# Secondary Dominants



## millionrainbows

This thread is for anything related to secondary dominants. 

The C major scale is C-D-E-F-G-A-B. Its functions are I-ii-iii-IV-vi-viiº.

The secondary dominants of the above are A7-B7-C7-D7-E7, which are the V7s of D-E-F-G-A.

If this is accepted, then the question is: Why does viiº NOT have a secondary dominant?


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## millionrainbows

millionrainbows said:


> This thread is for anything related to secondary dominants.
> 
> The C major scale is C-D-E-F-G-A-B. Its functions are *I-ii-iii-IV-vi-viiº.
> *
> The secondary dominants of the above are A7-B7-C7-D7-E7, which are the V7s of D-E-F-G-A.
> 
> If this is accepted, then the question is: Why does viiº NOT have a secondary dominant?


CORRECTION: I left out V.


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## Guest

Becasue VII° (a diminished triad) cannot function as a *tonic*, it cannot be _*tonicized*_, unlike the other degrees.


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## millionrainbows

TalkingHead said:


> Becasue VII° (a diminished triad) cannot function as a *tonic*, it cannot be _*tonicized*_, unlike the other degrees.


I agree. Why can't it?


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## Woodduck

millionrainbows said:


> I agree. Why can't it?


Because it sounds like crap?


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## millionrainbows

Woodduck said:


> Because it sounds like crap?


I'm surprised you would even post such a thing, knowing how much you like Wagner's music. 

Hey, we can move on to the minor functions, if we finish up here without getting derailed or shut down.


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## Richannes Wrahms

Also, it would be F#7 which would clash with the tonality of C.


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## Woodduck

millionrainbows said:


> I'm surprised you would even post such a thing, knowing how much you like Wagner's music.
> 
> Hey, we can move on to the minor functions, if we finish up here without getting derailed or shut down.


Of course I'm being semifacetious. Diabolus in musica has his place, just like the real devil (who isn't real, though he crops up on TC from time to time), but not at the center of a tonal hierarchy. A dominant at the diminished fifth? Pfui! The unrelated chords and clashing overtones would be bedlam. It would be like a crowd of strangers showing up at your door and claiming to be your sons, daughters, brothers, sisters and cousins twice removed. In short, it would sound like crap, which is why no one ever does it.

I will leave more detailed explanations of crap to our professors. I'm just a humble ballet accompanist.


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## millionrainbows

Woodduck said:


> Of course I'm being semifacetious. Diabolus in musica has his place, just like the real devil (who isn't real, though he crops up on TC from time to time), but not at the center of a tonal hierarchy. A dominant at the diminished fifth? Pfui! The unrelated chords and clashing overtones would be bedlam. It would be like a crowd of strangers showing up at your door and claiming to be your sons, daughters, brothers, sisters and cousins twice removed. In short, it would sound like crap, which is why no one ever does it.
> 
> I will leave more detailed explanations of crap to our professors. I'm just a humble ballet accompanist.


Still, nobody has precisely answered the question: why is there no secondary dominant for viiº? If it is not suitable as a tonic (tonicization), then _why_ is it not suitable?


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## mikeh375

A dominant for the dim. triad that's a tritone higher _might_ be satisfying in a Locrian modal vein but that all depends on one's ears and if the composer can encourage or hoodwink the listener into suspending traditional tonal expectations I guess. If one could sell the diminished triad as a point of return and repose enough times throughout a piece and finally cadence with a dominant 7th on F (in the scale of C that is and complete with an e flat), that resolves to the dim. triad, then the tritone dominant could have a musical logic to my ears. Similarly, the dim triad might also be accepted as a tonic in the usual sense thanks to its tactical and repeated use throughout the piece, similar to how one might often 'touch base' with a true tonic chord in a normal scale.

Of course, there would be be no semitone leading note function, a natural to b being the best alternative (in C), but the flattened 7th of the dominant would resolve as expected (in this case, eflat to d) and the fifth of the dominant (f) would function correctly as a pivot between itself and the dim. tonic.

Despite that, it aint cadentially _Perfect_ as such, nor even is the tritone dominant functioning as a secondary dominant in the way I describe it or the way MR wishes to discuss it, but who wants perfection all the time? Besides there's nothing wrong with keeping music hanging...


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## millionrainbows

mikeh375 said:


> A dominant for the dim. triad that's a tritone higher _might_ be satisfying in a Locrian modal vein but that all depends on one's ears and if the composer can encourage or hoodwink the listener into suspending traditional tonal expectations I guess. If one could sell the diminished triad as a point of return and repose enough times throughout a piece and finally cadence with a dominant 7th on F (in the scale of C that is and complete with an e flat), that resolves to the dim. triad, then the tritone dominant could have a musical logic to my ears. Similarly, the dim triad might also be accepted as a tonic in the usual sense thanks to its tactical and repeated use throughout the piece, similar to how one might often 'touch base' with a true tonic chord in a normal scale.
> 
> Of course, there would be be no semitone leading note function, a natural to b being the best alternative (in C), but the flattened 7th of the dominant would resolve as expected (in this case, eflat to d) and the fifth of the dominant (f) would function correctly as a pivot between itself and the dim. tonic.
> 
> Despite that, it aint cadentially _Perfect_ as such, nor even is the tritone dominant functioning as a secondary dominant in the way I describe it or the way MR wishes to discuss it, but who wants perfection all the time? Besides there's nothing wrong with keeping music hanging...


The question is still "why is there no secondary dominant for viiº? If it is not suitable as a tonic (tonicization), then _why is it not suitable?"
_
Mikeh375 suggests above that a dominant chord be created, and 'worked around,' or that viiº be accepted as a tonic.

Woodduck said "because it sounds like crap." Is he referring to viiº or an imaginary secondary dominant, or the combination, or what? What would sound like crap, and why? His reply suggests that viiº could somehow have a dominant. No, I am not suggesting that, so the reply is "imaginary."

I am not suggesting that viiº should have a secondary dominant; *I agree with the basic premise that viiº doesn't have a dominant.
*
TalkingHead said that viiº doesn't have a dominant because it is somehow unsuitable as a tonic triad, and can't be 'tonicized.' I agree with this.

My question is very simple, maybe too simple, maybe too obvious to mention.

Why is there no secondary dominant for viiº? If it is not suitable as a tonic (tonicization), then _why is it not suitable?"_


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## mikeh375

but the dim. triad _can_ be suitable as a tonic, admittedly not in a standard scale and not for ears expecting the norm ....think music first, theory after. I suppose you want to talk about only maj/min scales then.


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## millionrainbows

mikeh375 said:


> but the dim. triad _can_ be suitable as a tonic, admittedly not in a standard scale and not for ears expecting the norm ....think music first, theory after. I suppose you want to talk about only maj/min scales then.


Pardon me, mikeh375, but to answer the question, you must accept the basic premise, clearly presented in the OP:
*

This thread is for anything related to secondary dominants. *(as presented)

The C major scale is C-D-E-F-G-A-B. Its functions are I-ii-iii-IV-V-vi-viiº.

The secondary dominants of the above are A7-B7-C7-D7-E7, which are the V7s of D-E-F-G-A.

*If this is accepted,* then the question is: Why does viiº NOT have a secondary dominant?

