity unto itself in Bach. The way inversions are given separate coverage in modern theory books, even in the Piston era, suggests that perhaps no one in classical theory ever completely accepted inversional equivalence, except for the sake of terminological convenience.


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## millionrainbows

EdwardBast said:


> Yeah, that's what I figured. The Bachs would likely have found Rameau out to lunch had they read him. I was thinking particularly of cases like the ii6/5 chord, which is an entity unto itself in Bach. The way inversions are given separate coverage in modern theory books,even in the Piston era, suggests that perhaps no one in classical theory ever completely accepted inversional equivalence.


I don't think you can escape the "harmonic truth" that "a C major is a C major is a C major." (apologies to Gertrude Stein).

This figured-bass thinking was perhaps a method which worked its way into the stylistic arsenal of composers, and yes, they had to be handled in specific ways, but the abstracted convenience of thinking harmonically is still in evidence to modern analysts. Figured-bass tends to get bogged-down in voice-leading details which ignore a purer, freer abstract distillation of harmonic considerations. And as harmony got more complex, what happened to figured bass thinking? It failed, or rejected more complex harmony. Figured bass is an ideological artifact of a bygone way of thinking. We have bigger, more complex fish to fry.


----------



## Guest

EdwardBast said:


> Yeah, that's what I figured. The Bachs would likely have found Rameau out to lunch had they read him. *I was thinking particularly of cases like the ii6/5 chord, which is an entity unto itself in Bach*. The way inversions are given separate coverage in modern theory books, even in the Piston era, suggests that perhaps no one in classical theory ever completely accepted inversional equivalence, except for the sake of terminological convenience.


I see that you have really been reading through your Riemenschneider "371" bible!! Bach does indeed use the ii6/5 in nearly 90% of his final cadences.


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## millionrainbows

" ...the separate bass line, with figures added above to indicate other chordal notes, shortly became "functional", as the sonorities became "harmonies", and music came to be seen in terms of a melody supported by chord progressions (homophony), rather than interlocking, equally important lines that are used in polyphony." WIK

Riemenschneider "371" refers to an edition of the Bach chorales.


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## EdwardBast

TalkingHead said:


> I see that you have really been reading through your Riemenschneider "371" bible!! Bach does indeed use the ii6/5 in nearly 90% of his final cadences.


For years, actually. I'm a theorist, among other things.

Do you have access to a statistical summary of harmonic usage in the chorales? I know it's been done but I forget by whom.


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## millionrainbows

EdwardBast said:


> Do you have access to a statistical summary of harmonic usage in the chorales? I know it's been done but I forget by whom.


Eww, music shouldn't be mixed with mathematics.


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## Guest

EdwardBast said:


> For years, actually. I'm a theorist, among other things.
> 
> *Do you have access to a statistical summary of harmonic usage in the chorales?* I know it's been done but I forget by whom.


I'm afraid I don't.
The only statistical reference I have is for the cadences, which you can find in *Malcolm Boyd*, _Chorale Harmonization and Instrumental Counterpoint_, Kahn & Averill (London), 1999. If you want, please send me a privare message and I can scan and send you the small analytical table of the cadences (for personal study purposes, of course).

Otherwise, for an excellent study of Bach's chorale practice I use *William Lovelock's* _The Harmonization of Bach's Chorales_. I believe it is no longer in print.


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## millionrainbows




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## EdwardBast

TalkingHead said:


> I'm afraid I don't.
> The only statistical reference I have is for the cadences, which you can find in *Malcolm Boyd*, _Chorale Harmonization and Instrumental Counterpoint_, Kahn & Averill (London), 1999. If you want, please send me a privare message and I can scan and send you the small analytical table of the cadences (for personal study purposes, of course).
> 
> Otherwise, for an excellent study of Bach's chorale practice I use *William Lovelock's* _The Harmonization of Bach's Chorales_. I believe it is no longer in print.


Thanks for those citations. I'll query on SMT and AMS discussion forums because I think that's where I heard this kind of data quoted.


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## BabyGiraffe

millionrainbows said:


> Is this a test?
> 
> A chord in all its inversions has the same root function (not bass note), and the same quality (major/minor).
> 
> Maybe in earlier times, it is treated differently...
> 
> In some _convoluted sense,_ it could be said that since figured bass notation recognizes each inversion separately from a bass note (not a root function), that they are not "equivalent" in that sense. Is this what is being gotten at, as some sort of test? Is this one of the academic hurdles one is expected to deal with?
> 
> WIK: Figured-bass numerals express distinct intervals in a chord *only as they relate to the bass note *(not a root function)*. They make no reference to the key of the progression (unlike Roman-numeral harmonic analysis).
> 
> *Because that would be "harmonic thinking." Right? Is this the trick?


Functional theory is based on the structure of diatonic scale in just intonation by Hugo Riemann (and this is just a small part of his theories).
Don't search for functions in older theories. You won't find them anywhere before his time (1849-1919); he introduced mathematical word "function" in musical context. This (German) theory is not popular at all in Britain and US, aside from simplified analysis using roman numerals (it's overcomplicated and the notation is horrible - see the book below; it's also unsuitable for non-classical music, just like any other "classical" theory). Schoenberg/Schenker's (Austrian) school is what is popular there.
You will find plenty of nonsense in both theories, imo.

https://archive.org/details/cu31924022305357/page/n3

It is funny how long it took for people to recognise various chord and scale "inversions" as permutations of the same abstract object. The same is valid for scales - there were even in the beginning of 20th century scale "cheat-sheets" that were listing the same scale in a different mode.

Edit: Interesting video on history of Roman numerals:


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## isorhythm

Woodduck said:


> You've piqued my interest. You can't back out now.


Well, one reason I haven't done it is that I'm not sure I have either the requisite knowledge of Wagner's music or the command of music theory to really support my case.

But the short version is that I think the claim of the "Wagner leads to atonality" people is being misunderstood: no one's actually saying that tonality isn't central to Wagner's music (as counterpoint is central to Bach's, even in the prelude that's just a sequence of of arpeggiated chords). The claim is that Wagner pushed the role of unstated tonics to the point where other phenomena (the linear movement of highly chromatic lines and the sheer sound of the harmonies that result), start to become as important to listeners' actual experience of the music as the underlying tonal grammar, and that suggested new directions to composers that ultimately led to atonality.

I was reminded of this recently when you quoted this book: "The manipulation of unstated tonics in motivic sequence then becomes a direct manipulation of an unconscious psychological process of projecting order. It is not an invention or deviation from the theoretical structure of tonal practice, but a realization of possibilities inherent within the system. As such it represents a profound stylistic advance, and the possibilities which it opened may remain largely unexplored by later composers."

I think the reason it was largely unexplored by later composers is that if you push it much further, the unconscious psychological process breaks down and most listeners cease perceiving the sequences of unstated tonics. Anyway that's how it is for me when I try to listen to Berg's piano sonata or Schoenberg's chamber symphony, and it seems very natural that those composers ended up going the way they did.


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## EdwardBast

TalkingHead said:


> Sure.
> For use of *IV7*:
> a) Jesu, joy of man's desiring;
> b) Nun ruhen alle Wälder;
> c) Ich dank' dir, lieber Herre.


I examined all chorales under these titles in Riemenscheider and didn't find examples of the use of a IV7 chord. The closest was Nun ruhen alle Wälder (no. 117), which has what looks like a IV7 on the first beat of the final bar. But on the last beat of the preceding bar we have a IV6, which makes the C on the next beat a passing tone.

In none of the versions of Ich dank' dir, lieber Herre in Riemenschneider did I find a IV7 chord, although there were a couple with the 7th as a passing tone.

Do you have anything more specific for these references - like which of the multiple settings you meant?


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## Woodduck

isorhythm said:


> Well, one reason I haven't done it is that I'm not sure I have either the requisite knowledge of Wagner's music or the command of music theory to really support my case.
> 
> But the short version is that I think the claim of the "Wagner leads to atonality" people is being misunderstood: no one's actually saying that tonality isn't central to Wagner's music (as counterpoint is central to Bach's, even in the prelude that's just a sequence of of arpeggiated chords). *The claim is that Wagner pushed the role of unstated tonics to the point where other phenomena (the linear movement of highly chromatic lines and the sheer sound of the harmonies that result), start to become as important to listeners' actual experience of the music as the underlying tonal grammar, and that suggested new directions to composers that ultimately led to atonality.*
> 
> I was reminded of this recently when you quoted this book: "The manipulation of unstated tonics in motivic sequence then becomes a direct manipulation of an unconscious psychological process of projecting order. It is not an invention or deviation from the theoretical structure of tonal practice, but a realization of possibilities inherent within the system. As such it represents a profound stylistic advance, and the possibilities which it opened may remain largely unexplored by later composers."
> 
> *I think the reason it was largely unexplored by later composers is that if you push it much further, the unconscious psychological process breaks down and most listeners cease perceiving the sequences of unstated tonics.* Anyway that's how it is for me when I try to listen to Berg's piano sonata or Schoenberg's chamber symphony, and it seems very natural that those composers ended up going the way they did.


Your explanation for the theories of the "Wagner leads to atonality people" is very conciliatory!  Actually, I don't think all those people have the same theory about how an expanded tonality "evolves" into atonality. There was Schoenberg's concept of "the emancipation of the dissonance,"which postulated that, over time, people learn to regard harmonies previously considered dissonant as consonant, and that logic therefore dictates that we go all the way and remove the tonal functions that provide the criteria for what's consonant and what isn't. Then there's the notion that because Romantic composers were making harmony more and more chromatic and using more chords that couldn't be "explained" by reference to theoretical systems then current, the obscuring of tonal centers which resulted would inevitably lead to a "breakdown of tonality" and its total abandonment as a constructive principle in music.

Wagner would have spat out his coffee at such notions. No composer in history was more attentive to tonal relationships than he was, or exercised more far-reaching and iron-handed control over them. He was, however, well aware of what a Pandora's box of potential abuses his enriched tonal vocabulary would open up for aspiring composers tempted by what he described as "effects without causes." Young composers, he said, would come to him with compositions filled with novel and complicated harmonies, hoping to be praised for their expressiveness and creativity, and he would be quick to set them straight.

Wagner's music does indeed force us to think of musical form - and this includes harmony - in ways that Bach's or Mozart's does not. But it no more implies, or suggests as desirable, the negation of the very principle of tonality than theirs does. I would dispute your suggestion that in his music "other phenomena (the linear movement of highly chromatic lines and the sheer sound of the harmonies that result), start to become as important to listeners' actual experience of the music as the underlying tonal grammar." Wagner's radical movement away from a "top-down" approach to harmonic structuring - in which the stations of tonal movement, the "functional" pillars of tonal harmony, are explicitly stated as the audible scaffolding of a basically abstract form - to a "bottom-up" approach - in which tonal structuring is guided by a sense of dramatic/expressive narrative inherent in the tonal language - is not a movement away from tonality but an extrapolation of a potential which had been present in it from the start and was in fact adumbrated many times in the work of earlier composers. What Wagner saw was the extent of that potential to create large-scale dramatic works in which the expressive language of tonal harmony could guide the creation of coherent musical statements without signaling its "mechanics" to the conscious mind of the listener.

A real comprehension of what Wagner was doing in his music depends first and foremost on an intuitive sense of its organicity, its underlying logic, and that depends on our ability to abandon the Classical expectation that musical form, particularly form based on tonal structures, is created and perceived "from the top down." The musical conservatives of his day were opposed to his conception of musical form; I've known people, even musicians, who are not comfortable with it even today, and can't listen to a Wagner opera without feeling disoriented and irritated by the refusal of the music to congeal into neat structures. Wagner's mature works are an uncompromising expression of the Romantic conception of music as the language of the soul, a language which comes "from the bottom up," and Wagner uses drama as the scaffolding on which our conscious mind can fixate while the music goes to work on our unconscious.

I've managed to get my hands on a copy of the book from which the excerpt you've quoted comes:_ "The manipulation of unstated tonics in motivic sequence then becomes a direct manipulation of an unconscious psychological process of projecting order. It is not an invention or deviation from the theoretical structure of tonal practice, but a realization of possibilities inherent within the system. As such it represents a profound stylistic advance, and the possibilities which it opened may remain largely unexplored by later composers."_ The book, "Musical Structures in Wagnerian Opera" by Marshall Tuttle, is a work of thorough scholarship and meticulous analysis, and it isn't an easy read (I'm skimming parts of it first time around). But it's definitely confirming and filling out my long-standing intuitions about Wagner's music and how it works. Among other things, it helps me understand why his scores are full of changes of key signature when it's often impossible to find more than a bar or two that actually seems to be in the specified key - and why, despite surface appearances, Wagner stated that one should never leave a key until one has said everything necessary within it.

I understand Tuttle's suggestion that _"the possibilities which [Wagner's techniques] opened may remain largely unexplored by later composers"_ to indicate, not that composers declined to push his techniques further lest they inevitably confound the listener's tonal expectations or be forced to leave tonality behind, but that they simply could not manipulate the surface vocabulary of his style with the intuitive control of the layers of tonal organization, mediated through motivic sequence and metamorphosis, which enabled him to generate a sense of narrative inevitability and expressive specificity on a grand scale. There's a great deal of post-Wagnerian music that sounds "Wagnerian" but, in any profound sense, isn't. Tuttle's observation also points out the fundamental fact that Wagner's music took the form it did under the impetus of the need for dramatic expression - "dramatic" in the specific sense. Tuttle's book shows in (sometimes ponderous) detail how dramatic ideas and musical structures are inseparable in the operas, to the extent that, more than with any other composer, understanding the latter is essential to understanding the former, and how the precise manipulation of tonal relationships provides a key to that understanding. Wagner was so convinced that music could be an articulate language, and so relentless and thorough in the use of hamony's tools to achieve that end, that he would eventually call his operas "deeds of music made visible."

I would say that anyone who thinks that Wagner's music "leads to" atonality doesn't understand very much about it. Scholarly scuffles over how to name the Tristan chord are apt to be missing the forest for the trees.


----------



## millionrainbows

Once again, the defense of Wagner as the supreme tonalist must retreat back to a nebulous aesthetic, dramatic, and 'spiritual' position, because from a purely musical standpoint, there is nothing left to hide behind.

In Wagner, the absence of functional harmony as a primary structural element, and the reemergence of purely melodic-rhythmic forces as major determinants of musical form, and the emphasis on expressive chromaticism as a logical, perhaps inevitable consequence of the weakening of tonal centers (as in Wagner's Tristan und Isolde), had caused successive chords to relate more strongly to each other than to a common tonic firmly established by intermittent harmonic cadences. 
BTW, I hear Berg's op.1 Sonata as a prime example of this "circulating" travel around the chromatic scale, with no resolutions or cadences, as a prime example of the musical, technical aspects of this Wagnerian practice, which led to the abandonment of tonality (as we knew it).

Eventually, the 12 equidistant semitones superseded the diatonic scale (necessary for functional harmony), to the extent that melodic-rhythmic tensions and resolutions took the place of the harmonic cadences and modulations that had determined the structure of Western music for centuries.

Dramatic "Wagnerism" was a nebulous aesthetic more important to literature and philosophy. When the subject is music, the technical aspects are more important than dramatic, spiritual, or aesthetic notions.

So, while Wagner may have influenced the young Schoenberg's early dramatic works, the 12-tone works owe little to Wagner in dramatic or aesthetic ways so much as a abstract, technical and musical ways.

The repeated retreat back to Wagner's nebulous aesthetics is a cop-out to the real musical issues.

Instead of proclaiming that "anyone who thinks that Wagner's music leads to atonality doesn't understand very much about it," then why can't this be demonstrated? Because it can't.

"Scholarly scuffles over how to name the Tristan chord are apt to be missing the forest for the trees" is true, if they are not "Wagnerites" who subscribe to these nebulous aesthetic notions you refer to.

Apparently, to understand Wagner, one must have "an intuitive sense of its organicity."

Try it, man, it's organic!

I'm wondering if this statement:



> Among other things, it helps me understand why his scores are full of changes of key signature when it's often impossible to find more than a bar or two that actually seems to be in the specified key - and why, despite surface appearances, Wagner stated that one should never leave a key until one has said everything necessary within it."



...is actually a reference to Tuttle's claim that...

_"...__Wagner liberated the higher-level organizers of tonal structure (e.g., *orbits of keys-*known as *tonalities*-rather than just keys) from diatonic/scalar structures. That is, a piece ostensibly in C major was no longer limited to modulations to D minor, E minor, F major, G major, A minor, etc., but now the superset of modulatory choices could be determined by *motives.* This is demonstrated brilliantly in the orchestral introduction to Act I, Scene v of Tristan und Isolde (analyzed in Chapter 3), *where the modulations outline the Tristan chord itself. *_(I alluded to this sort of outlining in the discussion of Beethoven's Ninth) 
_
Tuttle also explains why previous analytical scholarship has not been able to identify this feature (in this case, it is because the *tonics are earmarked by half cadences rather than full cadences,* and a contrapuntally-biased theory like Schenkerian analysis can only account for what is literally in the score)."_

...and that this way of thinking, outlined in Leland Smith's *Handbook of Harmonic Analysis,* can be explained geometrically, as I tried to tell earlier academics:

From Leland Smith: _An analytical methodology called *linear harmonic analysis* is introduced, wherein modulations are treated as recursively referencing higher levels of tonal organization. This is profoundly different from a contrapuntally-inspired analytical system like Schenkerian analysis in that is allows for *the projection of elements which are not evident on the surface.* *Charts dubbed "Tonic Guide Tones" show the sequence of tonics of a wide variety of pieces,* and impressive results obtain, e.g., in the analysis of the prelude to Tristan und Isolde (pp. 129-147), where it is demonstrated that the Tristan chord becomes elevated from a surface-level sonority to an arbiter of tonal organization for the entire prelude (as it transits the keys of a, c, and e♭, ending with the sailor entering in G minor).

_


> I understand Tuttle's suggestion that _"the possibilities which [Wagner's techniques] opened may remain largely unexplored by later composers" _to indicate, not that composers declined to push his techniques further lest they inevitably confound the listener's tonal expectations or be forced to leave tonality behind, but that they simply could not manipulate the surface vocabulary of his style with the intuitive control of the layers of tonal organization, mediated through motivic sequence and metamorphosis, which enabled him to generate a sense of narrative inevitability and expressive specificity on a grand scale.


*
I think that this is now possible, using geometric analysis and thinking.*
As Dmitri Tymoczko concludes in _A Geometry of Music,_ _"Musicians who recoil from these (Second Viennese) post-Wagnerian extremes, but who did not want to write traditional music, would therefore need to go back to the drawing board, devising new approaches that could coexist more peacefully with tonality."

_Attention: Hey You! Back to the drawing board! And Dmitri Tymoczko's book is a helluva lot cheaper than the Tuttles or Leland Smith 300-600 dollar tomes.

And, as the cherry on top, Dmitri Tymoczko is a guitar player! Haha haa! :lol:


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## Roger Knox

EdwardBast said:


> For years, actually. I'm a theorist, among other things.
> 
> Do you have access to a statistical summary of harmonic usage in the chorales? I know it's been done but I forget by whom.


It was done by American theorist Allan McHose in _The Contrapuntal Harmonic Technique of the Eighteenth Century_ (Appleton-Century Crofts, 1947). But not perfectly: "Whereas he uses the study of over two hundred Bach chorales to illustrate one point, he refers to a study of all 371 chorales for statistics to demonstrate suspensions, ..."(David M. Thompson, _A History of Harmonic Theory in the United States_, Kent State University Press, 1980). Likely there has been a more consistent study since then.


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## isorhythm

Woodduck,

I think we're talking past each other a little bit. I'll happily admit that I don't know much about Wagner's music compared to you or EdwardBast or some other posters here. My point, however, is that it makes no sense to insist that Wagner's music doesn't imply or suggest moving away from tonality when, in actual fact, it _did _imply and suggest that to a number of very good composers. That's independent of Wagner's intentions and of how Wagner's music itself works. Art often suggests surprising new directions to others that the original artist didn't think of or even actively rejects.


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## Roger Knox

BabyGiraffe said:


> The best books on common practice are these that basically teach historical methods. These are very good, imo:
> 
> "The Art of Accompaniment from a Thorough-Bass: As Practiced in the XVII and XVIII Centuries" (2 volumes) - Arnold (Bach, Vivaldi etc lovers may find this one interesting,)
> 
> "Music in the Galant Style" - Gjerdingen (Mozart fans will love this)


Good point. We have the whole area of historically informed practice now that requires skill and expertise in harmony according to the period involved. It helps in Baroque "Chord progressions"/Music Theory/TalkClassical to discuss different approaches in theory and practice, which are not completely separated.


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## Roger Knox

*Walter Piston's Harmony (1941)*

"The appearance of Walter Piston's _Harmony_ (1941) marks a return to the practical philosophy of theory. ... Piston states that his theory is 'the collected and systematized deductions gathered by observing the practice of composers over a long time, and it attempts to set forth what is or has been their common practice. It tells not how music will be written in the future, but how music has been in the past.' Throughout the work Piston systematically rejects opportunities to support his statements with acoustical arguments.'" (David M. Thompson. _A History of Harmonic Theory in the United States._ Kent State University. Press, 1980.)

So, Walter Piston's (1894-1976) approach is empirical, his book full of examples by great composers. He uses (invents?) the phrase "common practice" for eighteenth & nineteenth century classical music. His studies composition (not harmony, which would have been redundant) in Paris with Nadia Boulanger. And no Riemann, Schoenberg, or Schenker. But to correct my earlier post, apart from the general point that Rameau influenced all subsequent harmonic theories, Piston's harmony isn't really French-derived. At the time it was an empirical reaction against some English theorists who pressed acoustic theory of harmony based on the higher overtones to excess.

He is making a crucial distinction between harmony for education of all advanced classical music students, and harmony for composers and improvisers interested in recent and new practices.


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## Roger Knox

BabyGiraffe said:


> Functional theory is based on the structure of diatonic scale in just intonation by Hugo Riemann (and this is just a small part of his theories).
> Don't search for functions in older theories. You won't find them anywhere before his time (1849-1919); he introduced mathematical word "function" in musical context. This (German) theory is not popular at all in Britain and US, aside from simplified analysis using roman numerals (it's overcomplicated and the notation is horrible - see the book below; it's also unsuitable for non-classical music, just like any other "classical" theory).


