# Why do root movements a fourth away tend to weaken the tonality of the key?



## millionrainbows

Root movements a fifth away tend to strengthen the tonality of the key, while root movements a fourth away tend to weaken the tonality of the key.
This is because we tend to hear a fifth as "root on bottom," and we tend to hear fourths as "root on top." This is due to the harmonic series.
Schoenberg explores this in his book _Structural Functions of Harmony.
_
Also, the structure of the harmonically imperfect C major diatonic scale adds to this weakening; the semitone E-F acts as a leading tone to reinforce F, not G or C; b-C reinforces C; but there is no leading tone to reinforce G.

So the "triumvirate" of IV-I-V is formed, as a section of the circle of fifths/fourths:

IV.......I......V

F.........C.....G

The C major scale is thus designed for travel, not harmonic stability. This is what I mean by "imperfect harmonically." In a sense, it's not really "imperfect" or flawed; it just is what it is, and does what it does.


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## EdwardBast

It would help if you could clarify what you mean by root movements a fifth away versus root movements a fourth away. 

Here are two diatonic circles of triads in C major. Which are you calling motion by 5ths and which motions by 4ths:

1. C - F - B° - Em - Am - Dm - G - C

2. C - G - Dm - Am - Em - B° - F - C

I don't care from a terminological perspective which way you name them, I'm only interested in knowing what motion you are saying is tonality weakening.


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## millionrainbows

EdwardBast said:


> It would help if you could clarify what you mean by root movements a fifth away versus root movements a fourth away.
> 
> Here are two diatonic circles of triads in C major. Which are you calling motion by 5ths and which motions by 4ths:
> 
> 1. C - F - B° - Em - Am - Dm - G - C
> 
> 2. C - G - Dm - Am - Em - B° - F - C
> 
> I don't care from a terminological perspective which way you name them, I'm only interested in knowing *what motion* you are saying is tonality weakening.


No, _*what motion combined with what interval.
*_
Apparently, from your question and the way you've posed it, you haven't quite 'grokked' the meaning of directionality in the circular, recursive scheme of tonality. This is what I keep saying is 'pitch identity' rather than 'pitch quantity.'

C up to F = C down to F, etc. Both reinforce F as a new tonic, because _we hear fourths as root on top, and fifth as root on bottom. This is a strong or ascending progression, since the destination root F has 'usurped' the power of the starting point C._

Root movement a fourth up (C-F) is equal to a fifth down (C-F); root movement a fifth down is equal to a fourth up.

"Directionality" is thus _movement in time which works in either direction;_ what are we "going to" and where are we "coming from." Where are we "ending up?"

Remember how you dismissed 'directionality' in the interval size thread? Well, don't dismiss it here.


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## EdwardBast

So you mean the direction of the first progression I wrote. I'm not dismissing directionality, just asking you which direction.  Your circumlocution brings to mind a bit of old wisdom: "The way out is through the door. Why is it that no one will use this method?"
-Confucious

Systematically exploiting motion in that direction is the way tonality was established. Your argument is absurd.


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## Woodduck

millionrainbows said:


> Root movements a fifth away tend to strengthen the tonality of the key, while root movements a fourth away tend to weaken the tonality of the key.
> This is because we tend to hear a fifth as "root on bottom," and we tend to hear fourths as "root on top." This is due to the harmonic series.
> Schoenberg explores this in his book _Structural Functions of Harmony.
> _


I don't understand this. Either you're not explaining what you mean clearly, or what you're trying to say doesn't make sense.

If we establish the tonality of C major, and then strike a C major chord with C as root, how does moving next to an F chord (root F, up or down from C) or a G chord (root G, up or down from C) either weaken or strengthen the tonality we've established? Dominant and subdominant relationships are both components of the system of relationships which constitute the tonality. What is it that's weakened or strengthened by the use of them? Or are you talking about something else?

Let me fish around a bit...

If, having not yet established a tonality, we strike a C chord in root position, and follow it immediately with an identically voiced G chord, we will perceive that we've moved from the tonic to the dominant in the tonality of C regardless of whether we've moved the root by a fourth downward or a fifth upward from C.

If, having not yet established a tonality, we strike a C chord in root position, and follow it immediately with an identically voiced F chord in root position, moving the root either a fourth up or a fifth down from C, we may perceive that we've moved from the dominant to the tonic in the tonality of F.

The difference in our perceptions in these two cases is presumably rooted in our expectations of how tonic, dominant and subdominant function in the tonal system we normally employ. If this is part of what you're saying, I understand it. But I don't see what difference it makes whether we've moved the root by a fourth or a fifth, or how doing either one strengthens or weakens the sense of tonality. It seems to me that in doing either we're _establishing_ and _defining_ a tonality by means of its essential components.


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## millionrainbows

I'm surprised at your reactions, especially since this is a very logical concept by Schoenberg, with excerpts from the book. It's all been explained clearly by me. 
Unless there's a pedantic glitch, I too am mystified by your miscomprehension.

If it's not me, it must be Schoenberg. I'm just the messenger.


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## millionrainbows

Woodduck said:


> If, having not yet established a tonality, we strike a C chord in root position, and follow it immediately with an identically voiced G chord, we will perceive that we've moved from the tonic to the dominant in the tonality of C *regardless of whether we've moved the root by a fourth downward or a fifth upward from C. *


*
*
True. The two are equivalent.



> If, having not yet established a tonality, we strike a C chord in root position, and follow it immediately with an identically voiced F chord in root position, *moving the root either a fourth up or a fifth down from C, *we may perceive that we've moved from the dominant to the tonic in the tonality of F.


True.



> The difference in our perceptions in these two cases is presumably rooted in our expectations of how tonic, dominant and subdominant function in the tonal system we normally employ. If this is part of what you're saying, I understand it.


That's part of it.



> *But I don't see what difference it makes whether we've moved the root by a fourth or a fifth,* or how doing either one strengthens or weakens the sense of tonality. It seems to me that in doing either we're _establishing_ and _defining_ a tonality by means of its essential components.


That part of your statement doesn't make sense. There _is _a difference in moving the root by a fourth, depending on which direction.

Going *up* a fourth, C-F, establishes *F.* (fourths are heard as root on top). 
The root note of the first chord is degraded, becoming only the fifth of the second chord.

Going *down* a fourth is C-G, establishing *C*. This is equivalent to a fifth up, C-G, in which we hear fifths as root on bottom.
The fifth of the first chord always advances to become the root of the second chord.

(this is explained in the footnote of the book excerpt).

You guys are having a pedantic mind-glitch, I guess.


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## tdc

A similar concept is touched on in Rosen's book _The Classical Style_, he shows a diagram of the circle of 5ths (but not as a circle as two lines diverging away from each other) and suggests that the side going up in 5ths is more harmonically stable than the side going back in 4ths. He also states that the major scale is more harmonically stable than the minor scale, this is why Classical era composers chose to compose in major keys more often than minor.


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## millionrainbows

tdc said:


> A similar concept is touched on in Rosen's book _The Classical Style_, he shows a diagram of the circle of 5ths (but not as a circle as two lines diverging away from each other) and *suggests that the side going up in 5ths is more harmonically stable than the side going back in 4ths.* He also states that the major scale is more harmonically stable than the minor scale, this is why Classical era composers chose to compose in major keys more often than minor.