If it is because viiº cannot act as a tonic (tonicization), which I agree with, _then why can't it?

_The question seems simple enough to me.


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## mikeh375

ok fair enough, I admit I digressed a little. But to be fair, I still think it can have a secondary dominant, it's just not in the text books and I did bend the rules a little. A fair cop guv'nor


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## millionrainbows

mikeh375 said:


> ok fair enough, I admit I digressed a little. But to be fair, I still think it can have a secondary dominant, it's just not in the text books and I did bend the rules a little. A fair cop guv'nor


Thank you; We can digress after the basic question is answered, then perhaps move on to the minor scale functions.


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## Phil loves classical

I view the diminished triad as a contraction of the diminished 7th where all tones are equally apart, thus is tonically ambiguous, and can resolve to anything.


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## Guest

millionrainbows said:


> Why does viiº NOT have a secondary dominant?
> If it is because viiº cannot act as a tonic (tonicization), which I agree with, _then why can't it?
> _The question seems simple enough to me.


Well, if we're viewing the issue within the framework of CP harmony then the simple reason why there is no secondary dominant for the triad based on the seventh degree of the scale (vii°) is that *it cannot produce a satisfactory "V-I" perfect cadence* (in the new tonic).

Two expamples to illustrate this:

- Take the second degree of the C major scale (ii = D). Now build a chord on that second degree of the C major scale (D-F-A). 
- Now ask the question: What is the dominant of *ii* (triad D-F-A)? Answer: The dominant of *ii* is of course a 5th higher (or a fourth lower), that is, the note A. 
- Now build your chord on that note A (remember, it has to be a major chord to be a dominant chord) = A-C#-E.
- Resolve and figure this progression: Well, we've built our _secondary dominant_ (A-C#-E) and its normal resolution will be to its "tonic" (the original *ii* triad). In figured bass, this gives *V/ii - ii*. This means V of ii progresses to *ii*: a perfect cadence.

When you apply this procedure to the seventh degree of the scale (vii° = B-D-F = a _*diminished*_ triad) the process breaks down because a satisfactory perfect cadence is not produced. In other words, as rightly mentioned above, it sounds utter crap.

Now, it might well be that in jazz this is not the case - I really couldn't say.


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## mikeh375

Excellent TalkingH, except there will no doubt be an agenda concerning the instability of the scale because of the fourth step/tritone thingymbob or somesuch from MR... what say you Millions...

(it's a trap)


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## Guest

mikeh375 said:


> Excellent TalkingH, except there will no doubt be an agenda concerning the instability of the scale because of the fourth step/tritone thingymbob or somesuch from MR... what say you Millions...
> 
> (it's a trap)


Hah! I know Mike, don't worry, I took the bait knowing it would lead to some very interesting discussions! 
You have to realize that Million is very much like minimalist music _à la_ Reich: a process whereby the material is worked through over an extended period until most of the avenues have been exhausted, followed by a short _dénouement_.


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## millionrainbows

TalkingHead said:


> Well, if we're viewing the issue within the framework of CP harmony then the simple reason why there is no secondary dominant for the triad based on the seventh degree of the scale (vii°) is that *it cannot produce a satisfactory "V-I" perfect cadence* (in the new tonic).


I agree, but positing an imagined unsatisfactory cadence, complete with examples, is going ahead of the basic premise, because it involves imagining a dominant chord above viiº, _which does not exist in CP tonality. _

The premise must be accepted first: The function viiº _DOES NOT _have a secondary dominant.
If it is because viiº cannot act as a tonic (tonicization), which I agree with, then why can't it?


TalkingHead said:


> Now, it might well be that in jazz this is not the case - I really couldn't say.


What makes you think that? Are you labelling me as a jazzer? :lol: I'm joking.


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## millionrainbows

mikeh375 said:


> Excellent TalkingH, except there will no doubt be an agenda concerning the instability of the scale because of the fourth step/tritone thingymbob or somesuch from MR... what say you Millions...
> 
> (it's a trap)


Are you labelling me? :lol: Just joking. 
Your reply is close, very close, but no cigar.

No, really, this is just a simple question framed within CP tonality. I'm surprised nobody has come up with the primary answer, before all this speculating about "if it did" have a dominant, and "what it would sound like if it did." It's been "talked around" but nobody has stated it explicitly.
The basic premise has been stated clearly. No trap.

Clue: the simple answer concerns the viiº itself. Y'all should be able to get it now.


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## Guest

millionrainbows said:


> The premise must be accepted first: *The function viiº DOES NOT have a secondary dominant.
> If it is because viiº cannot act as a tonic (tonicization)*, which I agree with, then why can't it?


Yes, as far as I am concerned, that is so. In major and minor keys, *any triad that is major or minor* can be preceded by its own "dominant chord", be that a triad or a seventh chord. Thus, I also agree with me. :lol:
So come on, Million, what are you driving at?


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## millionrainbows

TalkingHead said:


> Yes, as far as I am concerned, that is so. In major and minor keys, *any triad that is major or minor* can be preceded by its own "dominant chord", be that a triad or a seventh chord. Thus, I also agree with me. :lol:
> So come on, Million, what are you driving at?


You're almost saying it; you're so close.

Yes, the triads that are major or minor can be preceded by a dominant chord called a 'secondary dominant.' This is evident in the OP premise.

The question still remains:

The function viiº _DOES NOT _have a secondary dominant.

•If it is because viiº cannot act as a tonic (tonicization), which I agree with, then _why_ can't it? 
_
•Why_ is viiº excluded from having a secondary dominant? 
_
•Why_ is it unsuitable as a tonic?


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## EdwardBast

millionrainbows said:


> The question is still "why is there no secondary dominant for viiº? If it is not suitable as a tonic (tonicization), then _why is it not suitable?"
> _


_

Because in the major-minor system diminished chords can't be tonics and only tonics or tonicized triads have dominants. It's in the basic definitions of dominant and tonic._


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## Guest

EdwardBast said:


> Because in the major-minor system diminished chords can't be tonics and only tonics or tonicized triads have dominants. It's in the basic definitions of dominant and tonic.


I thought I had already explained that!


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## Woodduck

By definition, a tonic chord in the major-minor system always consists of the first scale degree and the perfect fifth above it, with the major or minor third in between. 

Also by definition, the dominant of a key is the triad built on the scale degree a perfect fifth above or, in inversion, a fourth below the tonic. 

A triad built on the seventh degree of the major scale, using no chromatic alterations, can't contain a perfect fifth above or a perfect fourth below and thus can't meet the definition of a tonic, and since those tones don't exist for the construction of a dominant, there can be no dominant either.

As Mikeh375 says, we could build an artificial system centering on the seventh degree, but assuming one on B, the "dominant" would be an F major triad, which is already the dominant of Bb, and we'd have the further anomaly of our dominant being equidistant from its tonic whether counting steps from above or below it. 

This is all too weird, folks. Count me out.