Since I know nothing of how music theory is taught in Europe your post is useful! All I learned about Riemann was the T, S, and D functions and how chords are included in each. But now there is much more interest in Riemann in the English-speaking world.


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## millionrainbows

Roger Knox said:


> Since I know nothing of how music theory is taught in Europe your post is useful! All I learned about Riemann was the T, S, and D functions and how chords are included in each. But now there is much more interest in Riemann in the English-speaking world.


You would do well to heed his words. But on the other hand, he was talking to me.


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## millionrainbows

isorhythm said:


> Woodduck,
> 
> I think we're talking past each other a little bit.


That seems to be the norm for this thread. :lol:


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## Woodduck

Millionrainbows writes:

Once again, the defense of Wagner as the supreme tonalist must retreat back to a nebulous aesthetic, dramatic, and 'spiritual' position, because from a purely musical standpoint, there is nothing left to hide behind.

There is nothing nebulous about Wagner's compositional technique, with respect to tonality or anything else, and no one is hiding behind anything. I grant you that Wagner can sound "nebulous" to those who can't sense his logic (perhaps those looking for that reassuring V7 - l every four or eight bars). It took me exactly two hearings of _Tristan_ to "get it" at the age of fourteen, before I knew what V7 - l was. Keep trying, old boy.

By the way - no, not by the way, but centrally - the idea of "a purely musical standpoint" is as nebulous as ideas come. "Purely musical standpoints" exist only in theory textbooks.

In Wagner, the absence of functional harmony as a primary structural element, 

It _is_ a primary structural element.

and the reemergence of purely melodic-rhythmic forces as major determinants of musical form, 

Melodic and rhythmic forces have always been major determinants of musical form.

and the emphasis on expressive chromaticism as a logical, perhaps inevitable consequence of the weakening of tonal centers (as in Wagner's Tristan und Isolde), 

This is utterly confused. Wagner does not "emphasize" chomaticism; he employs it where he needs it, and doesn't where he doesn't. Where he does, he does so with its tonal implications firmly in hand. Moreover, chromaticism isn't a "consequence of the weakening of tonal centers." Furthermore, tonal centers do not "weaken." In Wagner they often move frequently, they're often hinted at or implied rather than stated outright, resolutions are delayed or deceptive - but the effect of those procedures depends on a continuous appeal to the listener's tonal sense.

The notion that tonality weakened over time and finally died is a medical diagnosis, not a description of how music works (and certainly not Wagner's music). And you talk about "nebulous" ideas!

had caused successive chords to relate more strongly to each other than to a common tonic firmly established by intermittent harmonic cadences. 

And how do successive chords "relate" to each other? What makes us feel that they do? Why does Wagner's harmony not sound random and chaotic? If you're looking for those "tonics firmly established by intermittent harmonic cadences" you will not find the answer to those questions and had better stick with Haydn (and your theory books).

BTW, I hear Berg's op.1 Sonata as a prime example of this "circulating" travel around the chromatic scale, with no resolutions or cadences, as a prime example of the musical, technical aspects of this Wagnerian practice,

Berg's sonata sounds sort of "Wagnerian" in being chromatic but is to a great extent harmonically random compared to Wagner. It relies blatantly on motivic repetition and dynamic energy to disguise this. Berg's gestures toward anchoring the piece in B minor are tricks only partly successful in masking the fact that it isn't really in B minor. Wagner would have sniffed at it and sent little Alban back home to study the prelude to _Tristan_ - or maybe just some Bach.

which led to the abandonment of tonality (as we knew it).

As we knew it. After Wagner we knew it even better.

Dramatic "Wagnerism" was a nebulous aesthetic more important to literature and philosophy. When the subject is music, the technical aspects are more important than dramatic, spiritual, or aesthetic notions.

As with your idea of a "purely musical standpoint," you here create a dichotomy between how music works on a psychological/expressive level and how it's described as "working" in theory. Tonality, which is the concept under dispute, is an aural/psychological phenomenon before its manifestations are categorized and the rules of any tonal system established. Systems and rules can change while tonality remains. But what's striking - and what may define his musical genius more than any other factor - is the extent to which Wagner's music, despite its apparent structural novelties, respects long-established rules, which he had no intention of discarding.

Those who chose to discard them were breathing the air of a different planet.


----------



## millionrainbows

Once again, the defense of Wagner as the supreme tonalist must retreat back to a nebulous aesthetic, dramatic, and 'spiritual' position, because from a purely musical standpoint, there is nothing left to hide behind.

There is nothing nebulous about Wagner's compositional technique, with respect to tonality or anything else, and no one is hiding behind anything. I grant you that Wagner can sound nebulous to those who can't sense his logic. It took me exactly two hearings of Tristan to accomplish that at the age of fourteen. Keep trying, old boy.

This is utterly confused. You keep referring to things like "a "bottom-up" approach - in which tonal structuring is guided by a sense of dramatic/expressive narrative inherent in the tonal language", but never explain this nebulous idea, which you purport is "an extrapolation of a potential which had been present in it from the start" without "signaling its mechanics to the conscious mind of the listener," ostensibly perceived by 14-year olds without signaling its "mechanics" to the conscious mind of the listener. HUH?

By the way - no, not by the way, but centrally - the idea of "a purely musical standpoint" is as nebulous as ideas come. "Purely musical standpoints" exist only in theory textbooks.

Yes, especially in the newer ones, such as Dmitri Tymoczko's _A Geometry of Music._

In Wagner, the absence of functional harmony as a primary structural element,

It _is a primary structural element.

_No, not as in functional diatonic harmony, according to Tuttle's ideas, which you cited:

"...Wagner liberated the higher-level organizers of tonal structure (e.g., orbits of keys-known as tonalities-rather than just keys) from diatonic/scalar structures. That is, a piece ostensibly in C major was no longer limited to modulations to D minor, E minor, F major, G major, A minor, etc., but now the superset of modulatory choices could be determined by motives.

...and the reemergence of purely melodic-rhythmic forces as major determinants of musical form,

Melodic and rhythmic forces have always been major determinants of musical form.

But never as autonomously, virtually taking the place of functional harmony.

...and the emphasis on expressive chromaticism as a logical, perhaps inevitable consequence of the weakening of tonal centers (as in Wagner's Tristan und Isolde),

This is utterly confused. Wagner does not "emphasize" chomaticism; he employs it where he needs it, and doesn't where he doesn't. Where he does, he does so with its tonal implications firmly in hand. 

Partially true, but chromaticism is nonetheless emphasized where clear tonal implications are too ambiguous. Who ya gonna call, Ghostbusters?

Moreover, chromaticism isn't a "consequence of the weakening of tonal centers." 

"Normal" diatonically-derived chromaticism is not; but he was dealing with "higher-level organizers of tonal structure (e.g., orbits of keys-known as tonalities-rather than just keys). This is not the same thing.

Furthermore, tonal centers do not "weaken." 

As they have become ambiguous to the degree that they can only be implied or hinted at, they can be said to have weakened. I'll give it a fifty-fifty chance of survival, but it may never be the same again.

In Wagner they often move frequently, they're often hinted at or implied rather than stated outright, resolutions are delayed or deceptive - but the effect of those things depends on the continued appeal to the listener's tonal sense.

There comes a point that Wagner's methods move too frequently, are ambiguous, deceptive, and delayed beyond perceptual abilities, and the net result can be justifiably called a "weakening of tonality" as we know it.

The notion that tonality weakened over time and finally died is a medical diagnosis, not a description of how music works (and certainly not Wagner's music). And you talk about "nebulous" ideas!

Tonality didn't die; it just smells funny.

Wagner can still be considered a "tonal" composer, if everything is referred back to that, but there comes a time that one must recognize that Wagner was thinking in a new, contrapuntal way, evidenced by his use of where the modulations outline the Tristan chord itself (I alluded to this sort of outlining in the discussion of Beethoven's Ninth)...

...and, as Tuttle noted (a source cited by you) his use of "tonic guide tones" which show the sequence of tonics of a wide variety of pieces.

In the analysis of the prelude to Tristan und Isolde (pp. 129-147), it is demonstrated that the Tristan chord becomes elevated from a surface-level sonority to an arbiter of tonal organization for the entire prelude (as it transits the keys of a, c, and e♭, ending in G minor). So, yes, it can ultimately be called "tonal" if one recognizes that this is a higher-level form of musical thinking.

I still think it's just as misleading to call it "tonal" without this qualifier than it is to say that is leads to atonality. It is a grey area in this respect.

Ultimately, Wagner's thinking can be seen clearly as geometric thinking, which can be construed as higher-level tonal thinking if one wishes; but it has its own, autonomous chromatic/geometric logic as well. If you are a pure tonalist, you have a strange bedfellow.


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## Guest

EdwardBast said:


> *I examined all chorales under these titles in Riemenscheider and didn't find examples of the use of a IV7 chord.* The closest was Nun ruhen alle Wälder (no. 117), which has what looks like a IV7 on the first beat of the final bar. But on the last beat of the preceding bar we have a IV6, which makes the C on the next beat a passing tone.
> 
> In none of the versions of Ich dank' dir, lieber Herre in Riemenschneider did I find a IV7 chord, although there were a couple with the 7th as a passing tone.
> 
> Do you have anything more specific for these references - like which of the multiple settings you meant?


Dear Edward,

Here is a pdf copy of the relevant page from *William Lovelock's* _The Harmonization of Bach's Chorales_ where he cites 3 examples of IV7. There are others, of course; I hope these suffice.


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## Guest

EdwardBast said:


> I examined all chorales under these titles in Riemenscheider and didn't find examples of the use of a IV7 chord. *The closest was Nun ruhen alle Wälder (no. 117), which has what looks like a IV7 on the first beat of the final bar. But on the last beat of the preceding bar we have a IV6, which makes the C on the next beat a passing tone*.
> 
> In none of the versions of Ich dank' dir, lieber Herre in Riemenschneider did I find a IV7 chord, although there were a couple with the 7th as a passing tone.
> 
> Do you have anything more specific for these references - like which of the multiple settings you meant?


I think I see what you mean - that the B in the soprano delays a ii6/5. But that negates Bach's consistent preparation of the 7th in the ii6/5. 
To try to clarify things, you consider Lovelock's IV7 figuring as a delayed ii6/5 which I don't think it is given that he always prepares the 7th in ii6/5.
The "Ich danke" example is perhaps the clearest use of the IV7.


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## Woodduck

millionrainbows said:


> You keep referring to things like "a "bottom-up" approach - in which tonal structuring is guided by a sense of dramatic/expressive narrative inherent in the tonal language", but never explain this nebulous idea, which you purport is "an extrapolation of a potential which had been present in it from the start" without "signaling its mechanics to the conscious mind of the listener," ostensibly perceived by 14-year olds without signaling its "mechanics" to the conscious mind of the listener. HUH?


By "bottom-up" I mean simply that Wagner's tonal structures are not chosen to fulfill the a priori requirements of abstract form - the "top-down" approach to composition - but arise out of and delineate expressive trajectories suggested by dramatic/narrative ideas. This was nothing new in music; the shapes of Beethoven's works are affected more than is often appreciated by "dramatic" considerations as opposed to "purely musical" ones, but he is only a particularly striking example of something that is always lurking behind the facade of "pure music" so cherished by "absolutists" like the unfortunate Hanslick (who finally had to admit that Wagner knew what he was doing).

There's nothing nebulous about noting that the expressive vocabulary of tonal music offered composers long before Wagner a cornucopia of devices ("inherent in the tonal language") by which music could be structured in terms of emotional narratives rather than "pure" abstract form, even if such an aesthetic was the exception rather than the rule. It's just that Wagner anchored his "impure" tendencies in the explicitly narrative form of drama for the stage, which in turn allowed him to release musical form from "top-down" templates to an unprecedented degree (and it should be noted that opera had already provided fruitful opportunities of this kind for other composers from Monteverdi to Weber). The challenge presented by this freedom was enormous; chaos could be averted only by an acute and thorough awareness and control of the elements of musical form, and this included tonal relationships. Wagner was intent on attaining that control, and I don't think there's any disputing that he did so, to a degree that's never been surpassed or, possibly, equaled - certainly not by those who, knowing they couldn't equal it, decided that leaving tonality behind was more comfortable, and more likely to be noticed, than struggling to compete with the master.

(BTW, I don't know how to use the function which allows one to break up a quoted post into parts for individual comment, which is why I use the device of color. Since you do know how to use it, you needn't imitate me. If you'd like to instruct me in it, I'll gladly convert to the standard method.)


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## EdwardBast

TalkingHead said:


> Dear Edward,
> 
> Here is a pdf copy of the relevant page from *William Lovelock's* _The Harmonization of Bach's Chorales_ where he cites 3 examples of IV7. There are others, of course; I hope these suffice.


Thanks!

The first two don't hold up: in "Jesu, joy of …" the 7th is a suspension, which resolves correctly to A only after the harmony changes. in _Nun ruhen alle Wälder_ the 7th is a passing tone within the subdominant harmony, as I noted before. (Riemenschneider has it in the key of A-flat.) The one that holds up is the weird one (_Ich dank' dir_) with the doubled D-sharp, the voice-crossing, and the consecutive 5ths between bass and tenor. What surprises me is that Lovelock thought the D# in the tenor was the "academically deplorable" element!  I would have picked the 5ths between tenor and bass that the D# is trying to cover, but I guess there is an embarrassment of deplorable riches here. If this is the best case that can be made for IV7, I'd say the conclusion has to be it's not part of the vocabulary. But maybe there were other better examples he didn't cite?


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## millionrainbows

(BTW, I don't know how to use the function which allows one to break up a quoted post into parts for individual comment, which is why I use the device of color. Since you do know how to use it, you needn't imitate me. If you'd like to instruct me in it, I'll gladly convert to the standard method.)

It's more work, actually, but simply highlight, copy and paste the part you want to separate, then manually type in [QUOTE (no slash)] at the front, and [/QUOTE] at the end to enclose it. No name is necessary, unless you want to convey a more impersonal tone. After the first one you do this way, you can copy & paste the [/QUOTE] to save a little time. Most of the time I do the opening quote with the name & number, then do the rest as just


> to save space.
> Don't forget, you can always directly insert your comments into the quote, but the mods don't seem to like that, although it is the easiest method. If you do it this way, be sure to put your comments in bold, or a different color, to lessen the confusion, with a disclaimer at the top explaining this. It may be necessary to type in 10 or so characters outside the quote, afterwards, to make it "take" as a post.


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## millionrainbows

> ...............


...............


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## Guest

EdwardBast said:


> Thanks!
> 
> The first two don't hold up: in "Jesu, joy of …" the 7th is a suspension, which resolves correctly to A only after the harmony changes. in _Nun ruhen alle Wälder_ the 7th is a passing tone within the subdominant harmony, as I noted before. (Riemenschneider has it in the key of A-flat.) *The one that holds up is the weird one (Ich dank' dir) with the doubled D-sharp, the voice-crossing, and the consecutive 5ths between bass and tenor. What surprises me is that Lovelock thought the D# in the tenor was the "academically deplorable" element!  I would have picked the 5ths between tenor and bass that the D# is trying to cover,* but I guess there is an embarrassment of deplorable riches here. If this is the best case that can be made for IV7, I'd say the conclusion has to be it's not part of the vocabulary. But maybe there were other better examples he didn't cite?


Yes, I see what you mean. The voice-crossing is prevalent in the chorales, we have no issue with that. The consecutive 5ths are "cleverly" avoided (very common in the chorales), but the doubled leading tone (D#) _*is*_ deplorable!
Are these the best examples of IV7 as a "stand-alone" major 7th chord? I can't say right now.
What does seem to be true is that I7 (major 7th) is *not* used by Bach.


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## EdwardBast

TalkingHead said:


> I think I see what you mean - that the B in the soprano delays a ii6/5. But that negates Bach's consistent preparation of the 7th in the ii6/5.
> To try to clarify things, you consider Lovelock's IV7 figuring as a delayed ii6/5 which I don't think it is given that he always prepares the 7th in ii6/5.
> The "Ich danke" example is perhaps the clearest use of the IV7.


I think we confuse things a bit by trying to apply Roman numerals where they are not much apropos. I don't think IV versus ii is meaningful here since linear considerations rule. In this case the B has to be suspended over for aesthetic reasons. (It sounds really clunky if one goes to A at the change across the bar, to ii4/3, which would mean 4ths in both hands, E-A on the lower staff, G-C on the treble). Moreover, Bach's solution for the B forms a chain with the C in the soprano, which is likewise suspended and resolves on the next harmony.

As I wrote above, I think the 7th in Ich dank' is a passing note within the subdominant.



TalkingHead said:


> Yes, I see what you mean. The voice-crossing is prevalent in the chorales, we have no issue with that. The consecutive 5ths are "cleverly" avoided (very common in the chorales), but the doubled leading tone (D#) _*is*_ deplorable!
> Are these the best examples of IV7 as a "stand-alone" major 7th chord? I can't say right now.
> What does seem to be true is that I7 (major 7th) is *not* used by Bach.


Yes, I think you're right. The D# is the most "deplorable."  Strange to see Bach back himself into a corner like this.


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## Woodduck

millionrainbows said:


> It's more work, actually, but simply highlight, copy and paste the part you want to separate, then manually type in [QUOTE (no slash)] at the front, and [(slash) QUOTE] at the end to enclose it. No name is necessary, unless you want to convey a more impersonal tone. After the first one you do this way, you can copy & paste the [.QUOTE] to save a little time. Most of the time I do the opening quote with the name & number, then do rest as just [(no slash)QUOTE] to save space.
> Don't forget, you can always directly insert your comments into the quote, but the mods don't seem to like that, although it is the easiest method. If you do it this way, be sure to put your comments in bold, or a different color, to lessen the confusion, with a disclaimer at the top explaining this. It may be necessary to type in 10 or so characters outside the quote, afterwards, to make it "take" as a post.


Thanks. I'll try that and see if it's comfortable. I wouldn't use the method of inserting comments inside quotes; it _looks_ confusing, and people aren't used to it. At least using a color for quotes is visually clear. StLukesGuildOhio used to do it and I thought it looked spiffy. Once I was quoting two people and used a different color for each one. Cheerful as Christmas.


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## EdwardBast

Roger Knox said:


> It was done by American theorist Allan McHose in _The Contrapuntal Harmonic Technique of the Eighteenth Century_ (Appleton-Century Crofts, 1947). But not perfectly: "Whereas he uses the study of over two hundred Bach chorales to illustrate one point, he refers to a study of all 371 chorales for statistics to demonstrate suspensions, ..."(David M. Thompson, _A History of Harmonic Theory in the United States_, Kent State University Press, 1980). Likely there has been a more consistent study since then.


Thanks Roger! The McHose might be it. It was on the bibliography list for a masters level history of theory course I took. Wasn't required to read it cover to cover. That list we just scanned and summarized contents and methods. But I've heard it from more modern sources too.


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## millionrainbows

@Woodduck, to sum up my position, I do see Wagner a a tonalist, but his later thinking and the later music exhibits methods (motivic guide tones, etc.) that enables movement from chord to chord, and it has to be referred back to tonality by tonal means. This same way of thinking could be used to go the opposite direction too, as Berg did in his op. 1.

I agree with Isorhythm's post #81, in which he says



> ...no one's actually saying that tonality isn't central to Wagner's music (as counterpoint is central to Bach's, even in the prelude that's just a sequence of of arpeggiated chords). The claim is that Wagner pushed the role of unstated tonics to the point where other phenomena (the linear movement of highly chromatic lines and the sheer sound of the harmonies that result), start to become as important to listeners' actual experience of the music as the underlying tonal grammar, and that suggested new directions to composers that ultimately led to atonality.




So ultimately, the decision on which way to go is ultimately an aesthetic one. And good luck on getting holds of that Tuttle book, as well as the Leland Smith. I wonder if its available as a download? I do hope you will check out the Dmitri Tymoczko book, because I suspect that ultimately, he is in accord with Tuttle and that tonalist camp concerning Wagner.


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## JosefinaHW

There's a question I've been meaning to ask since the Bach chorale harmonizations were first discussed and so many of you agreed that so many of these pieces are considered masterpieces of harmonization. I remember a few of you stating that you found Bach's cantatas boring. Of course, people change their minds, but my understanding is that many of the cantatas are structured and composed in light of the chorale of that particular liturgical date. I might be premature in asking this question since I cannot *personally* prove this to you, and I will not "call out" anyone in particular, but I wonder how you can say the cantatas are boring and yet recognize the brilliance of the chorale harmonizations?

I'm not sure that I expect a direct or public response to this question, but I've been meaning to ask it anyway.


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## Woodduck

JosefinaHW said:


> There's a question I've been meaning to ask since the Bach chorale harmonizations were first discussed and so many of you agreed that so many of these pieces are considered masterpieces of harmonization. I remember a few of you stating that you found Bach's cantatas boring. Of course, people change their minds, but my understanding is that many of the cantatas are structured and composed in light of the chorale of that particular liturgical date. I might be premature in asking this question since I cannot *personally* prove this to you, and I will not "call out" anyone in particular, but I wonder how you can say the cantatas are boring and yet recognize the brilliance of the chorale harmonizations?
> 
> I'm not sure that I expect a direct or public response to this question, but I've been meaning to ask it anyway.


Wouldn't that just fall under the category of personal taste? I know of people who find Wagner boring, which I find unimaginable, but I don't expect them to give me a convincing reason. I dare say there isn't any music, or any anything, that doesn't bore the daylights out of some apparently intelligent person who you or I think ought to know better!


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## JosefinaHW

Woodduck said:


> Wouldn't that just fall under the category of personal taste? I know of people who find Wagner boring, which I find unimaginable, but I don't expect them to give me a convincing reason. I dare say there isn't any music, or any anything, that doesn't bore the daylights out of some apparently intelligent person who you or I think ought to know better!


No, this does not fall under the category of personal taste. Several people in this thread have (finally) acknowledged that they own and have studied their Bach chorale harmonizations, so much to the point that those scores are old and weathered and worn, like a fabulous pair of favored shoes.

Again, I have read that many of the cantatas were composed and structured around the chorale(s) of the particular liturgical calendar.

How can one acknowledge their brilliance? Admit that these are masterpieces. Masterpieces of harmonization that have been studied generation after generation. And then state that the cantatas which were composed in light of them are boring?

That seems to me to be a complete contradiction.

(Please, don't play semantical games with me. I am being very direct and honest.)