 Yes, as long as you understand that fifths are stable with root on bottom (harmonically/vertically) or with root as first root note (horizontally).

This insight is a luxury of already "grokking" this concept, and may confuse things.


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## tdc

millionrainbows said:


> Yes, as long as you understand that fifths are stable with root on bottom (harmonically/vertically) or with root as first root note (horizontally).
> 
> This insight is a luxury of already "grokking" this concept, and may confuse things.


It doesn't seem confusing as much as possibly an example of stating something in a way that makes things sound more complex than is necessary, although maybe I'm failing to grasp something. Simply put if you reverse the order of the root with the fifth, a fifth is no longer a fifth but a fourth, so your point seems self evident. Is there something more to this I'm failing to "grok"?


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## millionrainbows

tdc said:


> It doesn't seem confusing as much as possibly an example of stating something in a way that makes things sound more complex than is necessary, although maybe I'm failing to grasp something. Simply put if you reverse the order of the root with the fifth, a fifth is no longer a fifth but a fourth, so your point seems self evident. Is there something more to this I'm failing to "grok"?


No, I'm just being cautious because of the presence of EdwardBast and Woodduck. You call it 'self evident,' they call it absurd and confusing.


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## jegreenwood

millionrainbows said:


> No, I'm just being cautious because of the presence of EdwardBast and Woodduck. You call it 'self evident,' they call it absurd and confusing.


But what exactly is your question? The question in the title of the thread seems to be answered by both Schoenberg and Rosen. Schoenberg's language seems a bit more ornate* than Rosen's, and Rosen adds one significant point - helpful, at least, to my understanding: all harmonics rise from a note. Thus, if I understand him correctly, the dominant, as the third harmonic, is more closely associated with the tonic than the subdominant. But as Woodduck says, neither of them, on their own, indicate a change of an established tonic in the composition.

As for your "harmonically imperfect C diatonic scale," are you saying there is something unique about C Major that distinguishes it from other major scales? (In the world of equal temperament.)

*And I would be careful of descriptive terms - Schoenberg describes the dominant as an inferior tone, while Rosen describes it as powerful, even though they are making the same point.


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## Woodduck

millionrainbows said:


> No, I'm just being cautious because of the presence of EdwardBast and Woodduck. You call it 'self evident,' they call it absurd and confusing.


Actually, EdwardBast and Woodduck call it absurd or confusing when it's absurd or confusing. We're pretty bright fellows who say things very precisely and appreciate the same in others. If we don't get what you're saying you might at least consider the possibility that you need to explain things better.


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## millionrainbows

jegreenwood said:


> But what exactly is your question? The question in the title of the thread seems to be answered by both Schoenberg and Rosen. Schoenberg's language seems a bit more ornate* than Rosen's, and Rosen adds one significant point - helpful, at least, to my understanding: all harmonics rise from a note. Thus, if I understand him correctly, the dominant, as the third harmonic, is more closely associated with the tonic than the subdominant. But as Woodduck says, neither of them, on their own, indicate a change of an established tonic in the composition.


Well then, conversely, you seem to have come to the same conclusion as Woodduck and EdwardBast, that points to this thread being absurd and confusing. If that satisfies you, fine.

I don't think Schoenberg's intent was to show how these root movements establish a large-scale tonal area, but rather to show tendencies in how they can weaken or strengthen tonal tendencies.



> As for your "harmonically imperfect C diatonic scale," are you saying there is something unique about C Major that distinguishes it from other major scales? (In the world of equal temperament.)


No, I don't wish to point out the C major scale's uniqueness; it does what it does. Considering scales _solely_ as vehicles for establishing tonality, there are other scales more suited for this, and the C major scale is not "perfect" in establishing tonality.

The example I always use comes from jazz, in which scales are matched with chords in terms of their maximum harmonic compatibility. 
One tenet of jazz is: when playing over a C major seventh chord, DO NOT use the C major scale; use C lydian. Why? Because of the note "F".



> *And I would be careful of descriptive terms - Schoenberg describes the dominant as an inferior tone, while Rosen describes it as powerful, even though they are making the same point.


I haven't read the Charles Rosen material, and I didn't bring him up, so _you_ should be careful who you ascribe these ideas to. The ideas I have exposed here all came from Schoenberg.


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## millionrainbows

Woodduck said:


> Actually, EdwardBast and Woodduck call it absurd or confusing when it's absurd or confusing. We're pretty bright fellows who say things very precisely and appreciate the same in others. If we don't get what you're saying you might at least consider the possibility that you need to explain things better.


Do I have to explain Schoenberg's ideas about root movement in order for you to understand or accept them? Again, I don't think Schoenberg's intent was to show how these root movements establish a large-scale tonal area (if that's your point), but rather to show _how they can weaken or strengthen tonal tendencies _

Your reply in post #5 already demonstrates that you seem to be missing a crucial point:



> But I don't see what difference it makes whether we've moved the root by a fourth or a fifth, or how doing either one strengthens or weakens the sense of tonality.


But if you are talking about other factors in establishing large areas of tonality, then these "microcosms" of tonal tendencies do not concern you. If they don't interest you, fine.

Frankly, I'm torn between wondering whether you & EdwardBast are sincerely confused, or whether you have some other reason for replying as you have.


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## jegreenwood

millionrainbows said:


> Well then, conversely, you seem to have come to the same conclusion as Woodduck and EdwardBast, that points to this thread being absurd and confusing. If that satisfies you, fine.
> 
> I don't think Schoenberg's intent was to show how these root movements establish a large-scale tonal area, but rather to show tendencies in how they can weaken or strengthen tonal tendencies.
> 
> No, I don't wish to point out the C major scale's uniqueness; it does what it does. Considering scales _solely_ as vehicles for establishing tonality, there are other scales more suited for this, and the C major scale is not "perfect" in establishing tonality.
> 
> The example I always use comes from jazz, in which scales are matched with chords in terms of their maximum harmonic compatibility.
> One tenet of jazz is: when playing over a C major seventh chord, DO NOT use the C major scale; use C lydian. Why? Because of the note "F".
> 
> I haven't read the Charles Rosen material, and I didn't bring him up, so _you_ should be careful who you ascribe these ideas to. The ideas I have exposed here all came from Schoenberg.


As for your first comment - I am perfectly satisfied. That despite the fact I have no idea what you mean by weakening total tendencies in this context. Schoenberg and Rosen make sense to me. You do not.

By the way, I never claimed you read the Rosen book (although you should). tdc mentioned it earlier in the thread as containing a similar concept.

As for your comment on C Major, I should probably let it go, as I don't know enough about jazz harmony, but are you saying that a jazz player would feel differently about what to play over a D Major seventh - i.e. something other than D lydian. If so, why?


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## Woodduck

millionrainbows said:


> Considering scales _solely_ as vehicles for establishing tonality, there are other scales more suited for this, and the C major scale is not "perfect" in establishing tonality.
> 
> The example I always use comes from jazz, in which scales are matched with chords in terms of their maximum harmonic compatibility.
> One tenet of jazz is: when playing over a C major seventh chord, DO NOT use the C major scale; use C lydian. Why? Because of the note "F".


How does the Lydian mode "establish tonality" more readily or decisively than the Ionian (major) mode? If you play either a major scale or a Lydian scale from C to C, in which scale does tonality sound "more established"? That depends on what system of tonality your sense of tonal relationships, and thus your expectation of where the music is likely to go, is rooted in.