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## Guest

Woodduck said:


> By definition, a tonic chord in the major-minor system always consists of the first scale degree and the perfect fifth above it, with the major or minor third in between.
> 
> Also by definition, the dominant of a key is the triad built on the scale degree a perfect fifth above or, in inversion, a fourth below the tonic.
> 
> A triad built on the seventh degree of the major scale, using no chromatic alterations, can't contain a perfect fifth above or a perfect fourth below and thus can't meet the definition of a tonic, and since those tones don't exist for the construction of a dominant, there can be no dominant either.
> 
> As Mikeh375 says, we could build an artificial system centering on the seventh degree, but assuming one on B, the "dominant" would be an F major triad, which is already the dominant of Bb, and we'd have the further anomaly of our dominant being equidistant from its tonic whether counting steps from above or below it.
> 
> *This is all too weird, folks. Count me out.*


Hang around a bit, Woodduck, we're waiting for the dénouement from MR. Otherwise, as far as I'm concerned, you, me, Mike and Edward are singing from the same hymn sheet.


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## Woodduck

TalkingHead said:


> Hang around a bit, Woodduck, we're waiting for the dénouement from MR. Otherwise, as far as I'm concerned, you, me, Mike and Edward are singing from the same hymn sheet.


I'm not leaving, merely looking on quietly in shock and awe.


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## Guest

TalkingHead said:


> Before member *Christabel* has a go at me for this, I did mean to write "because" and not what appears in my original post. Then again, I shouldn't be too worried about any intervention from Christabel (AKA a whole bunch of alternative forum names) because - so I hear - this forum is not worthy of her attention.


Don't you have anybody else to love you, Philip, Talking Head, Quijote?


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## millionrainbows

EdwardBast said:


> *Because in the major-minor system diminished chords can't be tonics and only tonics or tonicized triads have dominants.* It's in the basic definitions of dominant and tonic.


*I agree, *but the question has still not been explicitly answered.

The question is still "*Why* is there no secondary dominant for viiº? If it is not suitable as a tonic (tonicization), then *why is it not suitable?"
*


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## millionrainbows

Woodduck said:


> By definition, a tonic chord in the major-minor system always consists of the first scale degree and the perfect fifth above it, with the major or minor third in between.
> 
> Also by definition, the dominant of a key is the triad built on the scale degree a perfect fifth above or, in inversion, a fourth below the tonic.
> 
> *A triad built on the seventh degree of the major scale, *using no chromatic alterations, *can't contain a perfect fifth above or a perfect fourth below *and thus can't meet the definition of a tonic,and since those tones don't exist for the construction of a dominant, there can be no dominant either.
> 
> As Mikeh375 says, we could build an artificial system centering on the seventh degree, but assuming one on B, the "dominant" would be an F major triad, which is already the dominant of Bb, and we'd have the further anomaly of our dominant being equidistant from its tonic whether counting steps from above or below it.
> 
> This is all too weird, folks. Count me out.


Woodduck finally answered it, but not absolutely perfectly. 
The answer concentrates on the viiº triad, and its lack of a perfect fifth, and therefore its unsuitability as a tonic station with a secondary dominant.

We should all note that perfect fifths create stable triads.

BTW, *I highlighted only the portion which answers the question directly. *"Using no chromatic alterations" (in green) is extraneous: it is a given that viiº is a diminished triad.

viiº is a diminished triad, so the exclusionary "definition of a dominant" you gave (in red) is still indirect, since it deals with a dominant which does not exist.

The "definition of a tonic" which you mention (in blue) but did not explicitly define, couldn't be used because it was not explicitly stated except in relation to viiº as an exception. It did not focus directly on viiº, but merely excluded it from a definition of other tonic triads.

A more perfect answer would have *not* used the phrase "*can't contain a perfect fifth above or a perfect fourth below" *(in grey), but instead would say "viiº does not contain a perfect fifth," which focuses on the given viiº without referring to a prohibitive rule which was not stated explicitly.

Now we can move on to minor scale functions.


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## Woodduck

millionrainbows said:


> Woodduck finally answered it. The answer concentrates on the viiº triad, and its lack of a perfect fifth, and therefore its unsuitability as a tonic station with a secondary dominant.
> 
> We should all note that perfect fifths create stable triads.
> 
> Now we can move on to minor scale functions.


Looks like my "academic thought-style" paid off this time. :devil:


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## millionrainbows

Yes; this was a "reverse trap" set for academics, partly to test the general trust level. Notice my new edits before you relax. The edits expose academic habits which are unsatisfactory because they do not directly address the reasoning behind anything; they only prohibit or exclude. Good thinking should always address the direct nature of things. Thus, we can attempt to get closer to real music instead of ideas about music.


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## Woodduck

millionrainbows said:


> Yes; this was a "reverse trap" set for academics, partly to test the general trust level. Notice my new edits before you relax. The edits expose academic habits which are unsatisfactory because they do not directly address the reasoning behind anything; they only prohibit or exclude. Good thinking should always address the direct nature of things. Thus, we can attempt to get closer to real music instead of ideas about music.


Yes, professor. Your pop quizzes are challenging, but then I'm no academic, just a practicing musician.


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## millionrainbows

Woodduck said:


> Yes, professor. Your pop quizzes are challenging, but then I'm no academic, just a practicing musician.


Then I am wrong for saying such a thing in the context of an orthodox subject like "secondary dominants" which is the point I am trying to show by this thread.

But there are times I like to speculate outside those bounds, and am called "irrational." That's the big disappointment for me. Unlike listening to music and discussing it, the area of music theory is based on ideas, not simply opinion. That's the big difference that everyone needs to bear in mind.


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## Woodduck

millionrainbows said:


> Unlike listening to music and discussing it, the area of music theory is based on ideas, not simply opinion. That's the big difference that everyone needs to bear in mind.


Not _simply_ opinion, but opinion does factor in. You'll acknowledge, I think, that there are reasonable differences in how we analyze some things even within a given ideological framework. That applies particularly to tonal harmony in the late Romantic-Modern period, where chords can function simultaneously in more than one way, or even seem to resist functional analysis, and different people hear them differently. I think discussions we've had of the "Tristan chord" show this.


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## Guest

Can anyone tell me what *the slur with the dot below it* means here as I long ago forgot; it's been ages since I played the piano: use it or lose it, as they say! Bars 19, 20 and 21 of the third movement:


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## Woodduck

Christabel said:


> Can anyone tell me what *the slur with the dot below it* means here as I long ago forgot; it's been ages since I played the piano: use it or lose it, as they say! Bars 19, 20 and 21 of the third movement:


Not sure what he wants, but my best guess would be a slight detachment of the notes, a tiny bit of space between them. Not quite a staccato, which they'd be without the slur.


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## mikeh375

millionrainbows said:


> Then I am wrong for saying such a thing in the context of an orthodox subject like "secondary dominants" which is the point I am trying to show by this thread.
> 
> But there are times I like to speculate outside those bounds, and am called "irrational." That's the big disappointment for me. Unlike listening to music and discussing it, *the area of music theory is based on ideas, not simply opinion*. That's the big difference that everyone needs to bear in mind.


Here's some more thinking out loud. 
Perhaps opinion is quite important here and maybe more so than 'ideas'. Aesthetic opinion can, via general consensus, accept new innovations in music that will introduce new theory and a new way of doing things. Also, theory often comes 'after the event' and it's success or failure is dependant on its efficacy in pragmatic situations. So here are two strands that influence theory. Firstly, that of opinion (or subjective evaluation perhaps), i.e. one that decides if an innovation or alternative way of doing things is worthy and perhaps more importantly, fruitful in a creative sense. And secondly, maybe a kind of opinionated pragmatism - is the new successful in performance? Does it innovate and communicate at the same time?
AND thirdly, I've digressed again haven't I?