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## Woodduck

JosefinaHW said:


> No, this does not fall under the category of personal taste. Several people in this thread have (finally) acknowledged that they own and have studied their Bach chorale harmonizations, so much to the point that those scores are old and weathered and worn, like a fabulous pair of favored shoes.
> 
> Again, I have read that many of the cantatas were composed and structured around the chorale(s) of the particular liturgical calendar.
> 
> How can one acknowledge their brilliance? Admit that these are masterpieces. Masterpieces of harmonization that have been studied generation after generation. And then state that the cantatas which were composed in light of them are boring?
> 
> That seems to me to be a complete contradiction.
> 
> (Please, don't play semantical games with me. I am being very direct and honest.)


What semantical games? There is no contradiction between knowing that music is excellent and being uninterested in listening to it. If you don't care for Beethoven's 9th, despite its generally acknowledged position as a great and significant work of music, you just don't care for it. No arguments or justifications are required.


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## mikeh375

Woodduck said:


> ........ and I don't think there's any disputing that he did so, to a degree that's never been surpassed or, possibly, equaled - certainly not by those who, knowing they couldn't equal it, decided that leaving tonality behind was more comfortable, and more likely to be noticed, than struggling to compete with the master.


Some great posts Wooduck, exhilarating and illuminating - they've encouraged me to listen to Wagner again after a long, long hiatus. (As coincidence would have it, I found a complete score to Tristan in a charity shop the other day, for £5).

The quote above stands out as a little unfair though imv, perhaps you wouldn't mind expanding a little on that, after all, composers of high calibre step to their own music. I certainly don't consider atonality as a more _"comfortable"_ option to tonal, chromatic technique and rhetoric and it certainly wouldn't have been at that time. It would also be fair to say that the emotional narrative, rather than an 'absolute' paradigm will have been the driving force for most composers then as it still is now.

(btw, may I ask if you are a composer?)


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## Guest

JosefinaHW said:


> There's a question I've been meaning to ask since the Bach chorale harmonizations were first discussed and so many of you agreed that so many of these pieces are considered masterpieces of harmonization. I remember a few of you stating that you found Bach's cantatas boring. Of course, people change their minds, but my understanding is that many of the cantatas are structured and composed in light of the chorale of that particular liturgical date. I might be premature in asking this question since I cannot *personally* prove this to you, and I will not "call out" anyone in particular, but I wonder how you can say the cantatas are boring and yet recognize the brilliance of the chorale harmonizations?
> 
> I'm not sure that I expect a direct or public response to this question, but I've been meaning to ask it anyway.


The RM 371 is my "bible" and the Cantatas are far from boring. Bach boring? Bach is a volcano.


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## millionrainbows

Figured bass works for Bach, but it is too short-sighted limited in scope to be of value in music which modulates into other key areas. It can't identify new tonic areas. It doesn't relate different tonics to each other, it only relates the internal structure of a chord to one note.

It's like entering an enormous darkened room full of possibilities with only a flashlight for guidance.


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## millionrainbows

TalkingHead said:


> The RM 371 is my "bible" and the Cantatas are far from boring. Bach boring? Bach is a volcano.


Apparently TalkingHead is aware of something he said earlier.


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## millionrainbows

drmdjones said:


> EdwardBast is correct in every point he makes.


This is contradictory, since later drmdjones maintains that "there are no major seventh chords" in direct opposition to EdwardBast.



> EdwarBast said: It makes perfect sense to analyze chord progressions in Baroque music! And yes, what you are observing, the sequential repetition of motives on different scale steps, is a mainstay of the style. The underlying progressions supporting these sequences tend to use lots of root motion by fifths, as in, for example, the progression: iii - vi - ii - V - I - IV...Of course the concept of chord progression applies to the Baroque Era.


Woodduck backs this up:



> Woodduck said: I'm a bit baffled by this. Does anyone actually think that composers before the Classical period did not hear and conceive music in terms of harmonic progression? To think that they didn't, wouldn't we have to believe that they achieved a satisfactory succession of harmonies not consciously and intentionally but incidentally, solely through the application of rules governing the movement of contrapuntal melodic lines?


But, in contradiction, drdmjones says:



> drdmjones said:There are no major 7th chords in Bach (or Mozart, Beethoven, Mendelssohn, Schubert, Brahms).


_MR said: It would have been much clearer to say "The concept of chord progression applies to the Baroque, except in certain cases."
__*To say that the concept of chord progression applies to the Baroque is rather misleading. *Besides, the dissonant tones which weren't considered harmonic tones at the time would apply past the Baroque era, into CP classical.
__So really, the whole concept of chord progression in Baroque as well as CP tonality is riddled with exceptions like this, which are exceptions to a __modern__ or __jazz__ concept of what qualifies as a "chord," much less a "chord progression."_



> EdwardBast said: This has no clarity whatever and it wasn't what I was saying...Baroque harmonic practice is part of CP. Please learn what the terms you are using mean. There is enough confusion in the world without sowing more...Jazz and modern conceptions aren't relevant here. ...what you wrote: "non-harmonic tones such as a major seventh chord" makes no sense.


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## millionrainbows

Woodduck said:


> What semantical games? There is no contradiction between knowing that music is excellent and being uninterested in listening to it. If you don't care for Beethoven's 9th, despite its generally acknowledged position as a great and significant work of music, you just don't care for it. No arguments or justifications are required.


There will be a significant loss of credibility to such an opinion in light of consensus opinion. The chorales are accepted as masterpieces of harmonization by experts, and they are prototypes of the cantatas, so acknowledging one without the other would render such an imbalanced opinion as the "fringe" view of an outsider.


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## EdwardBast

millionrainbows said:


> Figured bass works for Bach, but it is too short-sighted limited in scope to be of value in music which modulates into other key areas. *It can't identify new tonic areas. It doesn't relate different tonics to each other,* it only relates the internal structure of a chord to one note.


To the extent it is necessary, key signatures do that.



millionrainbows said:


> It's like entering an enormous darkened room full of possibilities with only a flashlight for guidance.


It provides precisely enough information for skilled players to produce a number of different but fully valid performances. The unskilled find darkness and confusion everywhere they look.


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## millionrainbows

EdwardBast said:


> To the extent it is necessary, key signatures do that.


I said that figured bass "doesn't relate different tonics to each other." All a key signature does is indicate the key. It does not indication dual-functions in modulations.



> It provides precisely enough information for skilled players to produce a number of different but fully valid performances.


Wow, that's impressive. They can play in one key!

Figured bass is just an archaic set of instructions. It can't be used to analyze chord functions in progressions, unless Roman numerals are used to clarify it.



> The unskilled find darkness and confusion everywhere they look.


He who would search for pearls must dive below.


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## Roger Knox

Motto of Nashville songwriters who've studied Hugo Riemann: _"Three functions and the Truth."_


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## Guest

millionrainbows said:


> Figured bass works for Bach, but it is too short-sighted limited in scope to be of value in music which modulates into other key areas. It can't identify new tonic areas. It doesn't relate different tonics to each other, it only relates the internal structure of a chord to one note.
> 
> It's like entering an enormous darkened room full of possibilities with only a flashlight for guidance.


Are you saying, from an analytical "eyes on the score" point of view, that figured bass doesn't identify modulations ("new tonic areas") as easily as Roman numerals (e.g. V/VI [V of VI])?

Edit: I see you have already answered this just above.


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## Guest

millionrainbows said:


> There will be a significant loss of credibility to such an opinion in light of consensus opinion. The chorales are accepted as masterpieces of harmonization by experts, *and they are prototypes of the cantatas*, so acknowledging one without the other would render such an imbalanced opinion as the "fringe" view of an outsider.


Well, I know what you're trying to say but I wouldn't call them _prototypes_; more a source of generative material.


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## Guest

millionrainbows said:


> I said that figured bass "doesn't relate different tonics to each other." *All a key signature does is indicate the key.*


Normally yes. But in the "371" there are a good few instances where Bach uses 3 flats (indicating C minor, for example) but in fact it "sounds" as F minor.


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## Woodduck

TalkingHead said:


> Normally yes. But in the "371" there are a good few instances where Bach uses 3 flats (indicating C minor, for example) but in fact it "sounds" as F minor.


That's interesting and surprising. A survival of modal thinking?

Would it be correct to say that a "key" is not identical to a "tonality"? The key may be three flats, but the tonality is F minor. Any number of tonalities might be traversed or suggested within a given key signature.


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## Woodduck

mikeh375 said:


> Some great posts Wooduck, exhilarating and illuminating - they've encouraged me to listen to Wagner again after a long, long hiatus. (As coincidence would have it, I found a complete score to Tristan in a charity shop the other day, for £5).
> 
> The quote above stands out as a little unfair though imv, perhaps you wouldn't mind expanding a little on that, after all, composers of high calibre step to their own music. I certainly don't consider atonality as a more _"comfortable"_ option to tonal, chromatic technique and rhetoric and it certainly wouldn't have been at that time. It would also be fair to say that the emotional narrative, rather than an 'absolute' paradigm will have been the driving force for most composers then as it still is now.
> 
> (btw, may I ask if you are a composer?)


Thanks, Mike. I admit to being a little mischevous with that last comment. It was probably inspired by something I read about Schoenberg, Berg, Webern and friends gathered around a piano one fine evening (I'm indulging my pictorial imagination here), studying the score of _Tristan_ and wondering how the heck anyone could "go beyond Wagner." There are different ways of interpreting that, but with respect to his overall achievement in exploiting the accumulated resources of tonal music to create works of immense scope and depth, "going beyond Wagner" is something no one has done or, until we can learn to breed genius in the laboratory, will do. The score of _Parsifal_ is a virtual summation of the idioms of Western music since Palestrina, but it, like _Tristan_ before it, goes on to discover previously unexploited possibilities of tonal harmony which proved highly suggestive and challenged composers to "go beyond" in ways that could be dangerous to those who failed to perceive the pitfalls. The chromatic surfaces of the music were obviously a seductive siren, but the breadth of vision and the powers of synthesis and organization which enabled Wagner to exploit harmony to maximum effect were not so easily imitated. I think the most perceptive composers at the end of the 19th century knew that they would have to study Wagner, but warily, always consulting the compass of their personal souls in order to reamain true to themselves.

It would make sense that German/Austrian composers felt themselves under the greatest pressure to process the Wagnerian experience and come up with something perhaps less earth-shaking but still significant and viable, and I don't think anyone was more troubled by the problem than the intensely ambitious and intellectual Schoenberg. His philosophical and theoretical justifications for his own post-Wagnerian revolution were in various respects both admirable and questionable, but I think his proclamation that his ideas would assure the preeminence of German music for the next 100 years can hardly, in light of how things actually turned out, strike us as anything but amusing hubris unless we understand how the specter of Wagner haunted him and ultimately forced him to take a radical step which he could rationalize as the one thing necessary, not merely to him as a solution to his own artistic problems, but to the foreordained course of music itself. If Wagner's harmony could be rationalized as presaging, even necessitating, atonality, then Schoenberg and his disciples could at last "go beyond" Wagner, not on Wagner's terms but on Schoenberg's, and Wagner would become prophet to a new Messiah.

What I'm suggesting is not that Schoenberg and friends considered atonal writing intrinsically more "comfortable" than tonal writing, but only that striking out on a new path is more gratifying to the ego than feeling oneself in competition with something one can never "go beyond."


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## millionrainbows

TalkingHead said:


> Normally yes. But in the "371" there are a good few instances where Bach uses 3 flats (indicating C minor, for example) but in fact it "sounds" as F minor.


Does that mean I'm wrong, or that you are grasping desperately at any exception you can muster?


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## millionrainbows

Woodduck said:


> Thanks, Mike. I admit to being a little mischevous with that last comment. It was probably inspired by something I read about Schoenberg, Berg, Webern and friends gathered around a piano one fine evening (I'm indulging my pictorial imagination here), studying the score of _Tristan_ and wondering how the heck anyone could "go beyond Wagner." There are different ways of interpreting that, but with respect to his overall achievement in exploiting the accumulated resources of tonal music to create works of immense scope and depth, "going beyond Wagner" is something no one has done or, until we can learn to breed genius in the laboratory, will do. The score of _Parsifal_ is a virtual summation of the idioms of Western music since Palestrina, but it, like _Tristan_ before it, goes on to discover previously unexploited possibilities of tonal harmony which proved highly suggestive and challenged composers to "go beyond" in ways that could be dangerous to those who failed to perceive the pitfalls. The chromatic surfaces of the music were obviously a seductive siren, but the breadth of vision and the powers of synthesis and organization which enabled Wagner to exploit harmony to maximum effect were not so easily imitated. I think the most perceptive composers at the end of the 19th century knew that they would have to study Wagner, but warily, always consulting the compass of their personal souls in order to reamain true to themselves.


i.e., "bad boys go to Hell."



> It would make sense that German/Austrian composers in general felt themselves under the greatest pressure to process the Wagnerian experience and come up with something perhaps less earth-shaking but still significant and viable, and I don't think anyone was more troubled by the problem than the intensely ambitious and intellectual Schoenberg. His philosophical and theoretical justifications for his own post-Wagnerian revolution were in various respects both admirable and questionable, but I think his proclamation that his ideas would assure the preeminence of German music for the next 100 years can hardly, in light of how things actually turned out, strike us as anything but amusing hubris unless we understand how the specter of Wagner haunted him and ultimately forced him to take a radical step which he could rationalize as the one thing necessary, not merely to him as a solution to his own artistic problems, but to the foreordained course of music itself. If Wagner's harmony could be rationalized as presaging, even necessitating, atonality, then Schoenberg and his disciples could at last "go beyond" Wagner, not on Wagner's terms but on Schoenberg's, and Wagner would become prophet to a new Messiah.


I think it's safe to say that Schoenberg got over the "German" thing around 1938. And the "Wagner" thing. :lol:



> What I'm suggesting is not that Schoenberg and friends considered atonal writing intrinsically more "comfortable" than tonal writing, but only that striking out on a new path is more gratifying to the ego than feeling oneself in competition with something one can never "go beyond."


That's good, as long as you're just "suggesting" it.

I think they saw that Wagner at his most daring did not go forward with the implications of that thinking, and instead retreated back to his comfort zone. I think Schoenberg already demonstrated his ability to equal Wagner in his early works, as did Webern with his Passacaglia op.1, and Berg with his op. 1.

Of course, that's only my opinion, and as you said, "There is no contradiction between knowing that music is excellent and being uninterested in listening to it. If you don't care for Beethoven's 9th, despite its generally acknowledged position as a great and significant work of music, you just don't care for it. No arguments or justifications are required."


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## Woodduck

millionrainbows said:


> I think they saw that Wagner at his most daring did not go forward with the implications of that thinking, and instead retreated back to his comfort zone. I think Schoenberg already demonstrated his ability to equal Wagner in his early works, as did Webern with his Passacaglia op.1, and Berg with his op. 1.
> 
> Of course, that's only my opinion, and as you said, "There is no contradiction between knowing that music is excellent and being uninterested in listening to it. If you don't care for Beethoven's 9th, despite its generally acknowledged position as a great and significant work of music, you just don't care for it. No arguments or justifications are required."


The idea that Wagner ever "retreated," musically or otherwise, and ever entered a creative "comfort zone" could only occur to someone who doesn't know his music very well.

I know the atonalist orthodoxy says that the the dissolution and abandonment of tonality is "implicit" in the Tristan chord. Heck, your stated view is that atonality is "implicit" in the C major scale, which strikes me as taking orthodoxy to a new (perhaps insane) level. Well, I'm unorthodox.

The early, tonal works of Schoenberg, Berg and Webern make effective use of some Wagnerian lessons, but whatever their success (which is variable) they attempt less than Wagner did and so can't be said to "equal" him. I certainly appreciate the works you mention, along with Schoenberg's _Verklarte Nacht_,_ Gurrelieder,_ some lovely songs, et al., but who can place any of them on the summit reserved for the peak achievements of Western culture? Wagner's mature operas have rested comfortably there for some time, gazing serenely at the landscape below while Schoenberg's predicted atonalist reign of 100 years has neither come nor gone.

I have to respect the ingenuity and accomplishments of Schoenberg and his sphere, but that doesn't necessitate buying into his attempt to make himself the fulfillment of the evolution of harmony and the fulcrum of history.


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## millionrainbows

Woodduck said:


> ...your stated view is that atonality is "implicit" in the C major scale, which strikes me as taking orthodoxy to a new (perhaps insane) level.


Not exactly; I never used the word "atonality." I said it was "harmonically unstable." That's why there are "non harmonic" tones which need resolving.



> The early, tonal works of Schoenberg, Berg and Webern make effective use of some Wagnerian lessons, but whatever their success (which is variable) they attempt less than Wagner did and so can't be said to "equal" him. I certainly appreciate the works you mention, along with Schoenberg's _Verklarte Nacht_,_ Gurrelieder,_ some lovely songs, et al., but who can place any of them on the summit reserved for the peak achievements of Western culture? Wagner's mature operas have rested comfortably there for some time, gazing serenely at the landscape below while Schoenberg's predicted atonalist reign of 100 years has neither come nor gone. I have to respect the ingenuity and accomplishments of Schoenberg and his sphere, but that doesn't necessitate buying into his attempt to make himself the fulfillment of the evolution of harmony and the fulcrum of history.


So, we differ.


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## JosefinaHW

TalkingHead said:


> The RM 371 is my "bible" and the Cantatas are far from boring. Bach boring? Bach is a volcano.


 :kiss::kiss::kiss: I am going to refer people to this post next time someone says Bach is not a "Tier One"  Composer (I hate those categorizations) or someone says the cantatas are boring! You have my eternal gratitude.


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## JosefinaHW

TalkingHead, please consider using your post as your signature line!


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## mikeh375

Woodduck said:


> Thanks, Mike. I admit to being a little mischevous with that last comment. It was probably inspired by something I read about Schoenberg, Berg, Webern and friends gathered around a piano one fine evening (I'm indulging my pictorial imagination here), studying the score of _Tristan_ and wondering how the heck anyone could "go beyond Wagner." There are different ways of interpreting that, but with respect to his overall achievement in exploiting the accumulated resources of tonal music to create works of immense scope and depth, "going beyond Wagner" is something no one has done or, until we can learn to breed genius in the laboratory, will do. The score of _Parsifal_ is a virtual summation of the idioms of Western music since Palestrina, but it, like _Tristan_ before it, goes on to discover previously unexploited possibilities of tonal harmony which proved highly suggestive and challenged composers to "go beyond" in ways that could be dangerous to those who failed to perceive the pitfalls. The chromatic surfaces of the music were obviously a seductive siren, but the breadth of vision and the powers of synthesis and organization which enabled Wagner to exploit harmony to maximum effect were not so easily imitated. I think the most perceptive composers at the end of the 19th century knew that they would have to study Wagner, but warily, always consulting the compass of their personal souls in order to reamain true to themselves.
> 
> It would make sense that German/Austrian composers felt themselves under the greatest pressure to process the Wagnerian experience and come up with something perhaps less earth-shaking but still significant and viable, and I don't think anyone was more troubled by the problem than the intensely ambitious and intellectual Schoenberg. His philosophical and theoretical justifications for his own post-Wagnerian revolution were in various respects both admirable and questionable, but I think his proclamation that his ideas would assure the preeminence of German music for the next 100 years can hardly, in light of how things actually turned out, strike us as anything but amusing hubris unless we understand how the specter of Wagner haunted him and ultimately forced him to take a radical step which he could rationalize as the one thing necessary, not merely to him as a solution to his own artistic problems, but to the foreordained course of music itself. If Wagner's harmony could be rationalized as presaging, even necessitating, atonality, then Schoenberg and his disciples could at last "go beyond" Wagner, not on Wagner's terms but on Schoenberg's, and Wagner would become prophet to a new Messiah.
> 
> What I'm suggesting is not that Schoenberg and friends considered atonal writing intrinsically more "comfortable" than tonal writing, but only that striking out on a new path is more gratifying to the ego than feeling oneself in competition with something one can never "go beyond."


Thanks Wooduck, I can see the three of them now, booze on the table, cigarettes in hand, telling dirty jokes and poking fun. Ok I'm taking liberties too, but composers can be very bitchy in my experience, even (especially) the lower league ones who sell their souls to media (and I should know). Britten, being one of the 20thC's greatest pianists, once improvised in the style of Walton and not in an appreciative way and witness Stravinsky's jealous reaction to the news that Britten's masterpiece, the War Requiem, was a great success at its premiere..."Well it can't be that good then" (paraphrased).
Ironically, as we all know, it was Webern, the pupil, who's work signalled the way forward in the 20thC. Berg too, enjoyed more success than the 'Master' (although Berg and Webern's gratitude to Schoenberg was undimmed and always acknowledged). The next seismic shift in musical thought after Wagner and Schoenberg's developing ideas was the emancipation of rhythm. Stravinsky takes the credit there obviously, but as time progressed, his innovations where developed by others to a point where it became a major contributor to the demise of modern music because rhythm, as John Adams has said, is "the great unifier ". Its ability to anchor the listener with regular pulse and aid in comprehension was subjected to what could be construed as the linear equivalent to Wagner's investigation of chromaticism but with more serious disorientating results.


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## millionrainbows

This must be another composer from Oregon, part of the current "good ol' boy system."


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## mikeh375

millionrainbows said:


> This must be another composer from Oregon, part of the current "good ol' boy system."


You can see and hear who I am...who are you?


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## Guest

Woodduck said:


> That's interesting and surprising. *A survival of modal thinking*?
> 
> *Would it be correct to say that a "key" is not identical to a "tonality"?* The key may be three flats, but the tonality is F minor. Any number of tonalities might be traversed or suggested within a given key signature.


Perhaps not so much a survival of modal thinking, more to do with Bach using modal melodies in his chorale harmonizations. 
I enclose a short PDF (two very short pages, promise!) from Boyd's "Chrorale Harmonization" that explains it better than I can (see below).

As for "keys" not being identical to "tonalities", yes, I would go along with what you say. For me, in Baroque and Classical music, the given key signature denotes the _main_ tonality of the piece and prepares the field of closely related keys (I, IV & V, and their relative minors or majors).

View attachment Bach's modal chorales (Malcolm Boyd, Bach Chorale Harmonization) Page 1.pdf

View attachment Bach's modal chorales (Malcolm Boyd, Bach Chorale Harmonization) Page 2.pdf


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## Guest

millionrainbows said:


> Does that mean I'm wrong, or that you are grasping desperately at any exception you can muster?