To my ear, conditioned by the predominance of the major tonality in Western music, the major scale sounds more "stable," with the F suggesting resolution down to the E, the "color" note of the tonic chord, than does the Lydian, with its F# nudging me toward G and the dominant key of which G is the tonic (the F# feeling all the more unstable because it creates a tritone with the tonic C). In a piece of music with an established tonality of C major, I would normally hear the occurrence of an F# as suggesting a modulation, while the presence of an F would not create that expectation. If, on the other hand, I were accustomed to music in the Lydian mode and didn't bring to it expectations of common practice tonality, I would expect the opposite to be the case: the F# would not suggest movement to another tonal area, while the intrusion of an F might do so.

For this reason, the idea of a particular scale _as such_ being intrinsically "stable" vs. "built for movement," or serving to "establish tonality," seems to me untenable. A scale is a resource for a system of tonality, and its component notes will seem as stable or as unstable as the system dictates. In the tonality of jazz, the major scale's unstable "leading tone," the "B" in C major, ceases to lead and becomes a perfectly stable component of the tonic chord, proving that the B - and the scale as a whole - has no intrinsic tendencies.

(About jazz: I agree that F# above a C major 7th sounds better than F, which can set up a frightful tritone with that no-longer-"leading" B. The F can still be used, though, if a particularly mournful color is wanted.)


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## Bwv 1080

Woodduck said:


> (About jazz: I agree that F# above a C major 7th sounds better than F, which can set up a frightful tritone with that no-longer-"leading" B. The F can still be used


That is THE reason lydian tends to be used over major chords in Jazz, no other explanation is necessary, also when extending maj chords, the #11 is almost always used. Its just color - ii chords are still minor and IV chords, not #ivdim are used



millionrainbows said:


> No, I don't wish to point out the C major scale's uniqueness; it does what it does. Considering scales _solely_ as vehicles for establishing tonality, there are other scales more suited for this, and the C major scale is not "perfect" in establishing tonality.
> 
> The example I always use comes from jazz, in which scales are matched with chords in terms of their maximum harmonic compatibility.
> One tenet of jazz is: when playing over a C major seventh chord, DO NOT use the C major scale; use C lydian. Why? Because of the note "F".


Scales don't establish tonality, harmony does. (try playing F Lydian over a d minor chord). Scales can imply harmony, but then the upper extensions dont matter much, in jazz, you really just need to get the third and the seventh right - everything else can be altered


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## millionrainbows

Woodduck said:


> (About jazz: I agree that F# above a C major 7th sounds better than F, which can set up a frightful tritone with that no-longer-"leading" B. The F can still be used, though, if a particularly mournful color is wanted.)


That's the point; the dissonant tritone F.



Bwv 1080 said:


> Scales don't establish tonality, harmony does. (try playing F Lydian over a d minor chord). Scales can imply harmony, but then the upper extensions dont matter much, in jazz, you really just need to get the third and the seventh right - everything else can be altered


Then you are purposely ignoring the points I am making which involve scales. I'm not interested in bickering. I've made the points I'm going to make about the C major scale and its tritone F.

The ideas here about root movement are Schoenberg's, not mine.


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## millionrainbows

The Schoenberg ideas seem simple to me, and they make sense both vertically and horizontally.

A root movement going clockwise (a fourth up) from C to F is what Schoenberg calls a "strong" or "ascending" progression; the root of the first chord is "degraded," becoming only the fifth of the second chord. Since the root of the first chord is weakened, We tend to hear the second chord as the new tonic.
Going counter-clockwise (a fifth down) from C to F produces the same result.

A root movement going counter-clockwise (a fourth down) from C to G is a "descending" progression. The fifth of the first chord, an "inferior" tone, always advances to become the root of the second chord. As the root of the first chord is unaffected, and its "inferior" tone is advanced, we tend to hear the first chord as remaining the tonic.
Going clockwise (a fifth up) from C to G produces the same result.

More on this can be found in Schoenberg' Harmonielehre, p. 140.


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## mikeh375

There's not much evidence of lydian scalar planing or harmony in earlier jazz...swing and trad...a different tenet then.


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## Bwv 1080

millionrainbows said:


> That's the point; the dissonant tritone F.
> 
> Then you are purposely ignoring the points I am making which involve scales. I'm not interested in bickering. I've made the points I'm going to make about the C major scale and its tritone F.
> 
> The ideas here about root movement are Schoenberg's, not mine.


Yes I am, the Schoenberg point about root movement is clear and well stated. I have read the book and also remember being taught this in undergrad theory. I don't buy using this as an argument for the Lydian mode having some special mojo over the major scale. Jazz players may use the #11 when extending or improvising on major chords, but they still use diatonic harmony based on the major scale - ii, Vdom, vii dim, etc. modal jazz, on the other hand, tends to not use functional harmony


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## Bwv 1080

mikeh375 said:


> There's not much evidence of lydian scalar planing or harmony in earlier jazz...swing and trad...a different tenet then.


Yes, because these upper extensions came along with bebop


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## mikeh375

Bwv 1080 said:


> Yes, because these upper extensions came along with bebop


yep..ex jazz guitarist here...


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## millionrainbows

Bwv 1080 said:


> Yes I am, the Schoenberg point about root movement is clear and well stated. I have read the book and also remember being taught this in undergrad theory. I don't buy using this as an argument for the Lydian mode having some special mojo over the major scale. Jazz players may use the #11 when extending or improvising on major chords, but they still use diatonic harmony based on the major scale - ii, Vdom, vii dim, etc. modal jazz, on the other hand, tends to not use functional harmony


I use my ears. When you play an F against a C major seventh chord, it sounds too dissonant, ugly, like it doesn't fit. That's because F is really the "set-up" note for travel _out _of C major, and it has a leading tone which reinforces this new key, E-F.

Most jazz players simply avoid F, and exploit the rest of the C major scale's similarity to a C major pentatonic C-D-E-G-A-B-D.

The Lydian scale, on the other hand, avoids the tritone F and reinforces G with leading tone F#-G. G is a more closely related key to C. George Russell based his Lydian Chromatic Concept on this. Who am I to argue with George Russell? If he were alive, I'd carry his luggage.

Jazz, and Russell's Lydian concept, is based on harmonic consonance and tonal gravity on a chord-by chord basis. The C major scale is clearly less suited for this than a Lydian is, if we are establishing C as our most stable, congruent center of tonal gravity.

Western diatonic harmony clearly has a different agenda than jazz; it is designed for travel outside of the home key.


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## Bwv 1080

millionrainbows said:


> The C major scale is clearly less suited for this than a Lydian is, if we are establishing C as our most stable, congruent center of tonal gravity.
> 
> Western diatonic harmony clearly has a different agenda than jazz; it is designed for travel outside of the home key.


Still not addressing my point - why is tonal harmony in both Jazz and Classical music based upon the triads built off the major chord rather than the Lydian mode? Jazz uses ii, not II and viidim, not viimin7. The #11 is just color. You contradict your whole point with Schoenberg if you try to do a ii-V-I off the lydian mode - ii becomes a dominant seventh chord and V is a major 7th - how does this establish tonality?