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## millionrainbows

Woodduck said:


> Not _simply_ opinion, but opinion does factor in. You'll acknowledge, I think, that there are reasonable differences in how we analyze some things even within a given ideological framework. That applies particularly to tonal harmony in the late Romantic-Modern period, where chords can function simultaneously in more than one way, or even seem to resist functional analysis, and different people hear them differently. I think discussions we've had of the "Tristan chord" show this.


Yes, it's called "different thought-styles."


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## millionrainbows

Christabel said:


> Can anyone tell me what *the slur with the dot below it* means here as I long ago forgot; it's been ages since I played the piano: use it or lose it, as they say! Bars 19, 20 and 21 of the third movement:


I thought this thread was for secondary dominants, and that we were going to discuss this as applied to minor keys. Just saying. I can't control what happens here, only suggest.


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## Guest

millionrainbows said:


> I thought this thread was for secondary dominants, and that we were going to discuss this as applied to minor keys. Just saying. I can't control what happens here, only suggest.


OK, it's the quickest one I could find with 'theory' but please just forget I asked.


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## millionrainbows

Christabel said:


> OK, it's the quickest one I could find with 'theory' but please just forget I asked.


That's beside the point, since your question was answered in post #38.
dgam, jga


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## Woodduck

millionrainbows said:


> Yes, it's called "different thought-styles."


That is not a response to my point.

The term "thought-styles" seems to be used only by you, and you're now in the process of riding that horse to death in thread after thread, evidently trying to make it a popular idiom on TC.

"Style" is word applicable to art, fashion and maybe cuisine. It's been popularly used since - when, the '70s? - in the cringey word "lifestyle," which we've all had to get used to (but fortunately are not compelled to use). "Thought-style" is at least as cringey.

Thinking is thinking. It 's either useful thinking or it isn't. What matters is whether it's conducive to an understanding of reality. In the case of harmonic analysis, there are different systems of analysis which may be applicable to a given example. A single analyst may apply more than one system to the case in question. He doesn't need to switch "thought-styles" in order to do so.

If you'd care to respond thoughtfully to my post, as I responded thoughtfully to yours, I would welcome it.


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## millionrainbows

Woodduck said:


> That is not a response to my point.
> 
> The term "thought-styles" seems to be used only by you, and you're now in the process of riding that horse to death in thread after thread, evidently trying to make it a popular idiom on TC.


Actually, I got the term from a dear friend who died, and I use it in his memory.



> "Style" is word applicable to art, fashion and maybe cuisine. It's been popularly used since - when, the '70s? - in the cringey word "lifestyle," which we've all had to get used to (but fortunately are not compelled to use). "Thought-style" is at least as cringey.


You are the one who asked "What the heck is a thought-style" in a mean-spirited context of a very toxic post towards me. If it irritates you, it's not my problem, and pointing it out to me repeatedly will make no difference.



> Thinking is thinking. It 's either useful thinking or it isn't. What matters is whether it's conducive to a understanding of reality. In the case of harmonic analysis, there are different systems of analysis which may be applicable to a given example. A single analyst may apply more than one system to the case in question. He doesn't need to switch "thought-styles" in order to do so.


If CP approach applies, such as the concept of "secondary dominants," then I have used it to prove a point.

The question is not really one of "switching thought-styles" or modes of thought, so much as_ simultaneously juggling different approaches, and not speaking as if one way is absolute, axiomatic, or a given.

_I am especially fond of ways of thinking about and experiencing music which involve _direct perception and experience of sound itself, rather than systems or "common practices."
_


> If you'd care to respond thoughtfully to my post, as I responded thoughtfully to yours, I would welcome it.


I've tried to. In fact, I have been constantly searching for some way to put your outlook into perspective, and to maintain my own dignity in the face of onslaughts which are quick, rushed, and give a very distinct and obvious impression that the intent is to invalidate me as a thinker and a person. Unlike yourself, from what you've said even recently, _I believe that our posts here are expressions of ourselves as real people._

I have thus considered this "the way of the internet," which may deflect the blame from individuals to a more "herd mentality."

("herd thought-style")


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## Woodduck

mikeh375 said:


> Here's some more thinking out loud.
> Perhaps *opinion is quite important here and maybe more so than 'ideas'.* Aesthetic opinion can, via general consensus, accept new innovations in music that will introduce new theory and a new way of doing things. Also, *theory often comes 'after the event' *and it's success or failure is dependant on its efficacy in pragmatic situations. So *here are two strands that influence theory. Firstly, that of opinion (or subjective evaluation perhaps), i.e. one that decides if an innovation or alternative way of doing things is worthy and perhaps more importantly, fruitful in a creative sense. And secondly, maybe a kind of opinionated pragmatism - is the new successful in performance? Does it innovate and communicate at the same time?*
> AND thirdly, I've *digressed* again haven't I?


It may be a digression, but it's a good one.


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## millionrainbows

mikeh375 said:


> Here's some more thinking out loud.
> Perhaps opinion is quite important here and maybe more so than 'ideas'. Aesthetic opinion can, via *general consensus*, accept new innovations in music that will introduce new theory and a new way of doing things. Also, theory often comes 'after the event' and it's success or failure is dependant on its *efficacy in pragmatic situations*. So here are two strands that influence theory. Firstly, that of opinion (or subjective evaluation perhaps), i.e. *one that decides if an innovation or alternative way of doing things is worthy and perhaps more importantly, fruitful in a creative sense*. And secondly, maybe a kind of *opinionated pragmatism *- is the new successful in performance? Does it innovate and communicate at the same time?
> AND thirdly, I've digressed again haven't I?


This sounds like a vague description of the academic thinking.
This kind of thinking (thought-style) can be bypassed by the direct experience of listening, not theories or systems of CP tonality.


----------



## Guest

millionrainbows said:


> That's beside the point, since your question was answered in post #38.
> dgam, jga


So why did you bother to comment? You have way too much free time on your hands.


----------



## mikeh375

millionrainbows said:


> This sounds like a vague description of the academic thinking.
> This kind of thinking (thought-style) can be bypassed by the direct experience of listening, not theories or systems of CP tonality.


No, it has nothing to do with academic thought and everything to do with the composing and playing of music.

Your kind of thinking here is a willful distortion of mine so I'll bypass it - thanks anyway though. Music first, theory later...is that clearer?


----------



## Bwv 1080

the dim or half dim vii chord is a sub for V, so V/V - vii dim is kosher.


----------



## millionrainbows

mikeh375 said:


> Here's some more thinking out loud.
> Perhaps opinion is quite important here and maybe more so than 'ideas'. Aesthetic opinion can, via general consensus, accept new innovations in music that will introduce new theory and a new way of doing things. Also, theory often comes 'after the event' and it's success or failure is dependant on its efficacy in pragmatic situations. So here are two strands that influence theory. Firstly, that of opinion (or subjective evaluation perhaps), i.e. one that decides if an innovation or alternative way of doing things is worthy and perhaps more importantly, fruitful in a creative sense. And secondly, maybe a kind of opinionated pragmatism - is the new successful in performance? Does it innovate and communicate at the same time?
> AND thirdly, I've digressed again haven't I?





mikeh375 said:


> No, it has nothing to do with academic thought and everything to do with the composing and playing of music. Your kind of thinking here is a willful distortion of mine so I'll bypass it - thanks anyway though. Music first, theory later...is that clearer?