Not at all. You said that "*All a key signature does is indicate the key."* This is perfectly true.
I am pointing out that there are a good few exceptions to that in the "371" where, for example, the key signature is G minor (two flats) but in reality it sounds as C minor (3 flats).


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## millionrainbows

Then you're taking liberties with the definition of "key" and "key signature." "Key signatures" define a diatonic scale that can be used in two modes, major or minor. The "key" of a work is defined in terms of the particular major or minor scale from which its principle pitches are drawn, and this is indicated by a "key signature."


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## EdwardBast

millionrainbows said:


> Not exactly; I never used the word "atonality." I said it was "harmonically unstable." That's why there are "non harmonic" tones which need resolving.


Saying a C major scale is harmonically unstable is absurd, by which I mean it doesn't even make enough sense to be incorrect. A C major scale is not a harmonic phenomenon. Saying there are "non harmonic" tones in a C major scale that "need resolving" is also a nonsensical statement. Any tone in a major scale can be a harmonic tone and any tone can be a non-harmonic tone. These terms have no meaning as you have used them because they only have meaning in specific contexts, which your statements have not provided. Harmonic tones often require resolution. The tonic note in C major can be a nonharmonic tone requiring resolution.

Even a sympathetic reading of your statement suggests you don't know what the term nonharmonic tone means.


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## Guest

JosefinaHW said:


> :kiss::kiss::kiss: I am going to refer people to this post next time someone says Bach is not a "Tier One"  Composer (I hate those categorizations) or someone says the cantatas are boring! You have my eternal gratitude.


Not at all!
Really though, I wouldn't get upset if peope say things like that. It's often born out of ignorance of these works or maybe they've been exposed to really bad performances using huge orchestral forces and singers with 3cm vibrato.


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## Guest

millionrainbows said:


> Then you're taking liberties with the definition of "key" and "key signature." *"Key signatures" define a diatonic scale that can be used in two modes, major or minor.* The "key" of a work is defined in terms of the particular major or minor scale from which its principle pitches are drawn, and this is indicated by a "key signature."


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## Guest

All I can say is that you should never leave home without your keys.


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## Roger Knox

TalkingHead said:


> Normally yes. But in the "371" there are a good few instances where Bach uses 3 flats (indicating C minor, for example) but in fact it "sounds" as F minor.


It may seem strange to us but that happened in the minor key, though modern editions may update the key signature. As I remember it in a treatise by Charles Masson, a significant predecessor of Rameau, the minor key was derived there from the Dorian mode (or Church Mode I), not from what is called the Aeolian mode. So in D minor there is no Bb but rather B-natural, the sixth note of the Dorian scale.


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## millionrainbows

EdwardBast said:


> Saying a C major scale is harmonically unstable is *absurd*, by which I mean *it doesn't even make enough sense to be incorrect.* A C major scale is not a harmonic phenomenon. Saying there are "non harmonic" tones in a C major scale that "need resolving" is also a *nonsensical statement*. Any tone in a major scale can be a harmonic tone and any tone can be a non-harmonic tone. These terms have *no meaning as you have used them *because they only have meaning in specific contexts, which *your statements have not provided. *Harmonic tones often require resolution. The tonic note in C major can be a nonharmonic tone requiring resolution.
> 
> Even a sympathetic reading of your statement suggests you don't know what the term nonharmonic tone means.


Talking to you is like cutting your way through a dense overgrowth of academic accumulation, with bothersome gnats flying around to add to the drudgery.

I'm not an academic thinker, as you apparently are. If you don't agree with my ideas, there's no need to start name-calling or making negative inferences. Get a grip, please!* :lol:
*
I'm looking at the C major scale itself as a harmonic reinforcer or indicator of the key of C major, and it does not do this as efficiently as it should, if what we wanted was a scale that reinforces the key of C major harmonically. As it stands, it appears that the C major scale is used not primarily harmonically, because it has tendencies which make it want to go to other keys; it is ambiguous in this sense. Because it does not reinforce C efficiently, I say it is harmonically unstable. More on this later.

To address your assertion that scales are not harmonic phenomena (you did say that, didn't you?), I have the following:

What are scales useful for, then? They are unordered, so there are cross-relations between every note in the scale with every other note. What does this mean? It means that scales have a harmonic content.
What is harmonic content, and what are cross-relations in a scale? It means that every note is related to every other note:

C Major scale: C-D-E-F-G-A-B

Relations: First note, C: 
C-D; C-E; C-F; C-G; C-A; C-B

Then, next note, D: 
D-E; D-F; D-G; D-A; D-B

Then, next note, E: 
E-F; E-G; E-A; E-B

Then, next note, F: 
F-G; F-A; F-B

Then, next note, G: 
G-A; G-B

Then, next note, A:
A-B

These intervals can be counted, to come up with a "harmonic content" of the scale: 
minor thirds: 2 (E-F, B-C)
major seconds: 5 (C-D, D-E, F-G, G-A, A-B)
minor thirds: 4: D-F, E-G, A-C, B-D)
major thirds: 3: C-E, F-A, G-B
fourths: 5: C-F, D-G, E-A, G-C, A-D
tritones: 1: (B-F)

20 relations; with 6 basic interval types (the rest are inversions): m2/M7, M2/m7, m3/M6, M3/m6, 4th/5th/, and tritone.

Now, to address my assertion that the C major scale is unstable:

The "diminished seventh" chord itself, supposedly built on the vii degree, is not really that at all: it's to be considered an incomplete G7 dominant (B-D-F), and should be resolved as that by assuming a G root, according to two respected sources: Walter Piston's Harmony and Schoenberg's Harmonielehre.

The "diminished seventh" is not really a chord at all, with its unstable tritone; it just reveals a glitch in the harmonic system, and is really the result of contrapuntal voice-leading.

The diminished seventh, with its tritone B-F, reveals the inherent instability of the C major scale, which was designed for "travel" out of the key, not to ultimately reinforce the key suggested by the scale. The diatonic C major scale, the chosen scale for most of our music, is also inherently unstable as far as being "totally tonal." It's built for movement, for unrest.

The interval C-F is a fourth; if we hear this as "root on top," then F Major (complete with leading tone E-F) is established, subordinating C, supposedly the "home" key. All this is due to the fact of the tritone F-B in the C major scale. 
In this light, we can see the truth of George Russell's assertion that the Lydian scale is "more tonal" if one wants to establish the scale root as the key.

The F lydian scale cycles through all 7 in perfect fifths before it circles back around to F, its key note: F-C-G-D-A-E-B (F). This is also why piano tuners start on F and tune by fifths.

If we try to "stack fifths" starting on C, we get C-G-D-A-E-B-(F#?). It doesn't work for a C major scale, as it has an "F."

When all the notes of a C major scale are sustained by ascending fifths, C-G-D-A-E-B, the consonance of perfect fifths falls apart when the clunker "F" is added on top.

The C major scale is structured so that there is a "leading tone" E-F (establishing F), as well as B-C (establishing C).

Significantly, the C lydian scale has a leading tone F#-G (establishing the more closely related V step of G) and B-C (establishing the scale key).

I'm not criticizing the C major scale; it's perfectly suited for what it is used for: to travel to other key areas due to its inherent instability, the tritone B-F, which ultimately manifests as the diminished chord.

In other words, the C major diatonic scale was designed to travel to other key areas, thus being inherently unstable, thus fulfilling its "harmonic destiny:" the diminished chord and the unravelling of the tonal fabric.

The dissolution of tonality is inherent in the structure of the major scale.


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## Roger Knox

Woodduck said:


> That's interesting and surprising. A survival of modal thinking?


Yes, that's it exactly! G minor - one flat. C minor - two flats. Evolution of minor from the Dorian mode.


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## millionrainbows

You guys are so academic! Do any of you know how to use a mode, or how to determine a scale or mode for playing over a chord progression, or do you just analyze Bach chorales? To each his own.


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## mikeh375

millionrainbows said:


> You guys are so academic! Do any of you know how to use a mode, or how to determine a scale or mode for playing over a chord progression, or do you just analyze Bach chorales? To each his own.


Yes to the first, no to the second...and you?


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## BabyGiraffe

millionrainbows said:


> I'm not criticizing the C major scale; it's perfectly suited for what it is used for: to travel to other key areas due to its inherent instability, the tritone B-F, which ultimately manifests as the diminished chord.
> 
> In other words, the C major diatonic scale was designed to travel to other key areas, thus being inherently unstable, thus fulfilling its "harmonic destiny:" the diminished chord and the unravelling of the tonal fabric.
> 
> The dissolution of tonality is inherent in the structure of the major scale.


Diatonic scale is basically the most consonant and stable 7 note scale in 5-limit just intonation and related tunings (like 12 equal) - it's basically a consonant chord. I disagree that it has anything to do with atonality.
You are also wrong when you talk about the tritone, because there is no tritone in classical meantone repertoire where we get a diminished fifth and augmented fourth. These are not ambigious in any way. I think that 12 equal is the only ambigious meantone tuning. All other accurate meantone tunings are not divisible by 2 and have no tritones (19 and 31 equal are well known. Much of classical music can be analysed as 12 notes out of 31, because there is almost no difference between 1/4 comma meantone and 31 equal.)
7 equal (Thai/Central Africa) feels pretty consonant and along with 5-equal (close to Indonesia/African ) give opportunities for "serial" and "atonal" systems that actually don't sound like garbage, despite being completely symmetrical. That's because they have decent approximations (for their size) of various harmonics and someone can compose atonal/tonal music that doesn't sound annoying (too bad that harmony there is garbage).


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## EdwardBast

millionrainbows said:


> You guys are so academic! Do any of you know how to use a mode, or how to determine a scale or mode for playing over a chord progression, or do you just analyze Bach chorales? To each his own.


This is a thread on Baroque chord progressions and by extension, Baroque theory. If you want to talk about modal improvisation in a modern context, why not start a thread on that instead of complaining about the subject matter under discussion here?

I'm not responding to your longer post because you're just restating ideas you've been posting for years and inserting more or less randomly into threads whether they have anything to do with the subject of the thread or not. I've already pointed out about twenty errors in the contents of that longer post in this thread and elsewhere.


----------



## Woodduck

mikeh375 said:


> The next seismic shift in musical thought after Wagner and Schoenberg's developing ideas was the emancipation of rhythm. Stravinsky takes the credit there obviously, but as time progressed, his innovations where developed by others to a point where it became a major contributor to the demise of modern music because rhythm, as John Adams has said, is "the great unifier ". *Its ability to anchor the listener with regular pulse and aid in comprehension was subjected to what could be construed as the linear equivalent to Wagner's investigation of chromaticism but with more serious disorientating results.*


Could you elaborate a bit? Disorienting in what way?


----------



## millionrainbows

> Diatonic scale is basically the most consonant and stable 7 note scale in 5-limit just intonation and related tunings (like 12 equal) - it's basically a consonant chord. I disagree that it has anything to do with atonality.



The 12 equal is equally related to a Pythagoran stacking of 3/2s: just stack 'em and even out the leftover comma, and viola! you have 12 ET.

By contrast, look on p. 39 of Doty's Just Intonation Primer and notice how a five-limit major scale is constructed. It consists of three interlocking major triads built on the tonic (1/1), dominant (3/2), and subdominant (4/3) scale degrees.

Begin by tuning a major triad on the tonic (1/1). This gives us the scale degrees 1/1, 5/4, and 3/3. Next, another major triad on the dominant degree, the fifth of the previous triad (3/2).This yields two additional tones, 9/8 and 15/8. Finally, we obtain the subdominant degree by tuning a fifth below (or a fourth above) 1/1, and then construct our last triad on this tone. This process gives us our final two scale tones, 4/3 and 5/3. Expressed in scale order, starting on the tonic, the scale degrees are 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, and 15/8.










Although the Syntonon diatonic has advantages over a Pythagoran ditone (generated from 3/2s and 4/3s), because of the ditone's weird thirds, it has the same "hierarchy" problems as modern scales because of its internal structure: the subdominant was generated by "changing direction" and going down a fifth (up a fourth) from 1/1 to the subdominant, now in-octave as a 4/3. This "harmonically degrades" the hierarchy of a stack of perfect fifths, in the same way that in modern scales, F-C-G-D-A-E-F sounds more consonant than C-G-D-A-E-B-F.


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## Woodduck

millionrainbows said:


> I'm not an academic thinker, as you apparently are.


Much of what you say sounds pretty academic to me. Maybe it's just that I'm a naive intuitive autodidact who's easily fooled by name-dropping, diagrams, and scientific-sounding terminology.



> I'm looking at the C major scale itself as a harmonic reinforcer or indicator of the key of C major, and it does not do this as efficiently as it should, if what we wanted was a scale that reinforces the key of C major harmonically.


Why look at a scale as a "harmonic reinforcer"? It's just a scale. What does "reinforces the key of C major harmonically" mean? Do keys need reinforcements? How can a scale reinforce a key?



> it has tendencies which make it want to go to other keys; it is ambiguous in this sense.


I don't find it ambiguous or having tendencies or wanting to do anything. It's just an array of pitches sitting there waiting for music to give its pitches tendencies.



> The C major scale is structured so that there is a "leading tone"


"B" is a leading tone only if music is structured so that "B" leads to "C." This thread has actually been talking about music in which it doesn't. In jazz, for example, seventh and ninth chords are often stable: "B" needn't "lead" anywhere - neither to "C" in C major, nor to "A" in A minor - even in a final cadence. Post-CP music has removed many "tendencies" from scales - or, more accurately, shown that they aren't inherent in the scales to begin with but merely imputed by convention.



> I'm not criticizing the C major scale; it's perfectly suited for what it is used for: to travel to other key areas due to its inherent instability, the tritone B-F, which ultimately manifests as the diminished chord.


A dim7 is constructed of overlapping tritones. It isn't something tritones "manifest."

The C major scale is also perfectly suited for _not_ traveling to other tonal areas. Any scale is suitable for traveling or not traveling to other tonal areas. It depends on the conventions of the music utilizing the scale. Music using a pentatonic scale, from which the tritone relationship is missing, may "want" to shift its tonal center from C to A or E if a melody is shaped in such a way as to make us hear it that way. Tonal instability is a property of music, not of scales.

The C major scale hasn't changed for centuries, but what composers do with the notes in it has. The scale has not told them what they must do; they have told the scale - tritone, leading tone, and all - what to do.



> In other words, the C major diatonic scale was designed to travel to other key areas, thus being inherently unstable, thus fulfilling its "harmonic destiny:" the diminished chord and the unravelling of the tonal fabric.
> 
> The dissolution of tonality is inherent in the structure of the major scale.


The fact that a tritone can be found between two notes of a scale doesn't dictate the ways in which that interval will be used, or whether it will be used at all (maybe it will be called "the devil" and avoided). It doesn't have to be used to build diminished chords any more than the seventh scale degree has to resolve to the eighth. The fact that within the Western tonal system certain notes of a scale can be used to create an effect of harmonic instability doesn't justify calling the scale itself unstable. But still less does it justify the leap of logic that would connect harmonic instability - "ambiguities" and "tendencies" - to the "dissolution" of tonality. Instability, ambiguity and tendencies _presuppose_ tonal expectations, which they frustrate or satisfy for structural and expressive purposes. Once the tritone is "emancipated" (to use Schoenberg's curious term) from tonality, it is not unstable and not ambiguous, because there is no longer a stable state - a tonic - to which it "tends," or about which uncertainty can be felt.

To say that the dissolution of tonality is inherent in the structure of the major scale is like saying that the dissolution of democratic society is inherent in a free press and the right to vote. We can talk and vote ourselves into dictatorship, but that doesn't make the loss of political rights inherent in the structure of democracy.


----------



## Larkenfield

‘The "diminished seventh" chord itself, supposedly built on the vii degree, is not really that at all: it's to be considered an incomplete G7 dominant (B-D-F), and should be resolved as that by assuming a G root, according to two respected sources: Walter Piston's Harmony and Schoenberg's Harmonielehre.’
——
Add the A of the C-major scale to the B-D-F and you have the half-diminished chord that naturally resolves to the E minor chord of the scale. Mahler started off his Seventh Symphony with a half-diminished chord but did not resolve it to the tonic. B-D-F is part of the half-diminished and is much more than an incomplete dominant seventh because it has a different root than a dominant G chord.


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## BabyGiraffe

millionrainbows said:


> ...


Syntonic comma and Pythagorean comma (and similar differences) are called unison vectors in tuning theory, because they can be tempered to unison without distorting too much the final scale (which can be represented by different unison vectors and ratios).

Depending on what we will play, we can have many different interpetations of diatonic scale in just intonation, using ratios like 10/9 =minor whole tone, 27/20 = acute fourth, 27/16 = pythagorean major sixth etc. These are all valid ratios and can actually be heard in real performances when the orchestra plays, despite not existing in normal textbooks. 
Ben Johnston has some string quartets, I think, where he notated just intonation; I can imagine how horrific it looks for an end result that will sound basically the same as letting the players to use their ears (of course, he uses some enharmonic tricks in his compositions, but you get what I mean - it's probably not worth it to overcomplicate the notation for minor results).

How we will rationalize the construction of various scales for keyboards is another topic. The method you mentioned was popularised by Zarlino, but he also mentions that this 7-note scale is expanded to 21 pitches gamut (by multiplying the scale steps with other ratios), not 12. It was known way before Zarlino to Greeks and Romans and they didn't rationalize it with chords. Their theory was based on tetrachords.

12 equal is not just a simplified representation of 5 or 3-limit (generated by perfect fitths) diatonic. Hexatonic, octatonic, various "blues/oriental/gypsy/ethnic" or symmetrical 9, 10, 11 (this one is the chromatic, skipping the tritone) notes scales exist in it and are better represented in bigger divisions of the octave (and lead to bigger "tonalities" that are not generated by stacking perfect fifths).
It is interesting that all this stuff became popular (at least in art music, pop/folk music is still stuck in a pentatonic/diatonic frame) only after adoption of 12 equal, because in the Classical/Baroque/Renaissance/Medieval era they would be distorted (at least when played on organs and harpsichords, and piano ).


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## millionrainbows

Larkenfield said:


> 'The "diminished seventh" chord itself, supposedly built on the vii degree, is not really that at all: it's to be considered an incomplete G7 dominant (B-D-F), and should be resolved as that by assuming a G root, according to two respected sources: Walter Piston's Harmony and Schoenberg's Harmonielehre.'
> --
> Add the A of the C-major scale to the B-D-F and you have the half-diminished chord that naturally resolves to the E minor chord of the scale. Mahler started off his Seventh Symphony with a half-diminished chord but did not resolve it to the tonic. B-D-F is part of the half-diminished and is much more than an incomplete dominant seventh because it has a different root than a dominant G chord.


That makes perfect sense to me. I'd never thought of it that way.


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## millionrainbows

BabyGiraffe said:


> 12 equal is not just a simplified representation of 5 or 3-limit (generated by perfect fitths) diatonic. Hexatonic, octatonic, various "blues/oriental/gypsy/ethnic" or symmetrical 9, 10, 11 (this one is the chromatic, skipping the tritone) notes scales exist in it and are better represented in bigger divisions of the octave (and lead to bigger "tonalities" that are not generated by stacking perfect fifths).


I understand this, but it's the stacking of fifths that is the most important point. This has harmonic consequences. If you stack fifths C-G-D-A-E, stopping at five, you get the pentatonic scale C-D-E-G-A, which you will notice has no tritone and no fourth degree. This scale is therefore more consonant than the diatonic major scale, since it has no tritones.


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## BabyGiraffe

millionrainbows said:


> I understand this, but it's the stacking of fifths that is the most important point. This has harmonic consequences. If you stack fifths C-G-D-A-E, stopping at five, you get the pentatonic scale C-D-E-G-A, which you will notice has no tritone and no fourth degree. This scale is therefore more consonant than the diatonic major scale, since it has no tritones.


Pentatonic scale has only 5 degrees. You are trying to shove it into some heptatonic models. Many of your favourite atonal theorists and composers explored 5, 6 etc note scales as their own thing. It also sounds like its own unique tonality (after listening to just traditional Chinese/Japanese music for a few days, Western diatonic may sound "chromatic" for a short period of time).
We have a "wolf" interval similar to the tritone in the black note pentatonic, it's 400 or its inversion - 800 cents, instead of 500/700 (when we stack fourths or fifths).

I think hexatonics are the most important in 12 ET, because of the symmetry and complementarity in it.

Of course, it's more consonant, the more intervals in the chord, more dissonance we get. Still, I don't listen to music that uses the whole diatonic as a chord...
I'm not sure, if there is a objective measure about how consonant are the intervals in a melody.
In general, smaller intervals around semitones are probably considered the most dissonant (way more dissonant than intervals around tritones ) and hard to distinguish or even play by amateurs (give a chromatic piece to a school brass band and just listen to the end result). 
Sometimes, small intervals can even sound wrong (like alterations, instead of new musical objects) when you play the chromatic scale - I guess it's something related to our pitch perception (some cognition "experts" have suggested melodies and scales with no more than 9 different notes) and psychological expectations; these two factors ruin many of theoretical musical resources like polytonality/non-octave divisions etc.
Tritones can sound pretty "cool" and are staple in all the spy-thrillers and blues/jazz. The simplest consonant ratio is 7/5, I don't think it's that great, but it doesn't sound wrong.


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## millionrainbows

BabyGiraffe said:


> Pentatonic scale has only 5 degrees. You are trying to shove it into some heptatonic models. Many of your favourite atonal theorists and composers explored 5, 6 etc note scales as their own thing. It also sounds like its own unique tonality (after listening to just traditional Chinese/Japanese music for a few days, Western diatonic may sound "chromatic" for a short period of time).
> We have a "wolf" interval similar to the tritone in the black note pentatonic, it's 400 or its inversion - 800 cents, instead of 500/700 (when we stack fourths or fifths).


With six-note scales, we get the most variety of intervals (Hanson) before redundancy sets in (i.e. repeats of intervals with no new interval introduced). The pentatonic doesn't have all six intervals; it is missing the tritone, so harmonically speaking, it is a very "consonant" i.e. tonic-reinforcing scale. 400 cents refers to the major third, and when you generate a scale from fifths, the thirds will suffer, but it is a less-important interval than the fifth, as far as harmonic stability over the entire range. That seems to be the difference in our thinking, I consider scales harmonically first and foremost.