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## millionrainbows

Bwv 1080 said:


> ...why is tonal harmony in both Jazz and Classical music based upon the triads built off the major chord rather than the Lydian mode? Jazz uses ii, not II and viidim, not viimin7. The #11 is just color. You contradict your whole point with Schoenberg if you try to do a ii-V-I off the lydian mode - ii becomes a dominant seventh chord and V is a major 7th - how does this establish tonality?


Why shouldn't jazz use a major scale on a "I" chord, and the triads built from it?

The problem arises that the 4th degree is dissonant to a major chord, and has a strong tendency to resolve to the 3rd. Also, if the major seventh is present in the chord, the 1st (8th) scaler step is relatively dissonant, having a tendency to "resolve" to the seventh.

The "pretty" notes are 2, 3, 5, 6, and 7. These form a minor pentatonic scale which can be constructed on the third of a major chord.

On the other hand, the Lydian scale is used for soloing over major seventh chords, and it is not one of the scales which jazz players use for construction of chords or for harmonic purposes.


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## Woodduck

Is V-I really a "stronger" progression than IV-I? In isolation, perhaps. But in a musical context, not always. Handel's choruses and Wagner's operas typically end with IV-I (plagal cadence), with an effect of great power, release, and finality which V-I would not equal. Did Schoenberg consider this? How would he account for it?


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## Woodduck

millionrainbows said:


> I use my ears. When you play an F against a C major seventh chord, it sounds too dissonant, ugly, like it doesn't fit. That's because F is really the "set-up" note for travel _out _of C major, and it has a leading tone which reinforces this new key, E-F.


I use my ears too, and they tell me that the F sounds rough over a C7 not because it wants to set up the key of F but simply because it's fiercely dissonant with both E and B. What it really wants to do is simply to resolve down to E.


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## Bwv 1080

millionrainbows said:


> Why shouldn't jazz use a major scale on a "I" chord, and the triads built from it?
> 
> The problem arises that the 4th degree is dissonant to a major chord, and has a strong tendency to resolve to the 3rd. Also, if the major seventh is present in the chord, the 1st (8th) scaler step is relatively dissonant, having a tendency to "resolve" to the seventh.
> 
> The "pretty" notes are 2, 3, 5, 6, and 7. These form a minor pentatonic scale which can be constructed on the third of a major chord.
> 
> On the other hand, the Lydian scale is used for soloing over major seventh chords, and it is not one of the scales which jazz players use for construction of chords or for harmonic purposes.


I think you just paraphrased what I said, which gets back to what does the Lydian mode have to do with Schoenberg's observation about root movement? 
Some Jazz tunes do use chords built from diatonic modes, I dont have a Lydian example, but _So What_ and _Impressions_ are built on chords diatonic to the Dorian mode - but there is no real concept of functional harmony in these pieces.


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## millionrainbows

Woodduck said:


> Is V-I really a "stronger" progression than IV-I? In isolation, perhaps. But in a musical context, not always. Handel's choruses and Wagner's operas typically end with IV-I (plagal cadence), with an effect of great power, release, and finality which V-I would not equal. Did Schoenberg consider this? How would he account for it?


Well, you're opening a whole world of possibilities, now. The Schoenberg root movement ideas should be taken as he intended, as underlying principles, tendencies, and generalizations.

It seems that extreme exaggeration of these ideas, and the lydian information presented, are the basic way used to invalidate them. For example, I never said that the lydian scale should completely displace the major scale, even in determining harmony from triads based on it. I merely said that the lydian scale is more suited for soloing over a major 7th chord than the major scale with its F.

And still, V-I (a fourth up) will always sound as "root on top" as fourths always will.

There is a "vertical" dimension to tonality which I seem to always be emphasizing, and which you always seem to be countering with your horizontal, narrative ideas. Both are necessary, but I believe the vertical aspects are more primal and important, since there are so many ways to change perceptions of tonality with repetition and other devices which, to me, seem more contrived, less basic; in other words, they are more like ways of manipulating perception, which is a much more vague area than harmonics, intervals, etc.


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## millionrainbows

Woodduck said:


> I use my ears too, and they tell me that the F sounds rough over a C7 not because it wants to set up the key of F but simply because it's fiercely dissonant with both E and B. What it really wants to do is simply to resolve down to E.


I know. I just added the part about modulation to F, as an additional overall reason that F is not a perfect fit for reinforcing the key of C major, as it suggests F as a new key.


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## millionrainbows

Bwv 1080 said:


> I think you just paraphrased what I said, which gets back to what does the Lydian mode have to do with Schoenberg's observation about root movement?
> Some Jazz tunes do use chords built from diatonic modes, I dont have a Lydian example, but _So What_ and _Impressions_ are built on chords diatonic to the Dorian mode - but there is no real concept of functional harmony in these pieces.


My point was to counter your 'demand' for 'proof' that the lydian completely replace Ionian; which was not my assertion.

"Functional harmony" is for classical music. Jazz uses modes of the major scale, harmonic minor, and melodic minor, and it uses the triads built on these modes in a "functional" way. For example, in Dorian mode the i chord is minor, and the IV chord is major. This is a typical use of dorian, as in Santana's "Evil Ways." In normal minor mode (aeolian), the iv chord would be minor.
So, the use of modes, and triads built on the steps, does have real harmonic consequences; to call these "non-functional" begins to sound misleading and pedantic.

Practical composers and songwriters are not really concerned with distinctions such as those you stated; they just want to "get'er done."


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## Bwv 1080

If you do not understand the concept of functional harmony then perhaps go back and start there, it might allay your obvious confusion here


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## millionrainbows

Bwv 1080 said:


> If you do not understand the concept of functional harmony then perhaps go back and start there, it might allay your obvious confusion here


I don't know what you're talking about. I though EdwardBast and Woodduck were confused. And remember that Schoenberg's book is titled "Structural Functions of Harmony."







(Notice how well-worn my copy is...)


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## Bwv 1080

millionrainbows said:


> I don't know what you're talking about.


https://en.wikipedia.org/wiki/Function_(music)

http://www2.siba.fi/muste1/index.php?id=85&la=en


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## millionrainbows

Bwv 1080 said:


> https://en.wikipedia.org/wiki/Function_(music)
> 
> http://www2.siba.fi/muste1/index.php?id=85&la=en


No, I mean in regards to this discussion. You don't even know me, and are now entering ad-hominem territory with this stunt. You appear to be stuck in an academic mindset. What on earth are you doing talking about jazz, of all things?

If you do not understand Schoenberg's concepts of root movement as applied to functional harmony, then read the book. It might allay your obvious confusion here.


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## millionrainbows

Woodduck said:


> Is V-I really a "stronger" progression than IV-I?


I'm sure you'll find some way to say that it's not.


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## Woodduck

millionrainbows said:


> I'm sure you'll find some way to say that it's not.


It should be obvious that sometimes it is not. I say "sometimes," depending on musical context. Context matters to me as a listener. "Rules" are nice, but the exceptions that prove them - and sometimes reveal them to be merely academic and arid - are more interesting.

This discussion is precisely parallel to the one we're having about dissonance and how it's perceived and defined. Your physics lectures are all very well, but composers and listeners can do without them.


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## Bwv 1080

millionrainbows said:


> No, I mean in regards to this discussion. You don't even know me, and are now entering ad-hominem territory with this stunt. You appear to be stuck in an academic mindset. What on earth are you doing talking about jazz, of all things?
> 
> If you do not understand Schoenberg's concepts of root movement as applied to functional harmony, then read the book. It might allay your obvious confusion here.