Your ideas apply in many situations, but that's for your 'consensus opinion group' in whatever musical situation you are in yourself: church, choir, men's glee club, etc.

I'm not just talking theory, I'm talking about performance and using your ears to express your personality and being; to make art out of music.

I just don't agree with the general idea that CP music theory is the 'foundation' of all our music. It's part of another era. If a person is composing music these days, then soundtrack music is much 'freer' and not bound by CP tonal practices and rules, especially in the harmonic realm. Yes, there is useful information to be gleaned from CP, such as good-sounding voice leading.

As Pat Martino the jazz guitarist knows, the very language (notation, ideas, concepts) we use to communicate music emerged from a source that ends up favoring the keyboard, not the guitar or other instruments. It's diatonically based, as well, and only really includes major/minor scales. Modern modal thinking had to come in later. Key signatures are rather archaic if you are composing music which changes a lot or is very chromatic.

Yes, anyone who wants to call himself a musician has learned this system and its key signatures, etc; and has learned to work with it, and work around it.

So what's the alternative? None, really, it's the system we are stuck with. But I ask that we be less rigid about music in general, and when talking theory, because music can be created by ear, and ideas about music need not be bound by CP practices, especially in the realm of chords.


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## millionrainbows

Christabel said:


> So why did you bother to comment? You have way too much free time on your hands.


It was just a tap on the shoulder, like when somebody is talking on a cell phone in the middle of the grocery aisle.


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## Guest

Christabel said:


> Can anyone tell me what *the slur with the dot below it* means here as I long ago forgot; it's been ages since I played the piano: use it or lose it, as they say! Bars 19, 20 and 21 of the third movement:


I'm pretty sure this is not an attempt at thread derailment. 
Come on, Christabel, it don't take [sic] a planetary-sized brain to open a new thread on piano articulation.


----------



## Guest

Some people feel they need that for one, small question; others have lives to live and take the easier path. Planetary-sized brains can always find better things to do. Simples.


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## Guest

Christabel said:


> Some people feel they need that for one, small question; *others have lives to live and take the easier path*. Planetary-sized brains can always find better things to do. Simples.


Oh really? I think if you made the effort and posted such queries in a dedicated thread you might find an interested audience.
Off you go, brains.


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## Guest

Minute details of what happens on an internet message board, chapter and verse, seem to be your particular obsession. Haven't you got some interesting, challenging books to read or meals to be getting on with?

I don't care about an 'interested audience', just the answer to a simple question. If you didn't know that you only had to say so. But you've got my attention; that's what you wanted, isn't it?


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## Woodduck

There's nothing quite like music theory to bring out the dark side of human nature.


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## Guest

Woodduck said:


> There's nothing quite like music theory to bring out the dark side of human nature.


:lol: You never attended any music analysis conferences, Woodduck?


----------



## Guest

Christabel said:


> Haven't you got some interesting, *challenging books* to read or *meals to be getting on with?*


I have, I have! One is "How to make friends and influence people" but I just can't get my head around it! On the meals side, I'm working on recipes to help those with weight issues and dietary regimes to boost the IQ of Jordan Peterson groupies, that's how caring I am.



Christabel said:


> *I don't care about an 'interested audience'* [...]


Are you serious? Is that why you post left, right and centre on various forums, on Twitter and write "Mrs Enid Scroggs, outraged of Bankstown" letters to the Sydney newspapers?


----------



## Woodduck

TalkingHead said:


> :lol: You never attended any music analysis conferences, Woodduck?


I can't think about that now. I'm social distancing.


----------



## Guest

Woodduck said:


> I can't think about that now. I'm social distancing.


Wise, very wise. May the spirit of the Secondary Dominant bless your persecuted - may I say, in some esoteric way, circumcised - diminished triad.


----------



## Woodduck

TalkingHead said:


> Wise, very wise. May the spirit of the Secondary Dominant bless your persecuted - may I say, in some esoteric way, circumcised - diminished triad.


That makes me want to listen to Gershon Sirota, and I'm not even Jewish.


----------



## millionrainbows

The *parallel minor chords* in relation to C major, and their functions.

i-iiº-bIII-iv-v-bVI-bVII.
i is C minor, iiº is D diminished, bIII is Eb major, iv is F minor, v is G minor, bVI is Ab major, bVII is Bb major.

Any problem with this basic information? Any mistakes or typos?

If not, I'd like to go on to discuss *secondary diminished chords.* Each one of the secondary dominants discussed earlier has a corresponding "secondary diminished" chord.

Any problems so far?

I especially want to relate my experiences in the music theory courses I took, concerning diminished _sevenths._


----------



## millionrainbows

Okay, since no one wants to discuss secondary dominants in an orthodox CP context, I'll take off on some wild speculation that Woodduck and EdwardBast can shred and invalidate.

As you recall from the OP, the basic information is this:




> The C major scale is C-D-E-F-G-A-B. Its functions are I-ii-iii-IV-vi-viiº.





> The secondary dominants of the above are A7-B7-C7-D7-E7, which are the V7s of D-E-F-G-A.



The C is already taken care of, with its G7 dominant. Why doesn't viiº have a dominant?

I'll tell you what my ear says: it does!

In C major: When I learned about viiº in school, _I always doubted that viiº was actually a "triad" with a "root" on B._

Can you believe that? I always doubted this "given" CP axiom! My ear told me it was not true! And I believed my ear!

What a deluded beginner, you might say!
_
In fact, to this day, I still do not really consider diminished chords to be "real" triads._

I can hear Woodduck chiming in, saying _"Real triad? What is that?"_

It's what my ear tells me, not an ideology!

Would anyone care to continue, and find out what the "real" dominant of viiº is?


----------



## Woodduck

millionrainbows said:


> I can hear Woodduck chiming in, saying _"Real triad? What is that?"_


If you can hear Woodduck saying that, you need to stop bragging about your ear.


----------



## millionrainbows

Woodduck said:


> If you can hear Woodduck saying that, you need to stop bragging about your ear.


Ha ha ha! That's very logical.

But you come closer to that when you say "musical ideas" exist as "music in your head." Now you & the deaf Beethoven can go tiptoeing through the tulips together. :lol:

I didn't "brag about my ear;" I said I consider it first. It must be a good one, compared to what I've heard people saying who are blindly adhering to ideological CP 'axioms.'

Still no takers for secondary dominants?


----------



## Woodduck

millionrainbows said:


> Ha ha ha! That's very logical.


Logic is the funniest thing in the world, next to sex. Eden was a pretty dull place, forbidden fruit and all, but When Adam and Eve noticed they were naked and made the appropriate deductions based on the evidence, logic and sex were born simultaneously and Old Nobodaddy had his first laugh.

At least that's how I think it went.