> Of course, it's more consonant, the more intervals in the chord, more dissonance we get. Still, I don't listen to music that uses the whole diatonic as a chord...


I was trying to say earlier that scales do have "harmonic content" because of the intervals which are generated by cross-relations, called "interval vectors." This is the way I've learned to think about unordered scales, so it might as well be a "chord".



> I'm not sure, if there is a objective measure about how consonant are the intervals in a melody.


You could do a vector analysis of any melody, as I've demonstrated in my blog, with 12-tone rows. A tone row is an ordered set, like a melody, so its interval vector is much smaller than a scale. But any melody which is scale-derived (not a fixed ordered tone sequence) is better paired with the interval vector of the entire scale, since melodies are derived from an unordered set, called a scale.



> In general, smaller intervals around semitones are probably considered the most dissonant (way more dissonant than intervals around tritones ) and hard to distinguish or even play by amateurs (give a chromatic piece to a school brass band and just listen to the end result).


Again, I don't look at notes individually; I put them in harmonic context, so a tritone is dissonant as an interval when we compare it to a fifth, and when one of those tritone's notes is the tonic, it destabilizes the tonic, which is a harmonic consequence. On the other hand, tritones sound more stable when they are the b7 and major third of a chord, but this also has to be put in harmonic context with a tonic on "1".



> Tritones can sound pretty "cool" and are staple in all the spy-thrillers and blues/jazz. The simplest consonant ratio is 7/5, I don't think it's that great, but it doesn't sound wrong.


Again, this works in jazz as a tempered interval. to me, it's not necessary that it be a "just" ratio.


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## millionrainbows

Even in the introduction of the book "Essay on the True Art of Keyboard Playing" by C.P.E. Bach, the authors admit that Bach's thorough bass practice would become unwieldy as more chords were added to the harmonic collection. Rameau's 'root system' was far smaller and easier to work with.


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## millionrainbows

During the early eighteenth century, Jean-Phillipe Rameau articulated the modern notion of a chord, classifying basic musical objects based on their pitch-class content rather than their order or registral arrangement. Rameau implicitly suggested that three basic operations preserve the "chordal" or "harmonic" identity of a musical object: octave shifts, permutation (or reordering), and cardinality change (or note duplication). For instance, one can transform (C4, E4 G4) by reordering its notes to produce (E4, G4, C4), transposing the second note up an octave to produce (C4, E5, G4), or duplicating the third note to produce (C4, E4, G4,G4) - all without changing its right to be called a "C major chord." Furthermore, these transformations can be combined to produce an endless collection of objects, all representing the same chord: (E4, G4, C5), (G3, G4, C5, E4), (E2, G3, C4, E4, E5), and so on. To be a C major chord is simply to belong to this equivalency class - or in other words, to contain all and only the three pitch-classes C, E, and G. We can therefore represent the C major chord as the unordered set of pitch classes {C, E, G}. -Tymoczko, p. 36

I think figured bass is rather archaic unless one has an overview, and I think it's limited to that older style of music, and is really more of a "technique" which was used in lieu of harmonic/root thinking, which was not developed or accepted or used, whatever.

This figured-bass thinking was perhaps a method which worked its way into the stylistic arsenal of composers, and yes, they had to be handled in specific ways, but the abstracted convenience of thinking harmonically is still in evidence to modern analysts. Figured-bass tends to get bogged-down in voice-leading details which ignore a purer, freer abstract distillation of harmonic considerations. And as harmony got more complex, what happened to figured bass thinking? It failed, or rejected more complex harmony. Figured bass is an ideological artifact of a bygone way of thinking. We have bigger, more complex fish to fry.

A chord in all its inversions has the same root function (not bass note), and the same quality (major/minor).

Maybe in earlier times, it is treated differently...

In some _convoluted sense, it could be said that since figured bass notation recognizes each inversion separately from a bass note (not a root function), that they are not "equivalent" in that sense.

WIK: _Figured-bass numerals express distinct intervals in a chord only as they relate to the bass note (not a root function). They make no reference to the key of the progression (unlike Roman-numeral harmonic analysis).

Because that would be "harmonic thinking."


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## hammeredklavier

tdc said:


> Well it has all the notes of a maj7, it sounds like a maj7, it has all the harmonic flavor of a maj7. Call it what you want.


I was reminded of this thread the other day while listening to this piece, 







which contains this passage with
C-----
---B--Bb--
C----------
the "contrapuntal motion" of the top voice and bottom pedal creating an interval of what seems like a 'major seventh' (held down for the duration of a half note), "resolving" to a minor seventh (with the inner voices making it a dominant seventh?). I think it's interesting.

*[ 4:37 ]*


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## millionrainbows

Still, that "major seventh" is part of a passing movement of the voice down to the flat-seven. This is not harmonic thinking, this is not chord thinking, *this is contrapuntal thinking.*


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## Bwv 1080

Larkenfield said:


> 'The "diminished seventh" chord itself, supposedly built on the vii degree, is not really that at all: it's to be considered an incomplete G7 dominant (B-D-F), and should be resolved as that by assuming a G root, according to two respected sources: Walter Piston's Harmony and Schoenberg's Harmonielehre.'
> --
> Add the A of the C-major scale to the B-D-F and you have the half-diminished chord that naturally resolves to the E minor chord of the scale. Mahler started off his Seventh Symphony with a half-diminished chord but did not resolve it to the tonic. B-D-F is part of the half-diminished and is much more than an incomplete dominant seventh because it has a different root than a dominant G chord.


B half dim resolves to C, not em, it has the same dominant function as b dim. Its the top 4 notes of the dom 9th (which is recognized in CP harmony)


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## Bwv 1080

Theory codifies existing practice, which is what both Rameau and George Russell did and its value stems from how well it assists people in understanding the music, it does not really matter what nomenclature the music’s creators actually used. You cant understand baroque music without CP harmony. Maybe Bach thought in figured bass and counterpoint because had so internalized and mastered everything we understand as chord theory from that alone, but so what? CP harmony is in Bach and its a better model than figured bass and counterpoint alone


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## millionrainbows

Bwv 1080 said:


> B half dim resolves to C, not em, it has the same dominant function as b dim. Its the top 4 notes of the dom 9th (which is recognized in CP harmony)


Thinking freely, outside of CP rules, if B half dim is the ii degree of A minor, then it can resolve to some form of E (v or V7), then go to A (i). What's your point, to remind us of CP restrictions? Or is this a possibility you had never even considered?

Considering B-D-F-G# or B-D-F-A as being G or G 'dominant flat nine' chords with an unstated root is common procedure in jazz, and is even accepted as a way of conceiving the resolution of viiº to I by both Walter Piston and Arnold Schoenberg in their harmony textbooks. Is this theory forum supposed to be for CP theory only? It's best to know ALL of these things.


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## millionrainbows

Bwv 1080 said:


> Theory codifies existing practice, which is what both Rameau and George Russell did and its value stems from how well it assists people in understanding the music, it does not really matter what nomenclature the music's creators actually used. You cant understand baroque music without CP harmony.


*And that's another good reason you should know all of the different approaches, procedures, and names for things. Like 'super locrian,' 'diminished whole tone,' and 'altered dominant' all being names for the same scale, so you can communicate with people from different disciplines.*



> Maybe Bach thought in figured bass and counterpoint because had so internalized and mastered everything we understand as chord theory from that alone, but so what?


 I agree, but when the question of "did Bach use major seventh chords" is asked, invariably a CP academician will tell you that "chords did not exist in Baroque music."



> CP harmony is in Bach and its a better model than figured bass and counterpoint alone.


I agree, basically; but here's the friction I'm talking about:



millionrainbows said:


> _So really, the whole concept of chord progression in Baroque as well as CP tonality is riddled with exceptions like this, which are exceptions to a modern or jazz concept of what qualifies as a "chord," much less a "chord progression."_


_



unidentified academic said:



Baroque harmonic practice is part of CP. *Jazz and modern conceptions aren't relevant here. *

Non-harmonic tones include passing tones, neighbor tones, appoggiaturas, suspensions, etc.-*notes understood to be non-chord tones.* Therefore what you wrote: "non-harmonic tones such as a *major seventh chord" makes no sense.*

Click to expand...

_
Is this nit-picking or what? 
I made the 'mistake' of pointing out a CP/Baroque instance of a non-harmonic tone as sounding exactly like a major seventh chord, and I am chastised for 'calling it a chord' because 'chords didn't exist in the Baroque era.'

This is totally inflexible and argumentative, as well as confusing to many non-academics.


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## Bwv 1080

millionrainbows said:


> Thinking freely, outside of CP rules, if B half dim is the ii degree of A minor, then it can resolve to some form of E (v or V7), then go to A (i). What's your point, to remind us of CP restrictions? Or is this a possibility you had never even considered?
> 
> Considering B-D-F-G# or B-D-F-A as being G or G 'dominant flat nine' chords with an unstated root is common procedure in jazz, and is even accepted as a way of conceiving the resolution of viiº to I by both Walter Piston and Arnold Schoenberg in their harmony textbooks. Is this theory forum supposed to be for CP theory only? It's best to know ALL of these things.


Within CP rules ii half dim is a sub for the subdominant iv chord in minor, just as ii7 is in major


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## Bwv 1080

millionrainbows said:


> I agree, but when the question of "did Bach use major seventh chords" is asked, invariably a CP academician will tell you that "chords did not exist in Baroque music."
> .


Yes asking whether Bach used maj7 chords is like asking whether Dunstable used major triads


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## isorhythm

Literally no one will ever tell you "chords did not exist in Baroque music," as that would be wrong and insane.

Some notable major seventh chords in Bach are in WTC book 1 C major prelude. Since the piece a series of broken chords each lasting one measure, it would be very hard to argue that Bach wasn't thinking in terms of chords or that he considered the major sevenths to be less "real" than the other chords in the piece.

Another major seventh occurs in the ritornello of "Sheep may safely graze."

I'm sure there are many others, those two come to mind because they're very famous.


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## millionrainbows

isorhythm said:


> Literally no one will ever tell you "chords did not exist in Baroque music," as that would be wrong and insane.


I don't believe that. In fact, this entire thread starts with these words:



sealep said:


> I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. They seems to rise or fall on the diatonic scale by a step, repeating the same motif. Does that make sense? For example, Bach seems to like repeating downward scales on successively incrementing steps; building tension upward with the key, while descending melodically.





isorhythm said:


> Some notable major seventh chords in Bach are in WTC book 1 C major prelude. Since the piece a series of broken chords each lasting one measure, it would be very hard to argue that Bach wasn't thinking in terms of chords or that he considered the major sevenths to be less "real" than the other chords in the piece.
> 
> Another major seventh occurs in the ritornello of "Sheep may safely graze."
> 
> I'm sure there are many others, those two come to mind because they're very famous.


I agree that it *sounds* as if those are major seventh chords. But CP theory (and this includes Baroque) doesn't recognize these as chords. And I think Bach thought contrapuntally (not harmonically except in a very general sense).

This shows us that Bach and contrapuntal music in general is not based on how things sound harmonically, but is based on strictly-defined voice-leading procedures and concepts of "non-harmonic tones."


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## mikeh375

millionrainbows said:


> ....
> I agree that it *sounds* as if those are major seventh chords. But CP theory (and this includes Baroque) doesn't recognize these as chords. And I think Bach thought contrapuntally (not harmonically except in a very general sense).
> 
> This shows us that Bach and contrapuntal music in general is not based on how things sound harmonically, but is based on strictly-defined voice-leading procedures and concepts of "non-harmonic tones."


It's much more nuanced than that. It's fair to say that Bach did frequently let the line override the vertical, resulting in a particular harmonic spice that gives his work immense emotional power, but one can't write counterpoint in his style without harmonic thought and consideration - it's just not possible, the two trains of thought are the two sides of a single coin.

Part of Bach's genius was to expand the reach of the emotional potential in momentary dissonance imv. He did this by allowing the linear to follow it's own logic seemingly unimpeded at times, giving rise to clashes that as a result, seem inevitable but also calculated. However, the individual lines are also cogniscent of their vertical obligations and as such are also determined by the vertical.

Bach, as well as thinking contrapuntally, also _had_ to think harmonically and not just in a "very general sense", but rather from beat to beat, phrase to phrase, cadence to cadence and as a consideration for defining form.

The best way to gain a deep understanding of the synergy between harmonic and contrapuntal thought is to learn to write counterpoint in Bach's style, it then becomes clear that one needs the other in more than a superficial or general way.


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## 1996D

sealep said:


> I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. They seems to rise or fall on the diatonic scale by a step, repeating the same motif. Does that make sense? For example, Bach seems to like repeating downward scales on successively incrementing steps; building tension upward with the key, while descending melodically.


That's what they felt was appropriate to represent awe yet glorify the church without blasphemy. Baroque music is orderly and never sensual or leaning towards amorality.


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## BabyGiraffe

1996D said:


> That's what they felt was appropriate to represent awe yet glorify the church without blasphemy. Baroque music is orderly and never sensual or leaning towards amorality.


Music has nothing to do with morality and feelings!!! You can associate certain sounds with some kind of cultural norms, it doesn't mean anything.
And using stock motives/phrases/whole sequences has little to do with order or balance in composition, more with craftsmanship and commercial productivity + lack of creativity (or else Telemann wouldn't write 3000 compositions). And this remark can be applied to other musical periods and famous composers.


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## Bwv 1080

1996D said:


> That's what they felt was appropriate to represent awe yet glorify the church without blasphemy. Baroque music is orderly and never sensual or leaning towards amorality.


Baroque music's origins are in Opera with the goal of better expression of drama and human passions


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## millionrainbows

mikeh375 said:


> It's much more nuanced than that.


Okay, but I'm speaking generally. Bach did not think "now I'm going to a I major seventh chord" when writing. He may have heard the harmonic effect of a M7 "chord" but he saw it as a non-harmonic tone and treated it as that.



> It's fair to say that Bach did frequently let the line override the vertical, resulting in a particular harmonic spice that gives his work immense emotional power, but one can't write counterpoint in his style without harmonic thought and consideration - it's just not possible, the two trains of thought are the two sides of a single coin.


I didn't say that ALL harmonic thought was excluded; only instances of "I M7" which was used from the beginning as an example of a "non-harmonic tone" instead of being thought of as a chord.



> ...it's just not possible, the two trains of thought are the two sides of a single coin.


No they aren't. There are specific exclusions of "non-harmonic tones" as mentioned above. I'm focussing on differences, not on similarities.



> Part of Bach's genius was to expand the reach of the emotional potential in momentary dissonance imv. He did this by allowing the linear to follow it's own logic seemingly unimpeded at times, giving rise to clashes that as a result, seem inevitable but also calculated. However, the individual lines are also cogniscent of their vertical obligations and as such are also determined by the vertical.


Well, I don't know about this description. I hear contrapuntal music as distinctly different than music where chord changes are done in 'blocks.'



> Bach, as well as thinking contrapuntally, also *had to think harmonically* and not just in a "very general sense", but rather from beat to beat, phrase to phrase, cadence to cadence and as a consideration for defining form.


There's a flip side to that coin. If, as you say, harmonic thinking is _required_ in order to write music, then it was in an *undefined, vague form which no one can explain.* How did the Baroque "classify chords" if they did not recognize the idea of chords?

That's why I contend that Bach thought more predominantly linearly (because this was counterpoint). Otherwise, he would deliberately have used M7 chords. In fact, Bach did not think "in chords" nor did he recognize chord inversions.



> The best way to gain a deep understanding of the synergy between harmonic and contrapuntal thought is to learn to write counterpoint in Bach's style, it then becomes clear that one needs the other in more than a superficial or general way.


Harmonic thinking did not exist in Bach's time, *so no one has explained exactly how he thought about harmonic root movement or harmonic "progressions."* 
That is, unless he was "cheating" and thinking harmonically anyway. But how? Bach did not recognize "chord function" or "chord inversion."

If this is true, *Bach was WRONG in rejecting Rameau's theories of chord inversion.
*


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## millionrainbows

BabyGiraffe said:


> Music has nothing to do with morality and feelings!!! You can associate certain sounds with some kind of cultural norms, it doesn't mean anything.


That's wrong; it can be. As early as Gregorian chant, certain phrases represented Christ's ascension, crucifixion, etc.

The writers actually felt as if this had supernatural consequences. Who knows, maybe Messiaen still thought this in the 20th century. And it might be true, for all you know. But you're a total rationalist.


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## Woodduck

mikeh375 said:


> It's much more nuanced than that. It's fair to say that Bach did frequently let the line override the vertical, resulting in a particular harmonic spice that gives his work immense emotional power, but one can't write counterpoint in his style without harmonic thought and consideration - it's just not possible, the two trains of thought are the two sides of a single coin.
> 
> Part of Bach's genius was to expand the reach of the emotional potential in momentary dissonance imv. He did this by allowing the linear to follow it's own logic seemingly unimpeded at times, giving rise to clashes that as a result, seem inevitable but also calculated. However, the individual lines are also cogniscent of their vertical obligations and as such are also determined by the vertical.
> 
> Bach, as well as thinking contrapuntally, also _had_ to think harmonically and not just in a "very general sense", but rather from beat to beat, phrase to phrase, cadence to cadence and as a consideration for defining form.
> 
> The best way to gain a deep understanding of the synergy between harmonic and contrapuntal thought is to learn to write counterpoint in Bach's style, it then becomes clear that one needs the other in more than a superficial or general way.


Perfect. This is exactly the response I would have tried to formulate had the burden of the assignment not filled me with weariness and dread.

The idea that because Bach didn't entertain certain analytical notions (and do we know exactly what analytical notions he did entertain?), he didn't "think harmonically," is ridiculous. His harmonic thinking exceeded in complexity and power that of any other composer of his time, and it was precisely what enabled him to give coherence to his contrapuntal thinking, which also exceeded in complexity and power that of any other composer of his time.

"Thinking," in the act of composition, is not academic analysis.


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## isorhythm

millionrainbows said:


> *so no one has explained exactly how he thought about harmonic root movement or harmonic "progressions."*
> [/B]


If you want to get an idea of how he thought, you have to study his music. That's all there is to it.


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## mikeh375

isorhythm said:


> If you want to get an idea of how he thought, you have to study his music. That's all there is to it.


..even better...practise writing it.


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## Luchesi

BabyGiraffe said:


> Music has nothing to do with morality and feelings!!! You can associate certain sounds with some kind of cultural norms, it doesn't mean anything.
> And using stock motives/phrases/whole sequences has little to do with order or balance in composition, more with craftsmanship and commercial productivity + lack of creativity (or else Telemann wouldn't write 3000 compositions). And this remark can be applied to other musical periods and famous composers.


"Music has nothing to do with morality and feelings!!!"

Huh? What would call it if not feelings and lofty ideals?


----------



## Guest

mikeh375 said:


> ..even better...*practise writing it*.


That's right. I actually teach the harmonisation of Bach chorales at undergraduate level and I usually start off following Bach's own teaching method whereby I give my students the soprano and bass parts and ask them to compose the alto and tenor voices. This involves of course contrapuntal writing for those parts but also demands a firm anchoring of the A & S voices to the underlying harmonic structure.


----------



## millionrainbows

isorhythm said:


> If you want to get an idea of how he thought, you have to study his music. That's all there is to it.


Okay, I get it. It's okay to tell a modern harmonic thinker like myself that "major seventh chords on the I (tonic) degree do not really exist in Baroque music because they contain non-harmonic tones," but if this is used to demonstrate that, in this instance "Bach did not think harmonically" it's wrong?

It sounds like to me "non-harmonic tones" are being used as a bludgeon in invalidating the idea of a major seventh chord on the I (tonic) degree, because that's a jazz concept.

Why did the academic thinker who asserted that "chords were not recognized as such in the Baroque" even bring this up, then?

And beyond that, I still see problems with writing or analyzing music without using the idea of chords.

I think these defenders of Bach want it both ways, but they can't explain any of it.


----------



## millionrainbows

TalkingHead said:


> That's right. I actually teach the harmonisation of Bach chorales at undergraduate level and I usually start off following Bach's own teaching method whereby I give my students the soprano and bass parts and ask them to compose the alto and tenor voices. This involves of course contrapuntal writing for those parts but also demands a firm anchoring of the A & S voices to the underlying harmonic structure.


So, you are saying there is an "underlying harmonic structure?" How do you explain it?

_Remember, _these students have the advantage of modern harmonic, or at least later CP thinking.

An underlying harmonic structure sounds suspiciously like a harmonic plan which would indicate root movements and represents "functions" of chords. 
Are you saying that this harmonic planning was assumed, but never articulated?


----------



## 1996D

BabyGiraffe said:


> Music has nothing to do with morality and feelings!!! You can associate certain sounds with some kind of cultural norms, it doesn't mean anything.
> And using stock motives/phrases/whole sequences has little to do with order or balance in composition, more with craftsmanship and commercial productivity + lack of creativity (or else Telemann wouldn't write 3000 compositions). And this remark can be applied to other musical periods and famous composers.


The entire baroque movement had as a goal to glorify the church, who at that time had enormous power. Of course music is tied to morality and feelings, and even deeper in politics, culture, and societal values; it's baffling that you think otherwise.


----------



## millionrainbows

Luchesi said:


> "Music has nothing to do with morality and feelings!!!"
> 
> Huh? What would call it if not feelings and lofty ideals?


That person's being 'objective' in a purely formal sense, Luchesi. Ignore him, he doesn't have your innate European artistic sensibility; that's the typical 'ugly American' way of thinking.

They also reject jazz, the only music created in America which is recognized by Europeans.


----------



## millionrainbows

isorhythm said:


> If you want to get an idea of how he thought, you have to study his music. That's all there is to it.


Oh, a general explanation would suffice. I don't want to work you too hard. Anyway, you know how I love generalities! :lol:


----------



## millionrainbows

Woodduck said:


> The idea that because Bach didn't entertain certain analytical notions (and do we know exactly what analytical notions he did entertain?), he didn't "think harmonically," is ridiculous.


Then why did academics state in this thread, an assumption that the OP's post clearly recognized, that "chords" were not a conception in Baroque compositional practice? This is not after-the fact analysis; this is compositional thinking, and Bach adheres to the norms of 'non-harmonic tones.'