Im not the confused one here. I have read the book and have a degree in traditional music theory and also took jazz theory classes at UNT. Its apparent from your posts and interactions with others here that you lack the fundamental basis for reading either Schoenberg or George Russell.


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## millionrainbows

Bwv 1080 said:


> Im not the confused one here. I have read the book and have a degree in traditional music theory and also took jazz theory classes at UNT. Its apparent from your posts and interactions with others here that you lack the fundamental basis for reading either Schoenberg or George Russell.


Then you are compelled to say why, not just assert it. Too much typing work, I guess. What exactly about Schoenberg is it that you think I'm confused about?

And if you are a jazz theorist, I doubt that you understand the reasoning behind George Russell's preference of the lydian scale.

Go ahead, big man, explain some things. Stop the vague generalizations and the "you're dumb" games.


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## millionrainbows

Woodduck said:


> It should be obvious that sometimes it is not. I say "sometimes," depending on musical context. Context matters to me as a listener. "Rules" are nice, but the exceptions that prove them - and sometimes reveal them to be merely academic and arid - are more interesting.
> 
> This discussion is precisely parallel to the one we're having about dissonance and how it's perceived and defined. Your physics lectures are all very well, but composers and listeners can do without them.


There are always exceptions, but none of them do very much to "disprove" anything that Schoenberg has asserted in his book about root movement.


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## Bwv 1080

I dont know if Schoenberg and George Russell can be reconciled, but you have not made a convincing case here, nor can you address the fact that Bebop relies on traditional harmonic functions - tonic, dominant, subdominant (I provided the links for a definition that could be agreed upon) that dont exist in the Lydian scale. The preference for the Lydian scale is simple, the #11 sounds better played over a major chord


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## millionrainbows

Bwv 1080 said:


> I dont know if Schoenberg and George Russell can be reconciled, but you have not made a convincing case here, nor can you address the fact that Bebop relies on traditional harmonic functions - tonic, dominant, subdominant (I provided the links for a definition that could be agreed upon) that dont exist in the Lydian scale. The preference for the Lydian scale is simple, the #11 sounds better played over a major chord


So that's all you'll do, post links? 
The Lydian scale is not used to create harmonic functions, but as a source scale to gradually expand tonal gravity.
The preference for the Lydian scale by Russell was because it created a more stable center of tonality which could then be expanded.


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## BabyGiraffe

millionrainbows said:


> So that's all you'll do, post links?
> The Lydian scale is not used to create harmonic functions, but as a source scale to gradually expand tonal gravity.
> The preference for the Lydian scale by Russell was because it created a more stable center of tonality which could then be expanded.


It is well known that Lydian and Locrian are the least used modes (not much popular, folk or art music is written with them) and hardest to use harmonically, because it is easy to slip into another mode in the case of Lydian or they just don't work (if it had a perfect fifth, it would just be phrygian)- in the case of Locrian. 
Lydian was used historically in early church music, but once they started using triadic harmony, Lydian lost all popularity.

You are not saying anything meaningful with these words - "tonal gravity", "stable center of tonality which could then be expanded".
There is no such thing in music theory as tonal gravity. Moving semitones tend to emphasize the target pitch - it is a well known melodic motion, used all the time to finish a piece conclusively even when you use a scale without a major seventh interval; it also works in the other direction - for example: North African, Spanish and Balkan music - they use phrygian or the exotic tetrachord with augmented second (the one with diatonic semitone, major third, fourth); it can sound like downwards melodic cadence. Because of the semitone between diatonic tritone and perfect fifth in Lydian, amateur composers/players usually slip into ionian. Or in phrygian, because of the other semitone.
Perceived stability of the scale has to do with timbre (harmonics) and the pattern of the scale. Javanese Pelog scale is a good example - it is a dual of major scale and is dissonant on harmonic instruments (just like major scale would be dissonant on traditional Javanese instruments) - the scale pattern in 9 equal is 122 1 122 - notice the two tetrachords, joined by a interval around a semitone or by flattened neutral second, not by tone like in Greek scales theory. (Major scale in 12 is 221 2 221). I guess pattern recognition principle makes phrygian the least ambiguous "minor" mode.

If you check the article that BWV linked, you will see how diatonic scale functions harmonically. 
Riemann and Schoenberg's (and other theorists, of course) ideas to assign a harmonic function to all chords doesn't work in practice. Not only is 12 equal ambiguous, unlike more accurate temperament systems; we cannot reduce chromatic scale to just diatonic subsets - that's why functional analysis in music that is not composed using diatonic pattern fails, you need to understand the internal logic (pitch collections, chords, modulations) of the composition and they may have nothing to do with diatonic theory.


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## millionrainbows

BabyGiraffe said:


> Perceived stability of the scale has to do with timbre (harmonics) and the pattern of the scale.


If you go to a sustaining organ-type keyboard, you can prove the more harmonic stability of the Lydian scale:

You generate the scale by "stacking fifths" and bringing them back into one octave. Since our 12-note division of the octave is based on this Pythagoran procedure, the fifth (and its inversion, the fourth) are the only intervals (beside the minor second) which generate all 12 notes.

Lydian: F-C-G-D-A-E-B, which sounds consonant, because it is all fifths.

By contrast, the major scale: C-G-D-A-E-B-(F), which deviates from pure fifths with the note F, which creates a tritone B-F. It sounds terrible.


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## BabyGiraffe

millionrainbows said:


> If you go to a sustaining organ-type keyboard, you can prove the more harmonic stability of the Lydian scale:
> 
> You generate the scale by "stacking fifths" and bringing them back into one octave. Since our 12-note division of the octave is based on this Pythagoran procedure, the fifth (and its inversion, the fourth) are the only intervals (beside the minor second) which generate all 12 notes.
> 
> Lydian: F-C-G-D-A-E-B, which sounds consonant, because it is all fifths.
> 
> By contrast, the major scale: C-G-D-A-E-B-(F), which deviates from pure fifths with the note F, which creates a tritone B-F. It sounds terrible.


Are you implying that Lydian doesn't have a tritone or what? :lol: 
Only heptatonic scales that are very close to 7 equal won't have a tritone-like interval. Diatonic scale is not close to it to it, so it has a tritone.
You can generate the diatonic scale in many different ways (even using statistical physics, see the paper that I linked in one of your other threads), but you still didn't prove that Lydian sounds better or more stable than other modes.
Pythagorean version of diatonic will be better for playing quartal/quintal harmony, but sounds worse even than 12 equal, if you are after major/minor triads.

If you are after harmony with triads and tetrads/pentads (used in jazz and other more modern styles), you should inspect scales that contain such structures - think of it in terms of incidence or intersection relations.
Generating a scale by addition of one interval modulo octave won't help us find interesting chordal scales outside of diatonic, which is a trivial case. Even in microtonal world (where we should be able to find many new possibilities) few of these type of (stack one interval) scales create any meaningful structures for harmony unlike scales, created by intersection of harmonious chords.


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## millionrainbows

BabyGiraffe said:


> Are you implying that Lydian doesn't have a tritone or what? :lol:


It's the position _within the octave_ of the tritone that makes the difference.



> Only heptatonic scales that are very close to 7 equal won't have a tritone-like interval. Diatonic scale is not close to it to it, so it has a tritone.