----------



## mikeh375

Woodduck said:


> Logic is the funniest thing in the world, next to sex. Eden was a pretty dull place, forbidden fruit and all, but When Adam and Eve noticed they were naked and made the appropriate deductions based on the evidence, logic and sex were born simultaneously and Old Nobodaddy had his first laugh.
> 
> At least that's how I think it went.


ahhh, so we are talking about dominance and secondary dominance. Is that right?...no hang on...ohhh.


----------



## Woodduck

mikeh375 said:


> ahhh, so we are talking about dominance and secondary dominance. Is that right?...no hang on...ohhh.


I don't know whether Adam and Eve were into dominance. I suspect that secondary dominance had to wait for later generations to figure out. Maybe it's what provoked the great flood.


----------



## millionrainbows

Woodduck said:


> I don't know whether Adam and Eve were into dominance. I suspect that secondary dominance had to wait for later generations to figure out. Maybe it's what provoked the great flood.


Eve could use the snake as a whip. No takers on the viiº subject of post #64? I can bring in Walter Piston and Schoenberg as my back-ups. Does that scare anyone?


----------



## Woodduck

millionrainbows said:


> Eve could use the snake as a whip. No takers on the viiº subject of post #64? I can bring in Walter Piston and Schoenberg as my back-ups. Does that scare anyone?


OK, I'll bite. (Nobody named rainbows can scare me, BTW.) I do _not_ hear the tritone on vii as having a tonic or a dominant. Did you say that it's a CP "axiom" that B-D-E has a "root" on B? I've never heard of that axiom, and would doubt that CP theory actually accepts it - but then, as a musician who's picked up some theory on the fly, I don't really know what various theorists have said. In CP _practice_ tonic and dominant apply only to the major-minor system, which always places tonic and dominant key centers a perfect fifth (or fourth in inversion) apart and builds its tonal hierarchy from there.


----------



## mikeh375

.......................... ooops, see below..........................


----------



## mikeh375

millionrainbows said:


> *Eve could use the snake as a whip. *No takers on the viiº subject of post #64? I can bring in Walter Piston and Schoenberg as my back-ups. Does that scare anyone?


LOL. It bothers me a little that I can picture that....
I read Piston and Schoenberg many years ago, no, they don't scare me.

Anyone want to take a bet on our gurus "real" secondary dominant of the dim. triad on b being a dim. triad on F sharp? ....yes... I know...F sharp in C major!!! The Lydian wins out. Or something like that.


----------



## Guest

millionrainbows said:


> Eve could use the snake as a whip. No takers on the viiº subject of post #64? I can bring in *Walter Piston and Schoenberg* as my back-ups. Does that scare anyone?


I'll see your Piston and Schoenberg and raise you a trio of *William Lovelocks* and a *George Heussenstamm*. Put that in your shisha pipe and smoke it.


----------



## mikeh375

TalkingHead said:


> I'll see your Piston and Schoenberg and raise you a trio of *William Lovelocks* and a *George Heussenstamm*. Put that in your shisha pipe and smoke it.


I'll second Lovelock and raise you Hanson.


----------



## EdwardBast

mikeh375 said:


> Anyone want to take a bet on our gurus "real" secondary dominant of the dim. triad on b being a dim. triad on F sharp? ....yes... I know...F sharp in C major!!! The Lydian wins out. Or something like that.


You too, huh? I've been waiting for that inevitable groaner since the thread started.


----------



## millionrainbows

Woodduck said:


> OK, I'll bite. (Nobody named rainbows can scare me, BTW.) I do _not_ hear the tritone on vii as having a tonic or a dominant. Did you say that it's a CP "axiom" that B-D-E has a "root" on B? I've never heard of that axiom, and would doubt that CP theory actually accepts it - but then, as a musician who's picked up some theory on the fly, I don't really know what various theorists have said. *In CP practice tonic and dominant apply only to the major-minor system, *which always places tonic and dominant key centers a perfect fifth (or fourth in inversion) apart and builds its tonal hierarchy from there.


Well then, you've thrown a wrench in the gears.

If 'tonic' and 'dominant' apply only to _major-minor chords,_ then this is a separate issue which only partially explains, by exclusion, the CP 'given' that viiº (B) is not considered a tonic/secondary dominant station. It does not indicate why this is, so we are compelled to infer.

In order for the discussion to continue in CP terms, you must accept that functions are assigned to the seven scale steps in CP theory.

The 'given' CP theory [_tonics on C-D-E-F-G-A, with secondary dominants on A-B-C-D-E]_ admittedly _does_ imply that there is _['no tonic' on viiº (B)]_, but does this _only by omission;_ if viiº has no secondary dominant, it can be (only) _assumed_ that this is because it supposedly cannot function as a tonic on B.

So the viiº must be explained, in order to proceed. Two questions:

*Why does CP theory list viiº as a function?* Does viiº fit the designation of a function, and how might it differ? Is viiº a "function" like the others? What exactly is meant by "function," and does the viiº function have to meet any requirement to be considered as a true function like the other steps?

*Why is viiº called a triad? Is viiº a triad? Why, or how does it differ from other triads?

Are there answers to these questions, or can I "sit pretty," safe in the realization that the tritone B-F reveals a glitch in the CP major-minor system? Are these are the same old culprits of B and F, just as I've always maintained?

If Woodduck does not hear the tritone on viiº as having a tonic, then "should he?" What would be an advantage of hearing viiº in this way? Did Beethoven hear this? If so, what evidence in his works is there?

*BTW, mikehaines375's guess is wrong. Not F#.*

BTW, the diminished symbol is alt+0 (zero).
*


----------



## mikeh375

Mikehaines375 might be wrong (new member?), but as far as I can hear, a dim. chord on f sharp sounds reasonable as a secondary dominant. There aren't many pure dim. chord options as a secondary dominant to explore and the ones on e and c sound fine too as viiº's all imply dominants anyway. Does your way of thinking just involve the viiº triad with no extra notes or is your preference for a dominant 7th chord? (thanks for the keystroke btw, that was bugging me).
Diminished chords can also be spelt and resolve differently, is that part of your thinking?


----------



## millionrainbows

EdwardBast said:


> You too, huh? I've been waiting for that inevitable groaner since the thread started.


This supposed conclusion of mikeh375, and EdwardBast's implicit agreement, that this will be my answer is incorrect. My answer has back-up from common practice of Beethoven. You guys assume _way_ too much about me, and tend to underestimate me.


----------



## millionrainbows

mikeh375 said:


> Mikehaines375 might be wrong (new member?), but as far as I can hear, a dim. chord on f sharp sounds reasonable. There aren't many pure dim. chord options as a secondary dominant to explore and the ones on e and c sound fine too as viiº's all imply dominants anyway. Does your way of thinking just involve the viiº triad with no extra notes or is your preference for a dominant 7th chord? (thanks for the keystroke btw, that was bugging me).


Thank you for the civil answer, mikeh375. Regardless of the perception of certain members, my intentions are not sinister, and I'm not really a bad person. "I am worthy, I belong, and I have something valuable to contribute" as the saying goes.

My proposal is going to keep the viiº as it is, B-D-F, and not expanding it to a dim7 by adding F#.