> His harmonic thinking exceeded in complexity and power that of any other composer of his time, and it was precisely what enabled him to give coherence to his contrapuntal thinking, which also exceeded in complexity and power that of any other composer of his time. "Thinking," in the act of composition, is not academic analysis.


Now you are posing contradictory ideas, which you can't explain or describe, "except in writing music" or "analyzing Bach's music" which are inescapably tied to present-day harmonic thinking. Since Bach wasn't a theorist, it can't be analyzed except on its own terms.

It appears that the assertion that "chords were not recognized in Baroque era thinking" is therefore misleading, if not downright incorrect, whether he did or did not in retrospect. So, what's the explanation?

*Ironically,* then, Bach and contrapuntal music in general defers to _strictly-defined voice-leading procedures and linear "non-harmonic tones" in lieu of "harmonic ideas" _like chords and chord inversions. That sounds like a "theory of analysis" to me.

It also raises the question, "why did Bach reject Rameau's ideas?" (see C.P.E. Bach's _The True Art of Keyboard Playing)

_Plus, if theory is "after the fact" analysis of common practices, it seems misleading to separate them to the degree that has been attempted here, if the ideas are derived from the music itself.

I didn't say that ALL "modern style" harmonic thought was excluded; only instances similar to the "I M7" which was used from the beginning as an example of a "non-harmonic tone" instead of being thought of as a chord, or 'chords' like C-Eb-G-Ab (Cmin/Ab maj polychord in Sinfonia 9).

Bach always "defers" to the line, not harmony/chords. In this sense, if he was thinking harmonically, it deferred to counterpoint and was a much more primitive way 'harmonic' using the ear, which I've been an advocate for all along! Thanks for reinforcing my way of "harmonic" thinking.

If, as you say, harmonic thinking is _required_ in order to write music, then it was in an *undefined, vague form which no one can explain.* How did the Baroque "classify chords" if they did not recognize the idea of chords? Harmonic thinking did not exist in Bach's time, *so no one has explained exactly how he thought about harmonic root movement or harmonic "progressions."*


----------



## millionrainbows

1996D said:


> The entire baroque movement had as a goal to glorify the church, who at that time had enormous power. Of course music is tied to morality and feelings, and even deeper in politics, culture, and societal values; it's baffling that you think otherwise.


Yes, music is tied to those things, but BabyGiraffe was being "totally objective and rational" and was speaking of the music "objectively and formally," out of all contexts except its existence as "vibrations", excluding the human/subjective dimension. See my thread "Can Music Be Objectified" or something along those lines. There area many 'rational thinkers' out there.


----------



## 1996D

millionrainbows said:


> Yes, music is tied to those things, but BabyGiraffe was being "totally objective and rational" and was speaking of the music "objectively and formally," out of all contexts except its existence as "vibrations", excluding the human/subjective dimension. See my thread "Can Music Be Objectified" or something along those lines. There area many 'rational thinkers' out there.


It's either cowardice or lack of completeness as a human being.


----------



## isorhythm

Here, start with this:


----------



## Woodduck

millionrainbows said:


> Then why did academics state in this thread, an assumption that the OP's post clearly recognized, that "chords" were not a conception in Baroque compositional practice? This is not after-the fact analysis; this is compositional thinking, and Bach adheres to the norms of 'non-harmonic tones.'


The OP states: "I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. "

The reason he hears chord progressions is that the chord progressions are there to be heard. His intitial assumption is simply wrong.



> Now you are posing contradictory ideas, which you can't explain or describe, "except in writing music" or "analyzing Bach's music" which are inescapably tied to present-day harmonic thinking. Since Bach wasn't a theorist, it can't be analyzed except on its own terms.


Bach's music, on its own terms, is (more or less) contrapuntal with clear harmonic (tonal) organization. There is no contradiction in acknowledging these factors to be interdependent.



> It appears that the assertion that "chords were not recognized in Baroque era thinking" is therefore misleading, if not downright incorrect, whether he did or did not in retrospect.


Yes, it is incorrect, and obviously so. The first prelude in TWTC is a crystal-clear study in chord progression. But for anyone who can hear it, any movement of any of his concertos is too.



> So, what's the explanation?


For what?



> Ironically, then, Bach and contrapuntal music in general defers to _strictly-defined voice-leading procedures and linear "non-harmonic tones" in lieu of "harmonic ideas" _like chords and chord inversions. That sounds like a "theory of analysis" to me.


This formulation confuses theory with practice. We don't speak of procedures as being in lieu of ideas. Bach wasn't composing demonstrations of ideas, except in obvious instances (e.g. the possibilities of canon and fugue). His voice-leading principles didn't contradict principles of harmonic progression.



> It also raises the question, "why did Bach reject Rameau's ideas?" (see C.P.E. Bach's _The True Art of Keyboard Playing)_


_

I don't know enough to answer that. What exactly did Rameau say about harmony that Bach rejected? Whatever it was, it was a theoretical argument. Nothing about Bach's music suggests that "he was not a harmonic thinker."




Bach always "defers" to the line, not harmony/chords.

Click to expand...

Really? As, for instance, when he alters a fugal subject to make it fit a harmonic scheme?




In this sense, if he was thinking harmonically, it deferred to counterpoint and was a much more primitive way 'harmonic' using the ear, which I've been an advocate for all along! Thanks for reinforcing my way of "harmonic" thinking.

Click to expand...

I think we all advocate using the ear. The other one too.




If, as you say, harmonic thinking is required in order to write music, then it was in an undefined, vague form which no one can explain.

Click to expand...

What's vague about Bach's harmony?




How did the Baroque "classify chords" if they did not recognize the idea of chords? Harmonic thinking did not exist in Bach's time, so no one has explained exactly how he thought about harmonic root movement or harmonic "progressions."

Click to expand...

Does anyone know exactly how he thought "about" it? Is that the question? Or is the question whether and how he thought harmonically? You keep mixing up these two questions. It's no wonder this thread is thirteen pages long._


----------



## EdwardBast

millionrainbows said:


> Okay, I get it. It's okay to tell a modern harmonic thinker like myself that "major seventh chords on the I (tonic) degree do not really exist in Baroque music because they contain non-harmonic tones," but if this is used to demonstrate that, in this instance "Bach did not think harmonically" it's wrong?


Bach treated nearly all 7ths as linear dissonances. This doesn't mean he wasn't thinking harmonically. He was thinking of triads with linear dissonances as passing tones, suspensions, and so on. I'm not sure why you find this so difficult to grasp



millionrainbows said:


> Why did the academic thinker who asserted that "chords were not recognized as such in the Baroque" even bring this up, then?


Who said this?



millionrainbows said:


> It also raises the question, "why did Bach reject Rameau's ideas?" (see C.P.E. Bach's The True Art of Keyboard Playing)


You keep claiming this. I challenged you to show any evidence that J.S. Bach rejected Rameau's theories. You haven't.


----------



## millionrainbows

1996D said:


> It's either cowardice or lack of completeness as a human being.


I don't think you should make it personal; you should understand that this is the way BabyGiraffe thinks. He's actually quite knowledgable in the area of tuning, although he's not always clear to laymen.


----------



## millionrainbows

Woodduck said:


> The OP states: "I know the concept of chord progression is not applicable in the period of the Baroque. However, I cannot help but hear certain progressions as I listen to Bach orchestral suites or concertos, or Vivaldi for that matter. "
> 
> The reason he hears chord progressions is that the chord progressions are there to be heard. His intitial assumption is simply wrong.


Not wrong; I see exactly what he means. And your reply, as well as the general consensus, only reinforces what I said as far back as the "Music is Harmonic..." thread. I.E., the ear is the arbiter of what works musically.



> Bach's music, on its own terms, is (more or less) contrapuntal with clear harmonic (tonal) organization. There is no contradiction in acknowledging these factors to be interdependent.


Yes, but here's the rub: it has already been acknowledged that Bach was "thinking harmonically" without the benefit of a codified system of harmony, chord function, or root movement. There is only one possible conclusion: *Bach was doing it by "ear," on the basis of what he was hearing harmonically.* *Bach's "function" was derived by listening. Just as I always said earlier, to the distress of Woodduck and EdwardBast, "function" is a universal harmonic concept of "ear logic" which is based on how intervals sound in relation to I, the tonic/key note
*
https://www.talkclassical.com/blogs/millionrainbows/1174-function-harmonic-model-part.html



> The first prelude in TWTC is a crystal-clear study in chord progression. But for anyone who can hear it, any movement of any of his concertos is too.


You forgot to mention: harmonic theory of "function" was not developed in the Baroque. Bach was determining "function" by ear. Also, he was not writing "chord progressions" _per se;_ he was writing lines.



> This formulation confuses theory with practice. We don't speak of procedures as being in lieu of ideas. Bach wasn't composing demonstrations of ideas, except in obvious instances (e.g. the possibilities of canon and fugue). His voice-leading principles didn't contradict *principles of harmonic progression. *


"Principles of harmonic progression" was an idea not yet articulated. A procedure is a procedure. *Bach's procedures were based on what he heard, not on as-yet unformulated ideas of harmonic progression.*

This whole thread is proving all my earlier ideas about harmonic thinking and using the ear instead of rigid idea-constructs. Thank you, everyone!


----------



## millionrainbows

EdwardBast said:


> Bach treated nearly all 7ths as linear dissonances. This doesn't mean he wasn't thinking harmonically. He was thinking of triads with linear dissonances as passing tones, suspensions, and so on. I'm not sure why you find this so difficult to grasp.


I don't know why you can't see my point, then: Bach was doing it by ear. his linear rules were there, but any harmonic factors not covered by these rules were arrived at by listening. Everyone here has already admitted this fact.


----------



## EdwardBast

millionrainbows said:


> I don't know why you can't see my point, then: Bach was doing it by ear. his linear rules were there, but any harmonic factors not covered by these rules were arrived at by listening. Everyone here has already admitted this fact.


No one has admitted this alleged "fact." You have been asked several times to support your assertion that Bach rejected Rameau's theories. You haven't supported the assertion and you continue to make it. Once again, time to put up or shut up. Why shouldn't anyone reading this thread conclude that you are intentionally pushing misinformation?


----------



## millionrainbows

EdwardBast said:


> No one has admitted this alleged "fact." You have been asked several times to support your assertion that Bach rejected Rameau's theories. You haven't supported the assertion and you continue to make it. Once again, time to put up or shut up. Why shouldn't anyone reading this thread conclude that you are intentionally pushing misinformation?


EdwardBast, you need to understand that I don't want to have to transcribe a bunch of text from a book just for your pleasure. 
"Dance, *****, dance!" (bang bang!)

"Put up or shut up?"
Do some work yourself. Look at the book yourself. You expect ME to do the work YOU should be doing?

I've given the book (which should be in any musician's library).
Even if I did give you all that work, you'd just disagree with it anyway.

I'm not engaged in serious, committed discussion with you (except for cursory replies), because I think your main purpose is to invalidate me, not discuss ideas. In other words, I've already "given up" on you. This applies to anyone else whose main purpose is to invalidate.


----------



## millionrainbows

mikeh375 said:


> It's much more nuanced than that. It's fair to say that Bach did frequently let the line override the vertical, resulting in a particular harmonic spice that gives his work immense emotional power, but *one can't write counterpoint in his style without harmonic thought and consideration* - it's just not possible, the two trains of thought are the two sides of a single coin.
> 
> Part of Bach's genius was to expand the reach of the emotional potential in momentary dissonance imv. He did this by allowing the linear to follow it's own logic seemingly unimpeded at times, giving rise to clashes that as a result, seem inevitable but also calculated. However, *the individual lines are also cogniscent of their vertical obligations and as such are also determined by the vertical.*
> 
> *Bach*, as well as thinking contrapuntally, also *had to think harmonically *and not just in a "very general sense", but rather from beat to beat, phrase to phrase, cadence to cadence and as a consideration for defining form.
> 
> The best way to gain a deep understanding of the synergy between harmonic and contrapuntal thought is to learn to write counterpoint in Bach's style, it then becomes clear that one needs the other in more than a superficial or general way.


@EdwardBast:

As you see here, mike375 is making assertions which hint at what I'm saying, but with no book sources or conceptual backup. It's just "assumed" that Bach was thinking harmonically, maybe on some intuitive level, which remains unexplained by him, or anyone else here.

*I've done better than that, years ago in my blogs. I demonstrated, with plenty of backup info, that much of harmonic thinking, such as the idea of chord function and root relations, is based on the ear.* Here's the blog:

https://www.talkclassical.com/blogs/millionrainbows/1174-function-harmonic-model-part.html


----------



## mikeh375

MR just try writing Bachian counterpoint without an awareness of harmonic function and progression. The concept of writing contrapuntally and harmonically at the same time is clear to any composer who has studied and practised it. The two disciplines are intertwined and feed off each other.

I quote from Oldroyd's Technique and Spirit of Fugue...

_A great hindrance to contrapuntal work is poor harmonic basis. The power to choose chord progressions well - in a word, clear harmonic thinking - is the first essential. Weakness in this respect is too often an unsuspected cause of trouble....
_
That's back-up of something I know anyway as does any composer worth their salt.


----------



## millionrainbows

mikeh375 said:


> MR just try writing Bachian counterpoint without an awareness of harmonic function and progression. The concept of writing contrapuntally and harmonically at the same time is clear to any composer who has studied and practised it. The two disciplines are intertwined and feed off each other.
> 
> I quote from Oldroyd's Technique and Spirit of Fugue...
> 
> _A great hindrance to contrapuntal work is poor harmonic basis. The power to choose chord progressions well - in a word, clear harmonic thinking - is the first essential. Weakness in this respect is too often an unsuspected cause of trouble....
> _
> That's back-up of something I know anyway as does any composer worth their salt.


Oh, I completely agree with this. 
The aspect of this which I disagree with is the characterization of "composing by ear" as _"harmonic thinking,"_ which is misleading and not explicit enough. *Not so much the term itself, but the way it is being used.*
What is called "harmonic thinking" is just "using your ear" to hear the "harmonic truth." 
It has less to do with harmonic rules or regulations. It is derived from the act of hearing, not rules.
https://www.talkclassical.com/blogs/millionrainbows/1174-function-harmonic-model-part.html


----------



## Bwv 1080

What MR has pointed out through a number of sources here, is that the CP harmony is contained within the rules for part-writing and figured bass, with the chord nomenclature a later codification began by Rameau and not fully accepted until the later 18th century. Bach thought in figured bass, not roman numerals (which according to Wiki, began in 1774 with the work of JS Bach's student Johann Kirnberger's Die Kunst des reinen Satzes (wonder if there are any references to him in the work?). But, figured bass is a system for representing chords and harmony, not counterpoint, which began in the early 17th century


----------



## mikeh375

MR, when writing counterpoint, considerations of spacing are present. Spacing is a vertical dimension and has a considerable influence on how a part might proceed and what its possible subordinate role is to be at a particular vertical point. That is harmonic thinking whilst thinking in a linear fashion. 
I give you a page from Cherubini, admittedly just after Bach..._from his Treatise on Counterpoint and Fugue. _. Perhaps not the sort of thing you'd expect.


----------



## millionrainbows

Bwv 1080 said:


> What MR has pointed out through a number of sources here, is that the CP harmony is contained within the rules for part-writing and figured bass, with the chord nomenclature a later codification began by Rameau and not fully accepted until the later 18th century. Bach thought in figured bass, not roman numerals (which according to Wiki, began in 1774 with the work of JS Bach's student Johann Kirnberger's Die Kunst des reinen Satzes (wonder if there are any references to him in the work?). But, figured bass is a system for representing chords and harmony, not counterpoint, which began in the early 17th century


What I'd _rather_ point out is that "harmonic thinking" is possible without any rules; it operates more on the level of the ear, as a directly perceived "logic" of the senses.

Yes, figured bass is a system for representing chords and harmony, but only in relation to a bass note. It does not specify function _per se,_ which had not been invented.


----------



## isorhythm

millionrainbows said:


> What I'd _rather_ point out is that "harmonic thinking" is possible without any rules; it operates more on the level of the ear, asa directly perceived "logic" of the senses.
> 
> Yes, figured bass is a system for representing chords and harmony, but only in relation to a bass note. It does not specify function _per se,_ which had not been invented.


This is so vague I'm not sure exactly what you mean. All composers are guided by their ears, as well as by established practice.

You attach enormous, unwarranted importance to systems of nomenclature. Whether you use Roman numerals or figured bass notation to describe a chord, it's the same chord. Composers (of all eras) thought in terms of music, not symbols.

I don't know what Bach said about Rameau, but it wouldn't surprise me if he didn't like the idea that inversions of a triad are equivalent. They sound different and they're not interchangeable.


----------



## millionrainbows

isorhythm said:


> This is so vague I'm not sure exactly what you mean. All composers are guided by their ears, as well as by established practice.


What I'm saying is that "harmonic truths" such as "function" of roots and chords exists without any codification or established practices. It is a universal truth, one of the underlying principles of music.



> You attach enormous, unwarranted importance to systems of nomenclature. Whether you use Roman numerals or figured bass notation to describe a chord, it's the same chord. Composers (of all eras) thought in terms of music, not symbols.


To that extent, I agree. What I see missing is the acknowledgement that "harmonic hearing" is the underlying basis of all "systems," nomenclatures, and "practices" or rules. That's why I attach enormous, unwarranted importance to systems of nomenclature; because they are not truths unto themselves. They derive from more basic vertical "ear" perception.



> I don't know what Bach said about Rameau, but it wouldn't surprise me if he didn't like the idea that inversions of a triad are equivalent. They sound different and they're not interchangeable.


Not literally, but a G major chord has a root, in relation to a tonic, which gives it a function or importance which is determined harmonically, as an interval. 
Since Bach did not acknowledge this, or the fact that "a G is a G is a G," means that he was avoiding abstract thinking. If he did not recognize these equivalencies, he was being too specific and too literal.


----------



## millionrainbows

EdwardBast said:


> No one has admitted this alleged "fact." You have been asked several times to support your assertion that Bach rejected Rameau's theories. You haven't supported the assertion and you continue to make it. Once again, time to put up or shut up. Why shouldn't anyone reading this thread conclude that you are intentionally pushing misinformation?


From _Essay On The True Art Of Keyboard Playing _by C.P.E. Bach.

_Pg. 17: Bach and his father were acquainted with Rameau's theory, which has become the basis of most of the writings on harmony, but they disagreed with it. This was made known in a letter to Kirnberger...

...Bach's rejection of Rameau can be traced largely to the fact that the latter had a pronounced theory, whereas thorough-bass was essentially a practice.

Pg. 18: ...Where Rameau's emphasis rests on the vertical origins of a chord, Bach's rests on its behavior._


----------



## isorhythm

millionrainbows said:


> From _Essay On The True Art Of Keyboard Playing _by C.P.E. Bach.
> 
> _Pg. 17: Bach and his father were acquainted with Rameau's theory, which has become the basis of most of the writings on harmony, but they disagreed with it. This was made known in a letter to Kirnberger...
> 
> ...Bach's rejection of Rameau can be traced largely to the fact that the latter had a pronounced theory, whereas thorough-bass was essentially a practice.
> 
> Pg. 18: ...Where Rameau's emphasis rests on the vertical origins of a chord, Bach's rests on its behavior._


This sounds like it's from a modern introduction or annotation, not CPE Bach's own words, right?


----------



## EdwardBast

millionrainbows said:


> From _Essay On The True Art Of Keyboard Playing _by C.P.E. Bach.
> 
> _Pg. 17: Bach and his father were acquainted with Rameau's theory, which has become the basis of most of the writings on harmony, but they disagreed with it. This was made known in a letter to Kirnberger...
> 
> ...Bach's rejection of Rameau can be traced largely to the fact that the latter had a pronounced theory, whereas thorough-bass was essentially a practice.
> 
> Pg. 18: ...Where Rameau's emphasis rests on the vertical origins of a chord, Bach's rests on its behavior._


Clearly the above doesn't quote Bach nor does it establish "rejection" on his part. As I've noted before, figured bass is a system of notation, not a theory of harmony. Now I will refute your entire argument in this thread:

Throughout this thread and elsewhere you've been arguing a binary opposition of contrapuntal versus harmonic thinking, putting forth Bach as a quintessential example of a contrapuntal thinker. You've argued that he wasn't a harmonic thinker. This view has been rejected by me and every other respondent on this thread with formal theoretical training, all of whom know that these two ways of looking at music have never existed in isolation and cannot be disentangled. Unfortunately for your position, this polar opposition of counterpoint/voice-leading versus chordal/harmonic thought was not accepted even in the Renaissance, at the very height and dominance of contrapuntal art, by the authors of counterpoint treatises.

Gioseffo Zarlino's _Le Istitutione harmoniche_ (1558) is one of the most influential theoretical treatises of all time. It codified the compositional practice of the early 16thc as practiced by Adrian Willaert, Josquin, Gombert, Lassus, et alia. The third part of the treatise, _The Art of Counterpart_,* addresses the harmonic elements of music in considerable detail. Zarlino emphasizes the supremacy of what we would call the triad in organizing music's vertical dimension. In a section on three and four voice counterpoint he states:

"Variety of extremes … is found only in the fifth and third. Since harmony is a unity of diverse elements, we must strive with all our might, in order to achieve perfection in harmony, to have these two consonances or their compounds sound in our compositions as much as possible. … musicians often write the sixth in place of the fifth, and this is fine."

So, in our terms, Zarlino is advocating the triad in root position or first inversion as the ideal vertical arrangement of harmonies to be favored over all others. He notes that in three part writing the fifth or third can be left out if using the octave results in a …

"… beautiful, elegant, and simple voice line. … However, in four-voice works, the error of omitting one of the two consonances would be greater because the extra part facilitates obedience to the rule."

The above shows that the best theorists and composers of counterpoint in the Renaissance thought extensively about harmony and advocated exactly the same supremacy of the triad as practiced throughout the Baroque era, in the work of J. S. Bach and beyond. What the Baroque composers added that brought to their music a modern conception of harmonic progression and tonal grounding was making root motion by fifths (or fourths) the ideal and the centerpiece of the style.

In short, your theory is refuted by the theoretical thought and compositional practice of centuries. Hundreds of years before Bach, even the most contrapuntal composers and theorists were thinking harmonically.

*I've quoted from page 188 of _The Art of Counterpoint_ as translated by Guy Marco and Claude Palisca (Norton, 1968).