Irrelevant. It's the inter-octave harmonic relation of the scale which are important.



> You can generate the diatonic scale in many different ways (even using statistical physics, see the paper that I linked in one of your other threads)...


But our 12-note division of the octave is based on the fifth, the most consonant interval besides the unison or octave.



> ...but you still didn't prove that Lydian sounds better or more stable than other modes.


Yes i did, but you must go to a sustaining keyboard to hear it.



> Pythagorean version of diatonic will be better for playing quartal/quintal harmony, but sounds worse even than 12 equal, if you are after major/minor triads.


That's not relevant to this discussion.


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## BabyGiraffe

You want to talk about Pythagorean tuning and then say that it being more dissonant is not relevant, wow. My man, take your Russel book and throw it in the garbage along with other pseudo music theory book where it belongs and stop spreading lydian nonsense. Thank you. And read the whole wikipedia article that Bwv linked, please.

"But our 12-note division of the octave is based on the fifth, the most consonant interval besides the unison or octave."
What?
You need good harmonic approximations of all intervals in your tuning system, if you want to compose music that is in tune. If only the perfect 5th was good, you get some kind of pythagorean temperament, which is worse for modern European style music in sound and it won't be even possible to play classical music in it, because it is not meantone.
For its size 12 is very great closed system - it approximates various harmonics well.


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## isorhythm

We don't get scales from stacking fifths - this is the basic mistake you're making. Thirds are as important as fifths.

Since you are into the acoustic stuff, you can think of it this way: a just third has a frequency ratio of 5:4. The third you get from stacking fifths has a ratio of 81:64, which sounds bad and isn't even an interval that humans can recognize or reproduce by ear. So forget about that.

In practice, in western classical music, the Lydian scale was always treated as unstable and rarely used in unaltered form even during the Renaissance.

Here is an anonymous medieval piece that I believe is strictly Lydian: 



 Does it sound more stable to you than major? Not to me, personally (though it's a very striking sound).

In fact it's hard to get Lydian to sound as stable as major. Think of Beethoven's Heiliger Dankgesang movement or Bruckner's Os justi, also.


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## Bwv 1080

FWIW Lydian (Kalyan Thaat) is more common in Hindustani music than Ionian, but nearly anything is harmonically stable when played over a drone

https://en.wikipedia.org/wiki/Kalyan_(thaat)


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## isorhythm

Bwv 1080 said:


> FWIW Lydian (Kalyan Thaat) is more common in Hindustani music than Ionian, but nearly anything is harmonically stable when played over a drone
> 
> https://en.wikipedia.org/wiki/Kalyan_(thaat)


Interesting. I'm not very knowledgeable about that music but I've noticed the Lydian scale being used a lot.

I don't want to claim that the Ionian scale is inherently the most stable either, since I think a lot of this is culturally determined; I just think that the history of western music is strong evidence against the Lydian being inherently the most stable.


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## millionrainbows

BabyGiraffe said:


> Y
> "But our 12-note division of the octave is based on the fifth, the most consonant interval besides the unison or octave."
> What?
> You need good harmonic approximations of all intervals in your tuning system, if you want to compose music that is in tune. If only the perfect 5th was good, you get some kind of pythagorean temperament, which is worse for modern European style music in sound and it won't be even possible to play classical music in it, because it is not meantone.


The fifth is where the 12-note octave division came from.
Our ET fifths are only 2 cents off. It is definitely the favored interval.
Fifths are what we base "root stations" on for the various key areas. If fifths are stable, key areas are estabished.



> You need good harmonic approximations of all intervals in your tuning system, if you want to compose music that is in tune.


But as we all know, that's not possible in ET.
All the various "temperaments" like mean-tone are based on the attempt to get better major thirds.


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## millionrainbows

isorhythm said:


> We don't get scales from stacking fifths - this is the basic mistake you're making. Thirds are as important as fifths.


Here is a pianist doing just that. You need to think about this some more before you blurt out replies.





The fifth is where the 12-note octave division came from.
Our ET fifths are only 2 cents off. It is definitely the favored interval.



> Since you are into the acoustic stuff, you can think of it this way: a just third has a frequency ratio of 5:4. The third you get from stacking fifths has a ratio of 81:64, which sounds bad and isn't even an interval that humans can recognize or reproduce by ear. So forget about that.


You mean forget about it in ET?
Our ET fifths are only 2 cents off. It is definitely the favored interval.
All the various "temperaments" like mean-tone are based on the attempt to get better major thirds.



> In practice, in western classical music, the Lydian scale was always treated as unstable and rarely used in unaltered form even during the Renaissance. Here is an anonymous medieval piece that I believe is strictly Lydian. Does it sound more stable to you than major? Not to me, personally (though it's a very striking sound). In fact it's hard to get Lydian to sound as stable as major. Think of Beethoven's Heiliger Dankgesang movement or Bruckner's Os justi, also.


The fact remains that if you play all the intervals of a Lydian scale at once, on a sustaining keyboard such as an organ, it sounds more harmoniously consonant. This is proof to the ear itself that Lydian is more stable.

You're making it sound as if the Lydian scale were not usable. This is FAR from the truth.





This following musician's idea of the fourth agrees completely with Schoenberg's "idea" of the fourth. This "resolution" of the fourth upward is revealed to be more of an acoustic principle than an "idea."


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## BabyGiraffe

millionrainbows:

"Diatonic" means "two tonics." The C major scale is "diatonic" because it has C and F as strong tonics."




You again demonstrate ignorance.

"Diatonic" comes from ancient Greek genera names - diatonic, chromatic and enharmonic. And it doesn't mean two tonics and diatonic scale is not called like that, because of it has C and F as strong tonics, wow. 
Where do you find such wrong ideas?
Why don't you check any good book on ancient Greek music? Even most musical encyclopedias will do this job.

And playing a heptatonic scale like a cluster is a terrible idea, all diatonic modes sound bad in this way. I cannot believe you think this is some kind of proof that Lydian is better than others.



millionrainbows:



" All the various "temperaments" like mean-tone are based on the attempt to get better major thirds."


No, temperament means that a just intonation musical system is compromised with non-integer ratios.

Heptatonic scale with two chromas 25/24 and 81/80 describes diatonic scale in just intonation (Zarlino/Ptolemy Intense Diatonic scale). 
Tempering 81/80 (syntonic comma) will give us any meantone diatonic scale.
Tempering 25/24 (chromatic semitone) will give us something that sounds like double harmonic scale, tuned to 10 equal.
Tempering both chromas gives us... 7 equal.

So, 7 equal, 12, 19 equal etc are all meantone tunings.
Different algorithms will give us various optimized meantone tunings.

In more accurate meantone tuning than 12 equal we have enharmonics as different pitches, so in 19 equal we have stuff like C# and Db, and Fb etc.

The basic step of 12 equal is diatonic semitone, in 19 equal - chromatic semitone, in 31 equal - minor diesis.

It is possible to use non-meantone scales for Western music, but this means that certain chord progressions will modulate instead of returning to the same pitch (and there is are wolf interval in diatonic and pentatonic scales), so there is no perfect system.