But *this explanation is contingent upon the questions in post #77 being answered, since Woodduck made the statements: 
*


> I do not hear the tritone on vii as having a tonic or a dominant


_
That's not what I said about viiº. Wooduck's reply is in keeping with the CP chart of secondary dominants, but that's __not what I said about viiº. I said:
__
_


> Why doesn't viiº have a dominant?
> 
> I'll tell you what my ear says: it does!
> 
> _I always doubted that viiº was actually a "triad" with a "root" on B._
> 
> _In fact, to this day, I still do not really consider diminished chords to be "real" triads._


Since I don't hear viiº as a tonic triad with root on B, I still consider it as part of the "tonic/dominant" system. When I say "it does have a dominant," it is of course a different kind of relationship, since B is not a tonic.

Woodduck also implies, and sides with, the implication that "function" does not imply a root, and also as a consequence that the term "triad" does not imply a root, since viiº can't function as a tonic (by exclusion from the chart of secondary dominant relationships), *but offers no evidence or argument for this assertion or attempts to clarify his rebuttals.*
_
_


> I do _not hear the tritone on vii as having a tonic or a dominant. *Did you say that it's a CP "axiom" that B-D-E has a "root" on B?* I've never heard of that axiom, and *would doubt that CP theory actually accepts it* - but then, as a musician who's picked up some theory on the fly, I don't really know what various theorists have said. *In CP **practice** tonic and dominant apply only to the major-minor system*, which always places tonic and dominant key centers a perfect fifth (or fourth in inversion) apart and builds its tonal hierarchy from there._


That explains why, by exclusion, viiº as a diminished triad is not considered as a secondary dominant, but offers no reason why; only rebuttals to my statements.


----------



## Woodduck

millionrainbows said:


> Woodduck also implies, and sides with, the implication that "function" does not imply a root, and also as a consequence that the term "triad" does not imply a root, since viiº can't function as a tonic (by exclusion from the chart of secondary dominant relationships), but offers no evidence or argument for this assertion or attempts to clarify his rebuttals.
> 
> That explains why, by exclusion, viiº as a diminished triad is not considered as a secondary dominant, but offers no reason why; only rebuttals to my statements.


Holy crap. I think we're in the midst of a theoretical pandemic. Cerebral hypertrophy?

I wasn't offering any "rebuttals." I simply said that I hear no tonicity in vii, that therefore I can't assign it a dominant, and that if there's no "primary dominant" there can be no "secondary dominant." Aren't you constantly asking people to say what they hear, without appeal to theory? Well, that's what I hear. Like it or lump it.


----------



## millionrainbows

Woodduck said:


> I simply said that I hear no tonicity in vii, that therefore I can't assign it a dominant, and that if there's no "primary dominant" there can be no "secondary dominant."


If you mean this strictly literally, as in "B is not the tonic," I agree. I hear no "tonic triad with B as root."

_That's not what I said about viiº. I said:


Why doesn't viiº have a dominant?

I'll tell you what my ear says: it does!

I always doubted that viiº was actually a "triad" with a "root" on B.

In fact, to this day, I still do not really consider diminished chords to be "real" triads.


Since I don't hear viiº as a tonic triad with root on B, I still consider it as part of the "tonic/dominant" system. When I say "it does have a dominant," it is of course a different kind of relationship, since B is not a tonic. Again, _I do hear "tonicity" in the notes B-D-F. Just not root on B.
B-D-F can be considered as part of a dominant triad, and that's the way Beethoven heard it as well.


> Aren't you constantly asking people to say what they hear, without appeal to theory? Well, that's what I hear. Like it or lump it.


I think you can hear it; it's because _I said it_ that you say you can't or you are nitpicking at some detail of how I said it instead of trying to acknowledge the idea.


----------



## Woodduck

millionrainbows said:


> If you mean this strictly literally, as in "B is not the tonic," I agree. I hear no "tonic triad with B as root."
> 
> _That's not what I said about viiº. I said:
> 
> 
> Why doesn't viiº have a dominant?
> 
> I'll tell you what my ear says: it does!
> 
> I always doubted that viiº was actually a "triad" with a "root" on B.
> 
> In fact, to this day, I still do not really consider diminished chords to be "real" triads.
> 
> 
> Since I don't hear viiº as a tonic triad with root on B, I still consider it as part of the "tonic/dominant" system. When I say "it does have a dominant," it is of course a different kind of relationship, since B is not a tonic. Again, _I do hear "tonicity" in the notes B-D-F. Just not root on B.
> B-D-F can be considered as part of a dominant triad, and that's the way Beethoven heard it as well.
> 
> I think you can hear it; it's because _I said it_ that you say you can't or you are nitpicking at some detail of how I said it instead of trying to acknowledge the idea.


Stop defending yourself against nonexistent attacks. If you think my statement unresponsive to yours, it may be because I don't really see what you want here. Can you put it in the form of a specific question?


----------



## millionrainbows

Woodduck said:


> Stop defending yourself against nonexistent attacks. If you think my statement unresponsive to yours, it may be because I don't really see what you want here. Can you put it in the form of a specific question?


Yes, I already did, in post #77. Two questions, then we can proceed:

*Why does CP theory list viiº as a function? *Does viiº fit the designation of a function, and how might it differ? Is viiº a "function" like the others? What exactly is meant by "function," and does the viiº function have to meet any requirement to be considered as a true function like the other steps?*

Why is viiº called a triad? *Is viiº a triad? Why, or how does it differ from other triads?

Are there answers to these questions, or can I "sit pretty," safe in the realization that the tritone B-F reveals a glitch in the CP major-minor system? Are these are the same old culprits of B and F, just as I've always maintained?

If Woodduck does not hear the tritone on viiº as having a tonic, then "should he?" What would be an advantage of hearing viiº in this way? Did Beethoven hear this? If so, what evidence in his works is there?


----------



## Woodduck

millionrainbows said:


> Yes, I already did, in post #77. Two questions, then we can proceed:
> 
> *Why does CP theory list viiº as a function? *Does viiº fit the designation of a function, and how might it differ? Is viiº a "function" like the others? What exactly is meant by "function," and does the viiº function have to meet any requirement to be considered as a true function like the other steps?*
> 
> Why is viiº called a triad? *Is viiº a triad? Why, or how does it differ from other triads?
> 
> Are there answers to these questions, or can I "sit pretty," safe in the realization that the tritone B-F reveals a glitch in the CP major-minor system? Are these are the same old culprits of B and F, just as I've always maintained?
> 
> If Woodduck does not hear the tritone on viiº as having a tonic, then "should he?" What would be an advantage of hearing viiº in this way? Did Beethoven hear this? If so, what evidence in his works is there?


Great Caesar's ghost. I ask for a specific question and you ask twenty questions.

I wonder how many people would participate in the theory forum if you didn't continuously bury it under truckloads of self-aggrandizement? How many members take one look at it and flee back to Current Listening?

You don't want dialogue. You want the world to kiss your "thought-style."


----------



## Guest

Post deleted, temporarily.


----------



## Guest

millionrainbows said:


> Yes; this was a "reverse trap" set for academics, *partly to test the general trust level.*


What do you mean by this? Explain.



millionrainbows said:


> Good thinking should always address the direct nature of things. Thus, we can attempt to get closer to real music instead of ideas about music.


Fine. Reams of text from you so far, and not one written or aural example. I'm not impressed.