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## millionrainbows

EdwardBast said:


> Clearly the above doesn't quote Bach nor does it establish "rejection" on his part. Now I will refute your entire argument in this thread:


See? I told you this would be your reaction.


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## isorhythm

As usual you will do anything to avoid talking about actual music - just words and more words.


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## Guest

Here's an example of quite straightforward two and three-part contrapuntal writing where the underlying chord progressions are crystal clear:


----------



## isorhythm

Just remembered an ideal illustration of what we're talking about, starting at 6:30 in the video below. Unfortunately a mis-timed ad comes in a couple seconds into the movement, at least for me - click past it and keep going.






The violin and keyboard right hand in this movement are playing a strict canon, while the keyboard left hand is outlining the chords. A perfect marriage of counterpoint and harmony. This kind of thing is why people think Bach was such a genius!


----------



## Guest

isorhythm said:


> Just remembered an ideal illustration of what we're talking about, starting at 6:30 in the video below. Unfortunately a mis-timed ad comes in a couple seconds into the movement, at least for me - click past it and keep going.
> 
> 
> 
> 
> 
> The violin and keyboard right hand in this movement are playing a strict canon, while the keyboard left hand is outlining the chords. A perfect marriage of counterpoint and harmony. This kind of thing is why people think Bach was such a genius!


Nice. The 'cello part is not exactly the same as the left hand part in the scrolling score but very well played.


----------



## millionrainbows

EdwardBast said:


> Gioseffo Zarlino's _Le Istitutione harmoniche_ (1558) is one of the most influential theoretical treatises of all time. It codified the compositional practice of the early 16thc as practiced by Adrian Willaert, Josquin, Gombert, Lassus, et alia. The third part of the treatise, _The Art of Counterpart_,* addresses the harmonic elements of music in considerable detail. Zarlino emphasizes the supremacy of what we would call the triad in organizing music's vertical dimension. In a section on three and four voice counterpoint he states:
> 
> "Variety of extremes … is found only in the fifth and third. Since harmony is a unity of diverse elements, we must strive with all our might, in order to achieve perfection in harmony, to have these two consonances or their compounds sound in our compositions as much as possible. … musicians often write the sixth in place of the fifth, and this is fine."


This is just talking about figured bass. Yes, figured bass is a system for representing chords and harmony, *but only in relation to a bass note.* It does not specify function _per se, _which had not been invented. So this is not truly "harmonic thinking" as we now know it.

"Harmonic thinking" is possible without any rules; it operates more on the level of the ear, as a directly perceived "logic" of the senses.

Yes, Bach was thinking harmonically" but *without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.
*
*This proves my blog assertion: "function" is a characteristic which is inherent in the scale itself, as an interval in relation to a keynote or tonic.
*
In a scale, the pull towards a tonic is inherently determined by vertical harmonic factors, not horizontal "emphasis" by repetition or accent. That comes later.

This chart has been posted already.

1. minor seventh (C-Bb) 9:16
2. major seventh (C-B) 8:15
3. major second (C-D) 8:9
4. minor sixth (C-Ab) 5:8
5. minor third (C-Eb) 5:6
6. major third (C-E) 4:5
7. major sixth (C-A) 3:5
8. perfect fourth (C-F) 3:4
9. perfect fifth (C-G) 2:3
10. octave (C-C') 1:2
11. unison (C-C) 1:1

So a C major scale's horizontal functions correspond to these harmonic relations; and one can observe how these functions were derived:

I - 1:1
ii - 8:9
iii - 4:5
IV - 3:4
V - 2:3
vi - 3:5
vii - 8:15

Their importance in establishing the tonality can be ranked by the order of consonance to dissonance, with smaller-number ratios being more consonant.

I - 1:1
V - 2:3
IV - 3:4
vi - 3:5
iii - 4:5
ii - 8:9
vii - 8:15

*Using this model, a "function" hierarchy can be applied to any scale, after the degrees of dissonance are ranked.

Whole Tone scale: C-D-D-F#-G#-A#
*
C - 1:1
D -8:9
E -4:5
F#- 45:32
G# - 8:5
A# - 16:9

Whether or not you attach Roman numerals to the above is optional; but by the numbers, one can see a ranking:

C - 1:1
E -4:5
G# - 8:5
D -8:9
A# - 16:9
F#- 45:32


----------



## millionrainbows

Bwv 1080 said:


> What MR has pointed out through a number of sources here, is that the CP harmony is contained within the rules for part-writing and figured bass, with the chord nomenclature a later codification began by Rameau and not fully accepted until the later 18th century. Bach thought in figured bass, not roman numerals (which according to Wiki, began in 1774 with the work of JS Bach's student Johann Kirnberger's Die Kunst des reinen Satzes (wonder if there are any references to him in the work?). But, *figured bass is a system for representing chords and harmony,* not counterpoint, which began in the early 17th century


Figured bass represents upper voicings against a bass note, not against a root note or a key note. In this sense, it is not harmonic as we know the term.
*Figured bass classifies voicings, not chords.

*Figured bass classifies chord voicings by groups: all seventh chord voicings, all 6/4 voicings, etc.

It does not distinguish or group "all C chords" because there is no reference to a root or the key. Roman numerals were used only later in figured bass.

Bach's system did not recognize chord inversions as being the same chord. It did not recognize chord function, or use chord progressions.

*So "where's the beef?"*


----------



## EdwardBast

millionrainbows said:


> This is just talking about figured bass. Yes, figured bass is a system for representing chords and harmony, *but only in relation to a bass note. It does not specify function **per se, which had not been invented. So this is not truly "harmonic thinking" as we now know it.*


*

You are repeating the same mistakes with which you began in this thread, over, and over, and over again. Bach's use of figured bass has nothing to do with his functional understanding of harmony. It was just a system of notation. Bach was not trying to represent function.



millionrainbows said:



"Harmonic thinking" is possible without any rules; it operates more on the level of the ear, as a directly perceived "logic" of the senses.

Click to expand...

But there were rules to harmonic thinking. As I demonstrated, they were set down in famous treatises on harmony and counterpoint generations before figured bass existed. Everyone including Bach knew them. The only one who doesn't know them is you, because you haven't made an effort to study the theory of classical music and its history.



millionrainbows said:



Yes, Bach was thinking harmonically" but without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.


Click to expand...

This is an unsupported and incorrect assertion. Of course Bach understood the chords he was using in a functional sense. It's obvious to anyone who has studied his music and learned to write progressions in his style - oh wait, you haven't done that so of course you don't understand this.

Oh, as a footnote, I love how whenever your assertions have been disproved you throw in the same irrelevant charts about intervals and scales, regardless of how little it has to do with the subject under discussion. No one is distracted or impressed by this attempt to appear learned.*


----------



## millionrainbows

EdwardBast said:


> You are repeating the same mistakes with which you began this thread, over, and over, and over again. Bach's use of figured bass has nothing to do with *his functional understanding of harmony*. It was just a system of notation. Bach was not trying to represent function.


Then it is not a "mistake" to say over, and over, and over again that Bach's figured bass system is not harmonic, and does not represent function or key.



> But there _were_ rules to harmonic thinking. As I demonstrated, they were set down in famous treatises on harmony and counterpoint generations before figured bass existed. Everyone including Bach knew them. *The only one who doesn't know them is you*, because you haven't made an effort to study the theory of classical music and its history.





> *Of course Bach understood the chords he was using in a functional sense. *


*
I agree. *Bach was thinking harmonically" but without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.



> It's obvious to anyone who has studied his music and learned to write progressions in his style


_Yes, I agree. Bach was thinking harmonically" but _*without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.
*


> It's obvious to anyone who has studied his music and learned to write progressions in his style.


Yes, it's obvious, but no one here has attempted to explain how this was done except me.

I question whether the notion of "functionality" should be the exclusive domain of CP tonality.

The underlying principle of function in CP tonality is an hierarchy derived from harmonic factors of dissonance, in relation to a root chord, now known as "I."

Thus, the others followed, and were named: ii, iii, IV, V, vi, and viiº. It simply makes the harmonic factors into horizontal functions.



> Oh, as a footnote, I love how whenever your assertions have been disproved you throw in the same irrelevant charts about intervals and scales, regardless of how little it has to do with the subject under discussion. No one is distracted or impressed by this attempt to appear learned.


Footnote duly noted.


----------



## millionrainbows

EdwardBast said:


> But there _were_ rules to harmonic thinking. As I demonstrated, they were set down in famous treatises on harmony and counterpoint generations before figured bass existed. Everyone including Bach knew them.


What you posted earlier as your "historical evidence" did not go into function or chord progression; it only talked about general harmonic principles like "triads."


----------



## EdwardBast

millionrainbows said:


> Then it is not a "mistake" to say over, and over, and over again that Bach's figured bass system is not harmonic, and does not represent function or key.
> 
> *
> I agree. *Bach was thinking harmonically" but without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.
> 
> It's obvious to anyone who has studied his music and learned to write progressions in his style
> 
> _Yes, I agree. Bach was thinking harmonically" but _*without any specified rules or principles such as "chord function" and "chord progression." He was doing this intuitively, by ear.
> *
> 
> Yes, it's obvious, but no one here has attempted to explain how this was done except me.
> 
> I question whether the notion of "functionality" should be the exclusive domain of CP tonality.
> 
> The underlying principle of function in CP tonality is an hierarchy derived from harmonic factors of dissonance, in relation to a root chord, now known as "I."
> 
> Thus, the others followed, and were named: ii, iii, IV, V, vi, and viiº. It simply makes the harmonic factors into horizontal functions.
> 
> Footnote duly noted.


Clearly your strategy is to just continue repeating errors and confirming your lack of comprehension of the theory and history of music until people get tired of correcting you.


----------



## millionrainbows

EdwardBast said:


> Clearly your strategy is to just continue repeating errors and confirming your lack of comprehension of the theory and history of music until people get tired of correcting you.


Nobody else has presented any explanation of how Bach used "function" when, at the time, it hadn't been codified yet.

It's not an "error" to present information in the form of charts and intervals which clearly show how this was done, by ear, based on degrees of consonance and dissonance in relation to a key note.

The fact is, *you have failed* in offering an explanation of chord function which is based on anything other than principles of hearing, which were later codified into prescribed functions.

Tonal music is harmonic; music is vertical. It is based on vertical, harmonic factors which are instantaneous, *based on hearing* degrees of consonance/dissonance to a key or tonic note.

Melodies in counterpoint have a harmonic basis; they suggest triads, and can outline triads. Bach's unaccompanied violin sonatas show that he was thinking harmonically. *But no one has offered an explanation of how this is possible, except me.*

*It is done by ear,* using intervals and their degrees of dissonance to a key note, and their other suggestions of triads.

The intervals have a dissonant/consonant quality determined by their ratio, all in relation to a "keynote" or unity of 1; our ears/brain experience this as an instantaneous visceral sensation.

The intervals have a scale degree and place in relation to "1" or the Tonic, and triads can be constructed on these steps/notes. The chords thus constructed can then be given a "function" which is modeled after this harmonic relation to the keynote. Function is dependent on forward progression in time, and context, and both rely on memory.

This harmonic model is where all "linear function" originates, and is still manifest as ratios (intervals) which were derived from physical harmonic phenomena, which existed first.


----------



## isorhythm

Got it - you absolutely refuse to do the one thing that could help you, study Bach's music. Nothing more to be said.


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## BabyGiraffe

Riemannian functional harmony is derived from heptatonic model of music, tuned to meantone (while heptatonic 5-limit music can be tuned to other temperaments where other chord progressions, not possible in meantone without enharmonics, can be realized). And it's not even capable of explaining like 1/5 of the progressions in romantic and modern period (which on top of that require enharmonic modulations in meantone (that's one of the main motivations of Neo-riemannian theory - to explain chromatic harmony in 12 equal.))

Imo, figured bass as an idea is more useful model for pure intonation music - over a bass note you can build a major or minor chord, or any of its inversions, and harmonize to your musical taste.

I doubt Bach was understanding his music in "functional sense" - this makes no sense, considering when this theory was invented and popularized, but certainly there are chromatic passages where he was using his "well-temperament tuning" in chromatic (12-tone fashion), not heptatonically.

Even, if this is slightly off-topic, since Million likes scale models, let's do one - 
Regardless of tuning, here is quantization of some of the most useful for harmony and melody 5-limit limit ratios, reduced to heptatonic model:

I. 1/1 -unison, 25/24 - chromatic semitone (this means that this semitone is tempered in 7 equal and, in accurate systems, you use it for modulation to other keys; obviously, diatonic and chromatic semitones are equated in 12 equal, potentially giving us the option to play confusing for the listeners tonicizations, not knowing, if you modulated or not)
II 16/15 - diatonic semitone (inverse of 15th octave reduced harmonic), 10/9 - minor whole tone, 9/8 - major whole tone (octave reduced 9th harmonic)
III 6/5 - minor third, 5/4 - major third (octave reduced 5th harmonic)
IV 32/25 - diminished fourth (inverse of 25th harmonic), 4/3 (inverse 3rd harmonic, reduced to octave), 25/18 (augmented fourth).
And that's it - you can get fifth, sixth and seventh degrees by inverting these modulo octave.

So, we get a heptatonic scale with variable scale degrees that can be useful for creation of most ethnic and non-ethnic modes in 12 equal (useful technique is using these as melodic tetrachordal blocks, giving us Arabic/Hindu/Greek take on scale construction, obviously playing alterations of the same scale degrees can sound potentially bad ).
Tempering 81/80 gives us a regular temperament and the ability to play meantone progressions (like the infamous in jazz 2-5-1 chains)... 



Here is the interesting part - we can quantize pure ratios to different (and they are not unique and there may be several such options for creation of abstract temperaments - check 17 equal for example, 17 tone scale can be mapped in several ways to 5-limit) pentatonic, hexatonic, octatonic, nonatonic etc hierarchies (think of black keys pentatonic, found in Eastern and African music; or some of the synthetic scales, used by Scriabin, Liszt, Stravinsky etc), giving us different perspectives on the usage of abstract temperaments/scales. For example here is a pentatonic one - 
I 1/1, 16/15 (diatonic semitone is a chroma!)
II 25/24, 10/9, 9/8, 6/5, 32/25 (!!!)
III 5/4, 4/3, 36/25 (!!!)
It doesn't look as pretty, giving options for improper and monotonically not ascending scales, but let's for examples check the intervals in the black keys pentatonic.


II 3 x 200.00000 cents
II 2 x 300.00000 cents

III 1 x 400.00000 cents
III 4 x 500.00000 cents

IV 4 x 700.00000 cents
IV 1 x 800.00000 cents

V 2 900.00000 cents
V 3 1000.00000 cents
Number of different intervals: 8 = 2.00000 / class

All this theory is backed by serious math (mainly linear and exterior algebra). (And can be useful for composing music/translating existing in/between different temperaments + just intonation)


----------



## Torkelburger

It only takes one or two times to play or compose something by ear before you start to understand how it functions though. You don’t compose over four decades by ear. Most of the time, each thing you figure out, you figure out once. I mean, once you sat down and figured out C, E, and G go together and sounds good to the ear, you don’t need to figure it out again a second time. The same goes for a chord progression. You start to learn how they function. Also, you don’t live in a cave on Mars with your fingers in your ears. You hear and play and read other pieces by Vivaldi or whoever and see and discover how chords function. So even giving you the benefit of the doubt, no one of Bach’s genius would compose by ear for very long, certainly not almost 5 decades.


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## Woodduck

In the absence of musical examples and statements from the composer, it's tiresome to be told over and over what Bach did and didn't know and think while composing.

We start out being told that "Bach was not a harmonic thinker." Now we're told that "Bach's unaccompanied violin sonatas show that he was thinking harmonically," but that *"no one has offered an explanation of how this is possible, except me."* [emphasis in the original] Moreover, "Nobody else has presented any explanation of how Bach used 'function' when, at the time, it hadn't been codified yet."

I haven't seen any such explanation of Bach's ability to think harmonically. I _do_ see what appears to be an assumption that there's something extraordinary about using compositional procedures that haven't been codified by theorists. That is a strange assumption, given that music theory is mainly just a way of thinking about the structure of existing music.

It was possible for Bach to "think harmonically" for the same reason it's possible for you, me, or anyone else to "think harmonically." Thinking in harmony is not an advanced compositional skill; knowledge of music theory is not required. All that's required is knowledge of music. I wrote an interesting and quite harmonically coherent little chromatic fugue at the age of 16 when I didn't know tonic from iced tea and had only things like Bach's organ works, Wagner's preludes, and years of singing hymns in church to guide my sense of where the harmony should go. There were a couple of instances of inelegant voice leading which a bit of theory knowledge would have had me on the lookout for, but in general I count it no disadvantage that I was enencumbered by such arcane concepts as inversional chord equivalence or hierarchies of dissonance. Whether or not Bach entertained these or other specific concepts, I'm sure that if a dilettante like me didn't need them to write convincing harmony, he didn't either.


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## millionrainbows

Use your logic, please.

The concept of "chord function" cannot exist without knowing the root of a chord as related to a key or tonic note. 
Bach was not interesting in identifying by analysis or in his figured-bass notation any chords _except by the voicings above a bass note,_ and this does not identify roots of chords.

So he had to be doing it by ear. That's what I've been saying all along. That's not a form of "harmonic thinking" that is touted in the counterpoint textbooks. That's "using your ear" (both of them). That's "harmonic hearing."

In this way, Bach MUST have been hearing root relations to a key note, in order to hear any sort of "function" which he might have heard. It's inescapable.

*This means my harmonic model (and all those charts I posted) are correct, because it is based on the perception of intervals, and not on codified theory.

*No one else has offered any explanation except ME.


----------



## millionrainbows

Woodduck said:


> It was possible for Bach to "think harmonically" for the same reason it's possible for you, me, or anyone else to "think harmonically." Thinking in harmony is not an advanced compositional skill; knowledge of music theory is not required. All that's required is knowledge of music. I wrote an interesting and quite harmonically coherent little chromatic fugue at the age of 16 when I didn't know tonic from iced tea and had only things like Bach's organ works, Wagner's preludes, and years of singing hymns in church to guide my sense of where the harmony should go. There were a couple of instances of inelegant voice leading which a bit of theory knowledge would have had me on the lookout for, but in general I count it no disadvantage that I was enencumbered by such arcane concepts as inversional chord equivalence or hierarchies of dissonance. Whether or not Bach entertained these or other specific concepts, I'm sure that if a dilettante like me didn't need them to write convincing harmony, he didn't either.


I agree with this. However, I DO think I've demonstrated how it was done, by ear, in the perception of intervals, i.e. scale degrees against a tonic note, as shown in the charts I posted.


----------



## Woodduck

millionrainbows said:


> I agree with this. However, I DO think I've demonstrated how it was done, by ear, in the perception of intervals, i.e. scale degrees against a tonic note, as shown in the charts I posted.


I don't see that a charting of intervals explains HOW anyone composes music, any more than identifying parts of speech explains HOW humans think coherently. Why do you think it does? You seem to be positing some powerful psychological forces at work that operate innately, regardless of the existing musical culture. Would Bach's "ear" have been guided to the same procedures if he'd not been the heir of Fux, Pachelbel and Buxtehude?


----------



## millionrainbows

Woodduck said:


> I don't see that a charting of intervals explains HOW anyone composes music, any more than identifying parts of speech explains HOW humans think coherently. Why do you think it does? You seem to be positing some powerful psychological forces at work that operate innately, regardless of the existing musical culture.


The chart of intervals and their consonance/dissonance ratios are representations of the way we hear. It's not ideas or psychology, it's the truth of sound itself as it hits our ears. It's called "music."



> Would Bach's "ear" have been guided to the same procedures if he'd not been the heir of Fux, Pachelbel and Buxtehude?


Bach's "ear" was his own, and that of a superior musical intelligence. This ability to hear music is innate in people, some more than others. Good musicians seem to have it.

Also, certain theoretical approaches recognize that if something sounds the same, or makes sense to the ear, theory & nomenclature are meaningless. This way of thinking favors the ear above all else.

I - 1:1
ii - 8:9
iii - 4:5
IV - 3:4
V - 2:3
vi - 3:5
vii - 8:15


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## Woodduck

Sorry, but that reads like a medieval text on alchemy. Are you saying that the perception of degrees of dissonance between the notes of a scale and a tonic note is a sufficient guide to the procedures of common practice harmony and "explains" how Bach knew how to write a cadence with a Neopolitan sixth in it?


----------



## mikeh375

millionrainbows said:


> Use your logic, please.
> 
> The concept of "chord function" cannot exist without knowing the root of a chord as related to a key or tonic note.
> Bach was not interesting in identifying by analysis or in his figured-bass notation any chords _except by the voicings above a bass note,_ and this does not identify roots of chords.
> 
> So he had to be doing it by ear. That's what I've been saying all along. That's not a form of "harmonic thinking" that is touted in the counterpoint textbooks. That's "using your ear" (both of them). That's "harmonic hearing."
> 
> In this way, Bach MUST have been hearing root relations to a key note, in order to hear any sort of "function" which he might have heard. It's inescapable.
> 
> *This means my harmonic model (and all those charts I posted) are correct, because it is based on the perception of intervals, and not on codified theory.
> 
> *No one else has offered any explanation except ME.


The ideas you express seem too black and white imv MR and miss the intimate relationship between counterpoint and harmony.
Does this shed any light?.....

View attachment oldroyd.tiff.pdf


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## millionrainbows

Woodduck said:


> Sorry, but that reads like a medieval text on alchemy. Are you saying that the perception of degrees of dissonance between the notes of a scale and a tonic note is a sufficient guide to the procedures of common practice harmony and "explains" how Bach knew how to write a cadence with a Neopolitan sixth in it?


No one else has "explained" how Bach used harmonic function. You haven't. All you can do is invalidate other ideas. Why don't you do some work on this? You can't just narcissistically expect everyone to agree with your self-serving "rationality."

There may be some stylistic non-essential procedures like "a cadence with a Neopolitan sixth" which were followed, but, yes, *I'm saying that the more basic perception of degrees of dissonance between the notes of a scale and a tonic note is done by ear, and the consonance/dissonance corresponds.

Here it is again.
*
What is the most closely-related chord to I? V, and so on. The correspondences follow with each chord function:

So a C major scale's horizontal functions correspond to these harmonic relations; and one can observe how these functions were derived:

I - 1:1
ii - 8:9
iii - 4:5
IV - 3:4
V - 2:3
vi - 3:5
vii - 8:15

*Their importance in establishing the tonality is ranked by the order of consonance to dissonance, with smaller-number ratios being more consonant.