How good is 12 equal as 5-limit system: major whole tone, perfect fourth and fifth are mistuned by 2-3 cents, everything else is out of tune. It is actually in-tune with high harmonics (considered dissonant) and approximates well intervals with factors with 17 and 19 in the ratios.
What does this tell us - that it's 3-limit Pythagorean system (because 9/8, 4/3 and 3/2 are almost perfect) or chromatic system, based on 17th or 19th harmonic.

19 equal is better in 5-limit, but also supports dissonant 23-limit ratios.

31 is good in 5, 7 (septimal blues/African intervals) and 11-limit (neutral seconds, neutral thirds).


----------



## millionrainbows

BabyGiraffe said:


> millionrainbows: "Diatonic" means "two tonics." The C major scale is "diatonic" because it has C and F as strong tonics."
> 
> You again demonstrate ignorance.


Be careful not to stray into ad-hominem territory, BabyGiraffe. I'm mystified that you even have a horse in this race, because you seem more concerned with microtonality and non-ET tunings than you do with straight-up tonality.

And unfortunately, you have quoted an edited-out statement which I have reserved for another thread. The element of surprise is now compromised. Thanks.



> "Diatonic" comes from ancient Greek genera names - diatonic, chromatic and enharmonic. And it doesn't mean two tonics and diatonic scale is not called like that, because of it has C and F as strong tonics, wow.
> Where do you find such wrong ideas?


There's good reason for this, and other theorists have expounded this idea before me. But that's for the other thread.



> And playing a heptatonic scale like a cluster is a terrible idea, all diatonic modes sound bad in this way. I cannot believe you think this is some kind of proof that Lydian is better than others.


That's not what I said to do; you must play the notes as fifths, spread out. Apparently, you have not done this. 
Even so, if you play the scale-cluster "chord" F-G-A-B, it sounds more rooted and consonant than C-D-E-F, which still sounds like a suspension.

millionrainbows: " All the various "temperaments" like mean-tone are based on the attempt to get better major thirds."



> No, temperament means that a just intonation musical system is compromised with non-integer ratios.


What I mean by "meantone" tunings is shown in this chart. How this may apply to your microtonal ideas is a whole 'nother can of worms, and not what this thread is concerned with.


----------



## BabyGiraffe

"you seem more concerned with microtonality and non-ET tunings than you do with straight-up tonality"

What? Are you implying that microtonality has nothing to do with tonality? Have you seen Zarlino's book on counterpoint? You will find there way too much microtonality for your taste, I guess.

There are at least 2 (by Barbour and Bosanquet) old scanned books on tuning, temperament and famous historical tunings online at archive.org 
I suggest comparing the pitch gamuts there with 12 tone selections from 19, 31, 43 and 55 equal. Were piano tuners in the time of Mozart and Beethoven also cranks, wow? You can also learn what is meantone and what is temperament from the books, too, because we see that you refuse to accept that you don't know what are you talking about. 
(Btw, there is a letter, written by Leopold Mozart on violin intonation that describes basically 55 equal). Check Chesnut, John Hind. 1977. "Mozart's teaching of intonation", Journal of the American Musicological Society, vol. 30 no. 2 [summer], pp. 254-271.

" And unfortunately, you have quoted an edited-out statement which I have reserved for another thread. The element of surprise is now compromised. Thanks."

So, it's my fault that you wrongly posted it here? My criticism for your disinformation is still valid.


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## BabyGiraffe

"That's not what I said to do; you must play the notes as fifths, spread out. Apparently, you have not done this. "

Well, obviously you will hear a chain of fifths, I don't know what it has to do with Lydian, because noone is dumb enough to use diatonic scale in such manner for any practical music . You won't hear the tritone, if you don't add one more note (or the volume being loud/distorted enough to hear non-linearities.)


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## millionrainbows

BabyGiraffe said:


> My criticism for your disinformation is still valid.


I question your "information." See the thread.

While you may be correct that different "in-octave" temperaments are essentially "microtonal," I think it's misleading to say that they are based on any sort of microtonal system like 19 or 31 tone ET.

Besides, ANY kind of equal temperament was not *precisely* achieved until after 1900, with the invention of electric frequency generators. Before that, it was all done by ear, using stopwatches.

Equal temperaments are generated and mathematically based on arbitrary numerical divisions of the octave, not ratios. They are used because* they happen to coincide closely with just ratios, but only coincidentally.*

ETs can "approximate" just ratios; that's why Harry Partch used 43-tone ET.

BTW, thanks again BabyGiraffe for posting my deleted statement. The jackals have already descended...


----------



## BabyGiraffe

millionrainbows said:


> I question your "information." See the thread.
> 
> While you may be correct that different "in-octave" temperaments are essentially "microtonal," I think it's misleading to say that they are based on any sort of microtonal system like 19 or 31 tone ET.
> 
> Equal temperaments are generated and mathematically based on arbitrary numerical divisions of the octave, not ratios. They are used because* they happen to coincide closely with just ratios, but only coincidentally.*
> 
> ETs can "approximate" just ratios; that's why Harry Partch used 43-tone ET.


...Mathematicians that were interested in music and tuning theory actually developed many algorithms in mathematical analysis in n-dimensions (so we can find best combinations of 5-limit or whatever intervals we like) to find best tunings. You are wrong, if you think you cannot approximate rationals with irrationals or vice versa. It's quite useful in all sorts of areas.
Anyway, for the human ear these rational and irrational intervals are indistinguishable. 
And the difference between meantone tunings, described in historical books and equal temperaments, supporting meantone, is usually a _fraction of the cent _- enough to close to octave, because any real meantone is also infinite in pitches like JI.

Harry Partch never used any ET. His 43 tone scale is 11 limit tonality diamond along with additional just intervals and is not tempered.
43 equal is actually a meantone (one of the best - with well balanced in mistuning major, minor thirds and fifths; 12 equal has good fifth, 19 equal has good minor third, 31 has good major third; 55 (Mozart's father tuning) is the only other decent small meantone, but it's even closer to 12 equal than all these, so 43 is the only good choice aside from 55 for best small meantone, imo ) tuning unlike his 43 just scale.

https://en.wikipedia.org/wiki/Harry_Partch's_43-tone_scale
https://en.wikipedia.org/wiki/Tonality_diamond

"Besides, ANY kind of equal temperament was not *precisely* achieved until after 1900, with the invention of electric frequency generators. Before that, it was all done by ear, using stopwatches."

How would you comment the fact that Renaissance and Classical era (and even early Romantic) music is based on meantone tunings, but we teach and analyse, and perform (outside of HIP) them using 12 equal? (And don't forget split keyboards on historical keyboard instruments). Of course, this works only because 12 equal supports meantone temperament (along with others like diaschismic, schismic, augmented and diminished temperaments and their corresponding just intonation scales- and all these can be tuned differently even in 12 equal and will have different number or triads and different characteristic chord progressions for each temperament. In fact, much modernist/avantgarde music can be reduced to augmented or diminished temperaments (depending on the composer)- which became available when 12 equal became used, because there is no difference between all of these in 12 equal. The most interesting part is that you can transcribe let's say something by Liszt in 27 equal (but not to any meantone, at least without enharmonic modulations), because music composed in one temperament can be translated between any equal tuning as long as its sticking to the "good" notes and it won't require real enharmonics; that's the main reason why meantone-12 works for Classical and Renaissance, but fails for more modern compositions).


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## isorhythm

Respectfully, this is an inordinate amount of attention paid to phenomena that pertain only to some logistical problems in the tuning of a handful of instruments and not to the vast majority of music made by humans, in which players and singers simply find their pitches by ear.


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## millionrainbows

That can be blamed on BabyGiraffe and his inaccurate distortions.


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## isorhythm

millionrainbows said:


> That can be blamed on BabyGiraffe and his inaccurate distortions.


I meant his stuff about tuning specifically, not the whole thread. I don't know if they're inaccurate.

I still want you to explain whether you think diatonic scales comes from stacking fifths, as you say in this thread, or from the just-intoned ratios (1:1, 9:8, 5:4, 4:3, 3:2, 5:3, 16:15) as you've said in other threads. These two models are of course totally contradictory.

My personal view, in case I haven't been clear, is that the diatonic scales, like all scales, evolved because people thought they made nice-sounding music, for various reasons including but not limited the physical phenomena you've noted.


----------



## millionrainbows

isorhythm said:


> I meant his stuff about tuning specifically, not the whole thread. I don't know if they're inaccurate.


I meant the whole thread.



> I still want you to explain whether you think diatonic scales comes from stacking fifths, as you say in this thread, or from the just-intoned ratios (1:1, 9:8, 5:4, 4:3, 3:2, 5:3, 16:15) as you've said in other threads. These two models are of course totally contradictory.


1:1 is not "incompatible" with any other octave. They are not "contradictory" unless you're looking for reasons to prove me "wrong."
If diatonic scales came from stacking perfect just 3:2 fifths, the difference was ironed-out long ago. Our present ET fifths are only 2 cents flat. This system favors the fifth, and hurts the major third. That's why mean-tone tunings tried to solve this.

If you think it was Greek tetrachords, that is also incompatible because we don't use Greek tuning. It's all incompatible and imperfect.



> My personal view, in case I haven't been clear, is that the diatonic scales, like all scales, evolved because people thought they made nice-sounding music, for various reasons including but not limited the physical phenomena you've noted.


If you "stack" fifths, first you get pentatonics: C-G-D-A E, rearranged in-octave as C-D-E-G-A. Notice that it has no tritone.

If you keep stacking, you get C-G-D-A-E-B-F#, unless you start from F: F-C-G-D-A-E-B.

We were "kissing the diatonic keyboard's a**" by starting on C.

Greek tetrachords? They were used separately, and had nothing to do with scales until later. They don't impress me very much. They are too intertwined with specific history, like the tuning of lyres, and don't have the theoretical elegance of stacked fifths.

3:2: a fifth is still a fifth. I'm not an advocate of "just" intervals like BabyGiraffe is.


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## isorhythm

I know I should let this go, but...

This is you, less than three months ago: https://www.talkclassical.com/61124-what-did-brahms-mean-2.html#post1643710

So what is a major third, according to you? Is it 5:4, or is it the result of stacking fifths, 81:64?

Put another way, when two unaccompanied singers sing a major third in harmony, what do you think they sing?


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## millionrainbows

isorhythm said:


> I know I should let this go, but...
> 
> This is you, less than three months ago: https://www.talkclassical.com/61124-what-did-brahms-mean-2.html#post1643710
> 
> So what is a major third, according to you? Is it 5:4, or is it the result of stacking fifths, 81:64?
> 
> Put another way, when two unaccompanied singers sing a major third in harmony, what do you think they sing?


A major third is a major third, based on a 5:4. In ET, this interval suffers the most from being 'just', at 14 cents flat.

Singers might adjust it. If they've got good ears, they can sing the ET interval.

I don't see how anything I said previously contradicts or disproves this. I'm flexible. I don't make rigid, inflexible pronouncements like BabyGiraffe. The Western music system is imperfect, and I've always stressed that point.


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## BabyGiraffe

isorhythm said:


> Respectfully, this is an inordinate amount of attention paid to phenomena that pertain only to some logistical problems in the tuning of a handful of instruments and not to the vast majority of music made by humans, in which players and singers simply find their pitches by ear.


If you really find pitches by ear, you run into problems like microtonal commas, because we are naturally approximating the best tuning, which is something based on small integers ratios, because these don't beat in a harsh manner, if we are after harmony, of course (it takes a lot of training to become a good singer that doesn't "correct" 12 ET intervals unintentionally - whether this is a good or not is another topic - autotune ruins good vocal performances, quantizing them to 12 equal, despite they were fine before that, despite not being exactly on the 12 pitches grid.).

(And let's not forget that people do what they know; if someone is really interested in new types of music or different takes on the same old stuff, it's way better to understand what is going on than blind experimentation).

Musical systems have different topology and paths in compositional spaces - if we represent a musical system/scale as a graph, we will traverse the nodes in variety of ways to reach our destinations; and these optimal graphs or travel path will be different in different tunings even when using the "same" 12 keys. 
Most of the Western music theory is based on the meantone graph, but this graph is useless for Turkish music for example (I find it fascinating that Turkish musicians use "wolf" fifths and other intervals not found in all music out there).

Isorhythm:
" So what is a major third, according to you? Is it 5:4, or is it the result of stacking fifths, 81:64?"

Intervals from around 370 up to 430 cents can function melodically as major thirds.
Only 5/4 (around 386 cents) will synchronise nicely with 5th harmonic of idealised harmonious instrument (organ, string, electric piano etc).
(We can even calculate the correct tempo that will synchronise even more the texture. Such beatless texture may sound very unnatural.)

12 ET M3rd of 400 cents will have minimum beating with pefect fifth of 720 cents. This is found in 15 equal (note, this doesn't take into account any inversion of the chord and minor chord, if we take them into the equation, this fails and we need flatter fifth and third than what is in 15 equal). 
15 equal doesn't work very well on harmonic instuments, but with additive synthesizers we can detune overtone partials, creating new variations of existing instruments that work better for certain less harmonic tunings.


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## isorhythm

BabyGiraffe said:


> *If you really find pitches by ear*, you run into problems like microtonal commas, because we are naturally approximating the best tuning, which is something based on small integers ratios, because these don't beat in a harsh manner, if we are after harmony, of course (it takes a lot of training to become a good singer that doesn't "correct" 12 ET intervals unintentionally - whether this is a good or not is another topic - autotune ruins good vocal performances, quantizing them to 12 equal, despite they were fine before that, despite not being exactly on the 12 pitches grid.)


It's not really an "if," it is in fact how it's done. No one sings 12ET by ear unless they're accompanied by a 12ET instrument. I doubt it's even possible. Maybe if you're singing a chromatic scale spanning an octave you'll come close. All this stuff about different tunings is just about the practical challenges presented by certain instruments. It's not as fundamental to music as you're making it.



BabyGiraffe said:


> Intervals from around 370 up to 430 cents can function melodically as major thirds.


Yes this is sort of my point.

I suspect that deviations from "ideal" pitch that arise for expressive reasons are bigger than than the differences between various tuning systems in most cases.


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## millionrainbows

isorhythm said:


> It's not really an "if," it is in fact how it's done. No one sings 12ET by ear unless they're accompanied by a 12ET instrument. I doubt it's even possible. Maybe if you're singing a chromatic scale spanning an octave you'll come close. All this stuff about different tunings is just about the practical challenges presented by certain instruments. It's not as fundamental to music as you're making it.


I disagree, Without accompaniment, I sing major thirds in ET. Anybody with a good ear does.


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