I - 1:1
V - 2:3
IV - 3:4
vi - 3:5
iii - 4:5
ii - 8:9
vii - 8:15*

Using this model, a "function" hierarchy can be applied to any scale, after the degrees of dissonance are ranked.

Furthermore, I'm asserting that "chord function" is not exclusive to CP harmony, but is an innate feature of any scale which can be used in a tonality.


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## BabyGiraffe

15/8 has higher complexity than 9/5, if you after consonant seventh degree. (And we get mixolydian mode, plus 9/5 is is close to seventh harmonic).And your given scale has wolf intervals, so some normal chords are ugly and modulate enharmonically, if you attempt typical progressions.
IF you actually read some of the functional harmony theorists, you will understand why major and minor are the structurally important ones, but it's not because of highest degree of consonance for sure...


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## millionrainbows

BabyGiraffe said:


> 15/8 has higher complexity than 9/5, if you after consonant seventh degree. (And we get mixolydian mode, plus 9/5 is is close to seventh harmonic).And your given scale has wolf intervals, so some normal chords are ugly and modulate enharmonically, if you attempt typical progressions.
> IF you actually read some of the functional harmony theorists, you will understand why major and minor are the structurally important ones, but it's not because of highest degree of consonance for sure...


That's weird...I thought that you, of all people, would believe in the primacy of the ear. I'm disappointed in you, Baby.


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## BabyGiraffe

millionrainbows said:


> That's weird...I thought that you, of all people, would believe in the primacy of the ear. I'm disappointed in you, Baby.


Check this graph.


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## millionrainbows

BabyGiraffe said:


> Check this graph.
> 
> View attachment 136016


The octave is still king, and look how close 3/2 and 4/3 are, the "triumvirate" of Western tonality.

This also corresponds to how closely related an interval (or root) is to "1" or tonic, as "functions."


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## mikeh375

errr...where's the music? Where's Papa gone?


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## EdwardBast

millionrainbows said:


> Furthermore, I'm asserting that "chord function" is not exclusive to CP harmony, but is an innate feature of any scale which can be used in a tonality.


"Chord function … is an innate feature of any scale which can be used in tonality?" This is meaningless. Chord function is not a feature of scales. The statement makes no sense whatever. Try again.


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## Woodduck

millionrainbows said:


> No one else has "explained" how Bach used harmonic function. You haven't. All you can do is invalidate other ideas. Why don't you do some work on this? You can't just narcissistically expect everyone to agree with your self-serving "rationality."


Jiminy Crickets! Narcissistically? Back to labeling and name-calling (and now I have confirmation that your use of that term yesterday was aimed at me, even though you denied it). Ho hum...

You're projecting mightily. I don't expect _everyone _to agree with _anything_, but apparently you do expect that, else you wouldn't repeat yourself over and over in _exactly_ the same words, hoping that everyone who might consider questioning you will either adopt them as a mantra, be stuck with an earworm, or just give up from brain fatigue.

Sorry, bubba, but what I'm really tryin' ta do is figger out what in the Sam Hill you're talkin' 'bout with this here "composition by ear" thang.



> There may be some stylistic non-essential procedures like "a cadence with a Neopolitan sixth" which were followed, but, yes, *I'm saying that the more basic perception of degrees of dissonance between the notes of a scale and a tonic note is done by ear, and the consonance/dissonance corresponds. *


If that's all I thought you were saying, I'd have no argument with you (up until "and the consonance/dissonance corresponds"- but hang on...) OF COURSE we can perceive - "by ear" - different degrees of consonance and dissonance among the intervals between a tonic note and the other notes of a scale (though I dare say that most people wouldn't know whether, e.g., a major third or a major sixth is more dissonant). But you appear to be saying much more than that. You appear to be saying that this basic fact of perception "EXPLAINS HOW" Bach - and presumably other people writing harmonic progressions - have arrived at the tonal system we call "common practice" and are able to know, while composing, what chord should follow what. If this is the claim you're making, it's an extraordinaryone, and it strikes me as insufficiently reasoned, as welol as reductive in the extreme. It certainly cries out for concrete demonstration. "The consonance/dissonance corresponds" doesn't _explain_ anything, even if there is actually a meaningful correspondence between something and something else.

Here is what you've said in this thread:

"Harmonic thinking did not exist in Bach's time, so no one has *explained exactly how he thought* about harmonic root movement or harmonic 'progressions.'"

"It has already been acknowledged that Bach was 'thinking harmonically' without the benefit of a codified system of harmony, chord function, or root movement. There is only one possible conclusion: Bach was doing it by 'ear,' on the basis of what he was hearing harmonically. Bach's *'function' was derived by listening."*

"Bach was determining 'function' by ear."

"Bach was doing it by ear. his *linear rules were there, but any harmonic factors not covered by these rules were arrived at by listening.*"

"*What is called 'harmonic thinking' is just 'using your ear' to hear the 'harmonic truth.'*
It has less to do with harmonic rules or regulations. It is derived from the act of hearing, not rules."

"'Harmonic thinking' is possible without any rules; it operates more on the level of the ear, as *a directly perceived 'logic' of the senses."*

"'Harmonic truths' such as *'function' of roots and chords exists without any codification or established practices. It is a universal truth, one of the underlying principles of music."
*
"'Harmonic hearing' is *the underlying basis of all 'systems,' nomenclatures, and 'practices'* or rules."

"*Tonal music *is harmonic; music is vertical. It *is based on vertical, harmonic factors which are instantaneous, based on hearing degrees of consonance/dissonance to a key or tonic note.*"

*"Melodies in counterpoint have a harmonic basis; they suggest triads, and can outline triads.* Bach's unaccompanied violin sonatas show that *he was thinking harmonically*. But no one has offered an explanation of how this is possible, except me. It is done by ear, *using intervals and their degrees of dissonance to a key note, and their other suggestions of triads.* The intervals have *a dissonant/consonant quality determined by their ratio, all in relation to a 'keynote'* or unity of 1; our ears/brain experience this as *an instantaneous visceral sensation.* The intervals have a scale degree and place in relation to '1' or the Tonic, and triads can be constructed on these steps/notes. The *chords* thus constructed *can then be given a 'function' which is modeled after this harmonic relation to the keynote.* Function is dependent on forward progression in time, and context, and both rely on memory.

*"This harmonic model is where all 'linear function' originates."*

I'm not about to analyze these statements one at a time, but I have to say that the general point they seem to be making would have much more credibility if they were accompanied by some explanation of HOW the imputed magical transformation of perception into music happens: how hearing different degrees of dissonance between scale notes and the tonic explains a composer's choice of harmonic progressions. Some musical examples might be useful in supporting your theory, but you don't even provide those.

As I look over the history of music, I see a great variety of harmonic practice. Tonality is a near-universal characteristic of music, but harmony in Western music is said to date back to about 900 A.D., and a lot changed over the succeeding millennium. Across time and cultures the human ear has presumably been quite capable of perceiving degrees of relative dissonance in various intervals, yet the treatment of harmony has been immensely varied. We observe certain common features in disparate cultures and styles, such as a preference for the fifth scale degree, an easily audible overtone of the tonic, which eventually became our dominant. But our tonal hierarchy and conventions of harmonic progression underwent a long development. Why so long? What was "the ear" doing over all that time? What were composers' ears telling them to do? What was Machaut's ear telling him in this:






In what way was Dufay's ear telling him what to write in this?






How about Ockeghem's ear:






Or Purcell's:






Or Gesualdo's:






I presume these composers could hear degrees of dissonance as well as Bach could, but they certainly had different intuitions about proper "function" in deciding what harmonies sounded right at any given moment. The ear was busy for hundreds of years before modern harmonic theory was formulated. What exactly was it telling the musical minds attached to it? How does the perception of degrees of dissonance, which should not change over time if the human ear doesn't, result in different modes or tonal systems? And how does it guide specific procedures? How does it guide the use of chromaticism? How does it account for the aptness of an authentic cadence, or a plagal one, or a deceptive one? Music is built on the increase and decrease of tensions, and degrees of dissonance are basic in harmonic music's accomplishment of that, but beyond a crude level - say, tonic to dominant increasing tension, the reverse decreasing it - how much can relative dissonance tell composers how to structure their music? Assuming it can tell them anything at all, doesn't it seem to have told them very different things? How, for a more far-flung example, does the following music reflect the scale's hierarchy of consonance and dissonance?






It probably isn't necessary to go outside the common practice tradition to make my point, which is that harmonic progression is so variable, and governed by so many factors, that there is no reason to suppose that composers arrive at a specific harmonic system, a codified or codifiable way of using harmony, solely or mainly by observing or sensing the acoustical properties of sound. And to go even farther (if that's what you're doing) and imagine that any composer is guided by that factor in the moment of composition to shape his work in any particular way is just inconceivable to me.

You've claimed a local patent on being able to "EXPLAIN HOW" Bach, under the influence of some subliminal perception of relative dissonance between the tonic and the roots of other chords, could think in terms of a harmonic idiom without referring to a codified classification of chords. Well, I'm not looking to infringe that patent, since I don't see that you've explained any such thing. In fact I don't even see that an explanation of that kind is necessary. If Bach had lived in the time of Binchois, he would have written modal polyphony with Landini cadences, and if he had lived in the time of Schoenberg, God only knows what sort of harmony he would have written. Bach learned to think harmonically the same way everybody else does: by hearing, performing, reading and writing music in the harmonic idiom of his own day, not by listening to spirit voices from the Celestial Academy of Acoustical Science.


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## millionrainbows

EdwardBast said:


> "Chord function … is an innate feature of any scale which can be used in tonality?" This is meaningless. Chord function is not a feature of scales. The statement makes no sense whatever. Try again.


It makes sense to me & my ear(s). You've never thought about it, apparently. If you can hear scale steps in relation to a tonic, you're hearing "function." All the classification in the world won't change that basic fact of perception. You're not an "ear guy," are you? Didn't think so.


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## millionrainbows

Another gargantuan invalidation-fest from you-know-who! Wow! Where do I begin? I'm gonna have to break this one down into manageable chunks, otherwise I'll choke.



Woodduck said:


> Jiminy Crickets! Narcissistically? Back to labeling and name-calling (and now I have confirmation that your use of that term yesterday was aimed at me, even though you denied it). Ho hum...


After observing your behavior on the "Religious Music Without Lyrics" thread, why do you even bother with "victim statements" like this?



> You're projecting mightily. I don't expect _everyone _to agree with _anything_, but apparently you do expect that, else you wouldn't repeat yourself over and over in _exactly_ the same words, hoping that everyone who might consider questioning you will either adopt them as a mantra, be stuck with an earworm, or just give up from brain fatigue.


No, it's just that I really feel you are unaware of the import of my ideas, and are hostile to me as a person, so it's a no-win situation. I just put my ideas out there, you can take 'em or leave 'em. It's not going to ruin my supper.


> Sorry, bubba, but what I'm really tryin' ta do is figger out what in the Sam Hill you're talkin' 'bout with this here "composition by ear" thang.


Maybe it's my motivation that eludes you, but it's really very simple, all in the charts I posted. All you have to be able to do is hear scale steps in relation to a tonic, and you're hearing "function" in its basic, pre-theory form. All the CP classification in the world won't change that basic fact of perception. You play piano, don't you? I assumed you were an "ear guy," but apparently your "edjumacation" is getting in your way.



> If that's all I thought you were saying, I'd have no argument with you (up until "and the consonance/dissonance corresponds"- but hang on...) OF COURSE we can perceive - "by ear" - different degrees of consonance and dissonance among the intervals between a tonic note and the other notes of a scale (though I dare say that most people wouldn't know whether, e.g., a major third or a major sixth is more dissonant). But you appear to be saying much more than that. You appear to be saying that this basic fact of perception "EXPLAINS HOW" Bach - and presumably other people writing harmonic progressions - have arrived at the tonal system we call "common practice" and are able to know, while composing, what chord should follow what. If this is the claim you're making, it's an extraordinaryone, and it strikes me as insufficiently reasoned, as well as reductive in the extreme. It certainly cries out for concrete demonstration. "The consonance/dissonance corresponds" doesn't _explain_ anything, even if there is actually a meaningful correspondence between something and something else.


Well, I'm not a historian, but I think this is the way all good musicians hear things. Whether or not it adheres to later codified practices is of no concern to me. Since there is no written record by Bach on theory, then at least I offer an explanation which is innate and universal. If you think it sucks, so be it, it won't bother me in the least.


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## millionrainbows

Woodduck said:


> Here is what you've said in this thread:
> 
> "Harmonic thinking did not exist in Bach's time, so no one has *explained exactly how he thought* about harmonic root movement or harmonic 'progressions.'"
> 
> "It has already been acknowledged that Bach was 'thinking harmonically' without the benefit of a codified system of harmony, chord function, or root movement. There is only one possible conclusion: Bach was doing it by 'ear,' on the basis of what he was hearing harmonically. Bach's *'function' was derived by listening."*
> 
> "Bach was determining 'function' by ear."
> 
> "Bach was doing it by ear. his *linear rules were there, but any harmonic factors not covered by these rules were arrived at by listening.*"
> 
> "*What is called 'harmonic thinking' is just 'using your ear' to hear the 'harmonic truth.'*
> It has less to do with harmonic rules or regulations. It is derived from the act of hearing, not rules."
> 
> "'Harmonic thinking' is possible without any rules; it operates more on the level of the ear, as *a directly perceived 'logic' of the senses."*
> 
> "'Harmonic truths' such as *'function' of roots and chords exists without any codification or established practices. It is a universal truth, one of the underlying principles of music."
> *
> "'Harmonic hearing' is *the underlying basis of all 'systems,' nomenclatures, and 'practices'* or rules."
> 
> "*Tonal music *is harmonic; music is vertical. It *is based on vertical, harmonic factors which are instantaneous, based on hearing degrees of consonance/dissonance to a key or tonic note.*"
> 
> *"Melodies in counterpoint have a harmonic basis; they suggest triads, and can outline triads.* Bach's unaccompanied violin sonatas show that *he was thinking harmonically*. But no one has offered an explanation of how this is possible, except me. It is done by ear, *using intervals and their degrees of dissonance to a key note, and their other suggestions of triads.* The intervals have *a dissonant/consonant quality determined by their ratio, all in relation to a 'keynote'* or unity of 1; our ears/brain experience this as *an instantaneous visceral sensation.* The intervals have a scale degree and place in relation to '1' or the Tonic, and triads can be constructed on these steps/notes. The *chords* thus constructed *can then be given a 'function' which is modeled after this harmonic relation to the keynote.* Function is dependent on forward progression in time, and context, and both rely on memory.
> 
> *"This harmonic model is where all 'linear function' originates."*
> 
> I'm not about to analyze these statements one at a time, but I have to say that the general point they seem to be making would have much more credibility if they were accompanied by some explanation of HOW the imputed magical transformation of perception into music happens: how hearing different degrees of dissonance between scale notes and the tonic explains a composer's choice of harmonic progressions. Some musical examples might be useful in supporting your theory, but you don't even provide those.


It seems simple to me. If a composer wants to move away from the tonic and create a chord progression, he does it on the basis of how closely-related the roots are to the tonic, and creates the progressions. This can be done with any scale, based on the degrees of relation (those ratios in the chart, and the rankings):

Their importance in establishing the tonality is ranked by the order of consonance to dissonance, with smaller-number ratios being more consonant.

I - 1:1
V - 2:3
IV - 3:4
vi - 3:5
iii - 4:5
ii - 8:9
vii - 8:15



> As I look over the history of music, I see a great variety of harmonic practice. Tonality is a near-universal characteristic of music, but harmony in Western music is said to date back to about 900 A.D., and a lot changed over the succeeding millennium. Across time and cultures the human ear has presumably been quite capable of perceiving degrees of relative dissonance in various intervals, yet the treatment of harmony has been immensely varied. We observe certain common features in disparate cultures and styles, such as a preference for the fifth scale degree, an easily audible overtone of the tonic, which eventually became our dominant. But our tonal hierarchy and conventions of harmonic progression underwent a long development. Why so long? What was "the ear" doing over all that time? What were composers' ears telling them to do?


Thanks for the examples anyway.



> I presume these composers could hear degrees of dissonance as well as Bach could, but they certainly had different intuitions about proper "function" in deciding what harmonies sounded right at any given moment. The ear was busy for hundreds of years before modern harmonic theory was formulated. What exactly was it telling the musical minds attached to it? How does the perception of degrees of dissonance, which should not change over time if the human ear doesn't, result in different modes or tonal systems? And how does it guide specific procedures? How does it guide the use of chromaticism? How does it account for the aptness of an authentic cadence, or a plagal one, or a deceptive one?


I guess you could say that this is up to the individual's own taste and knowledge of styles and what went before. I don't deny this legacy, I'm simply getting down to the root of it, pardon the pun.



> Music is built on the increase and decrease of tensions, and degrees of dissonance are basic in harmonic music's accomplishment of that, but beyond a crude level - say, tonic to dominant increasing tension, the reverse decreasing it - how much can relative dissonance tell composers how to structure their music? Assuming it can tell them anything at all, doesn't it seem to have told them very different things?


Thanks for the example anyway.



> It probably isn't necessary to go outside the common practice tradition to make my point, which is that harmonic progression is so variable, and governed by so many factors, that there is no reason to suppose that composers arrive at a specific harmonic system, a codified or codifiable way of using harmony, solely or mainly by observing or sensing the acoustical properties of sound. And to go even farther (if that's what you're doing) and imagine that any composer is guided by that factor in the moment of composition to shape his work in any particular way is just inconceivable to me.


Well, this sort of deep logic is also the subject of Arnold Schoenberg's textbook "Structural Functions of Harmony."



> You've claimed a local patent on being able to "EXPLAIN HOW" Bach, under the influence of some subliminal perception of relative dissonance between the tonic and the roots of other chords, could think in terms of a harmonic idiom without referring to a codified classification of chords.


That's an exaggeration, but I am the only one who has offered any concrete explanation. You're probably a close second. I would be wrong to say Bach wasn't influenced by the practices of his day (even though he rejected Rameau's ideas), but I've never said that.

Besides, my explanation gives the benefit to Bach "using his ears" rather than him simply "parroting" the procedures of the day.



> Well, I'm not looking to infringe that patent, since I don't see that you've explained any such thing. In fact I don't even see that an explanation of that kind is necessary.


Well, I do, especially when academicians pull things out of their hats like "chords were not used in the Baroque" and stuff like that.



> If Bach had lived in the time of Binchois, he would have written modal polyphony with Landini cadences, and if he had lived in the time of Schoenberg, God only knows what sort of harmony he would have written. Bach learned to think harmonically the same way everybody else does: by hearing, performing, reading and writing music in the harmonic idiom of his own day...


 I agree, I don't doubt that at all.



> ...not by listening to spirit voices from the Celestial Academy of Acoustical Science.


Yes, and be careful when you go to sleep tonight! I've heard that these "spirit voices" enter into you through the ears!


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## Woodduck

^^^ You're evading the elephant in the room, which I tried to place front and center: the variety of tonal systems, with their diverse conventions, throughout a long history of which common practice occupies only a portion. Your dismissal of this with "thanks for the examples anyway" tells me you're not capable of dealing with the problem they raise for your theory.

Your statement, "If a composer wants to move away from the tonic and create a chord progression, he does it on the basis of how closely-related the roots are to the tonic," is not true. Unless you have a special meaning in mind for the expression, "on the basis of," a composer does not have to concern himself with degrees of relationship to the tonic or be compelled by them in any way. There are certainly conventional relationships between chords, and it's true that the most commonly used chords and progressions use the chords closest to the tonic; the tonic-dominant relationship is basic to common practice, and the subdominant root is to the tonic root as the tonic root is to the dominant root. It isn't surprising that this "triumvirate" should have come to dominate common practice tonality (at least for a while), since the overtone of the fifth above the tonic is so audible and the harmony created between them so satisfying. But a composer who wants to move away from the tonic may do so in a number of directions - he can move to the supertonic or the mediant chord, for example - and he may proceed in any number of directions from there. Not even at a final cadence is there a necessity of sticking to the common V - I or IV - I formulas. In exactly what way do you feel composers are constrained by your hierarchy of dissonance?


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## BabyGiraffe

Woodduck said:


> the tonic-dominant relationship is basic to common practice, and the subdominant root is to the tonic root as the tonic root is to the dominant root.


 Overtone relationships are one, voice leading relationships - another topic, that's why subdominant relationship has more validity as natural move of chords, related to a key (but it's not major/minor "key"). The only legal moves that don't imply modulation and don't introduce enharmonics are these found in the C-Eb-E-F-G-Ab-A scale. There is no dominant chord there. This is the 5-limit hexagonal lattice. Many-many scales can be derived, if we use selection polygons that go around pitches that are close on this lattice.
Here is the tempered version in 12 equal.

https://en.wikipedia.org/wiki/Neo-Riemannian_theory#/media/File:Neo-Riemannian_Tonnetz.svg

If you want dominant and typical classical music progression, you want hidden 80/81 (or inverse) and prooobably meantone temperament to get rid of them. If you want "romantic" chord progressions, you will deal with both 81/80 and 128/125 and their product - 648/625, so the whole basis of classical music is artificial construct.


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## millionrainbows

Woodduck said:


> Your statement, "If a composer wants to move away from the tonic and create a chord progression, he does it on the basis of how closely-related the roots are to the tonic," is not true. Unless you have a special meaning in mind for the expression, "on the basis of," a composer does not have to concern himself with degrees of relationship to the tonic or be compelled by them in any way.


I think that's incorrect. As Schoenberg demonstrates in his book, certain root movements are stronger than others ands do different things. I think this is what Bach was doing, in addition to obvious voice-leading.

For instance, a root movement a fifth up (a fourth down), say, from C to G suggests a movement *away from the tonic*, because the ear hears fifths with "root on bottom."

A root movement a fourth up (a fifth down), say, G to C suggests a movement *to a tonic, *because the ear tends to hear fourths as "root on top."



> But a composer who wants to move away from the tonic may do so in a number of directions - he can move to the supertonic or the mediant chord, for example - and he may proceed in any number of directions from there. Not even at a final cadence is there a necessity of sticking to the common V - I or IV - I formulas.


True; that doesn't negate anything I've said.


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