----------



## Guest

millionrainbows said:


> I'm not just talking theory, I'm talking about performance and *using your ears to express your personality and being; to make art out of music*.


This is worryingly close to gibberish.



millionrainbows said:


> I just don't agree with the general idea that CP music theory is the 'foundation' of all our music. It's part of another era.


I don't folow you. You launch a thread on Secondary dominants (a feature of CP theory) and then mock us ("reverse academic trap") for trying to answer what we (or at least I) thought was a genuine enquiry. It was just another of your "I have a question to which I already have my answer; let's see if you can guess my intent" mind games. I think you are simply being disingenuous.



millionrainbows said:


> *If a person is composing music these days, then soundtrack music is much 'freer' and not bound by CP tonal practices and rules*, especially in the harmonic realm. Yes, there is useful information to be gleaned from CP, such as good-sounding voice leading.


No ****, Sherlock. Obviously CP applies to historical genres of music; obviously nobody expects film composers to follow CP rules. On the other hand, later genres of western music are very much informed by CP.



millionrainbows said:


> So what's the alternative? None, really, it's the system we are stuck with.


Gosh, you seem notationally fixated. Plenty of music out there that doesn't require notation of any sort. Use your ears, I'd say. 



millionrainbows said:


> But I ask that we be less rigid about music in general, and when talking theory, because music can be created by ear, and ideas about music need not be bound by CP practices, especially in the realm of chords.


I ask you not to be so presumptious. As for chords, jeez, you're so 18th century!


----------



## Guest

millionrainbows said:


> The *parallel minor chords* in relation to C major, and their functions. [...]
> Any problem with this basic information? Any mistakes or typos? [...] *Any problems so far? *


No. Why are you farting around. Get to the point.


----------



## Guest

millionrainbows said:


> *Okay, since no one wants to discuss secondary dominants in an orthodox CP context*, I'll take off on some wild speculation that Woodduck and EdwardBast can shred and invalidate.


*I* never said that. I signed up for this thread for exactly that reason.



millionrainbows said:


> [...] The C is already taken care of, with its G7 dominant. Why doesn't viiº have a dominant?
> I'll tell you what my ear says: it does!


 
Is that because you hear vii° as an incomplete V7 (in C major, G-*B-D-F*)? Is this your epiphany?


----------



## millionrainbows

TalkingHead said:


> *I* never said that. I signed up for this thread for exactly that reason.
> 
> Is that because you hear vii° as an incomplete V7 (in C major, G-*B-D-F*)? Is this your epiphany?[/COLOR]


Yes. I've always heard it that way. Wanna see how to resolve viiº? Just consult Walter Piston or Schoenberg, they had the same "epiphany." But there's too much negative feedback on many of these threads to make anyone want to continue.


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## Woodduck

millionrainbows said:


> Yes. I've always heard it that way. Wanna see how to resolve viiº? Just consult Walter Piston or Schoenberg, they had the same "epiphany." But there's too much negative feedback on many of these threads to make anyone want to continue.


So to get the sphinx's riddle solved, we're all supposed to go out and ask Walt Piston and Arnie Schoenberg?

"How to resolve vii" wasn't even one of the many questions in post #84. The question in the OP was "Why does viiº NOT have a secondary dominant?" In post #31 you said, "Woodduck finally answered it, but not absolutely perfectly."

This game of hide and seek hasn't been fun for several pages. For Pete's sake give us the "perfect" answer so we can all go home.


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## millionrainbows

Woodduck said:


> So to get the sphinx's riddle solved, we're all supposed to go out and ask Walt Piston and Arnie Schoenberg?
> 
> "How to resolve vii" wasn't even one of the many questions in post #84. The question in the OP was "Why does viiº NOT have a secondary dominant?" In post #31 you said, "Woodduck finally answered it, but not absolutely perfectly."
> 
> This game of hide and seek hasn't been fun for several pages. For Pete's sake *give us the "perfect" answer so we can all go home.*


No, go ahead and go home, Woodduck. I think the subject of secondary dominants, which was really only expository and as an aside, was designed to reveal possible frictions among members in a straightforward discussion "in CP terms on a CP subject," has served its purpose, anyway. 
Among other things, it revealed viiº as a harmonic glitch in the CP system, and TalkingHead learned how to make the diminished symbol by hitting alt+0 (I notice above that you need to also). How to resolve viiº is _part_ of the answer, necessary to an understanding, but nothing is definitive, is it? Whatever conclusions you want to draw from all this is up to you.

Anyway, on another theory thread you were appearing to have a 'nervous breakdown' and were pleading for me to 'stay away from you' (Striated and Smooth Space, what was post #70, removed) so I don't think you should pursue this further.


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## Woodduck

millionrainbows said:


> No, go ahead and go home, Woodduck.


You're stuck with me.



> I think the subject of secondary dominants, which was really only expository and as an aside, was designed to reveal possible frictions among members in a straightforward discussion "in CP terms on a CP subject," has served its purpose, anyway.


So you start a thread titled "Secondary Dominants," you focus it on the question "Why does viiº NOT have a secondary dominant?", and after seven pages of ****ing around with everyone you inform us that the apparent subject is "really only expository" and "an aside" which is _"designed to reveal possible frictions among members"? _



> I don't think you should pursue this further.


I don't think an honest person would have started this in the first place. We don't apreciate being manipulated and used as pawns in the mind-games of others, and then being told to "go home" when we object to being toyed with. TalkingHead said it well: "You launch a thread on Secondary dominants (a feature of CP theory) and then mock us ('reverse academic trap') for trying to answer what we (or at least I) thought was a genuine enquiry. It was just another of your 'I have a question to which I already have my answer; let's see if you can guess my intent' mind games. I think you are simply being disingenuous."


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## millionrainbows

Woodduck said:


> "How to resolve vii" wasn't even one of the many questions in post #84. The question in the OP was "Why does viiº NOT have a secondary dominant?" In post #31 you said, "Woodduck finally answered it, but not absolutely perfectly."
> 
> This game of hide and seek hasn't been fun for several pages. For Pete's sake give us the "perfect" answer so we can all go home.


The original context:



Woodduck said:


> For Pete's sake give us the "perfect" answer so we can all go home.





millionrainbows said:


> No, go ahead and go home, Woodduck.





Woodduck said:


> You're stuck with me.


Now, back to the present:


Woodduck said:


> So you start a thread titled "Secondary Dominants," you focus it on the question "Why does viiº NOT have a secondary dominant?", and after seven pages of ****ing around with everyone you inform us that the apparent subject is "really only expository" and "an aside" which is _"designed to reveal possible frictions among members"? _


It worked, didn't it? See the friction you've created? It proves that it's nearly impossible for me to start a thread without you derailing it, then overly-dramatically slinging around a lot of blame and laying guilt-trips on people. 


Woodduck said:


> I don't think an honest person would have started this in the first place. We don't apreciate being manipulated and used as pawns in the mind-games of others, and then being told to "go home" when we object to being toyed with.


I was just testing the waters, and it has turned out as I predicted. BTW, YOU mentioned "going home," not me, as seen above.


Woodduck said:


> TalkingHead said it well:...


I don't think you should speak for others. You're always telling me not to. If TalkingHead has something to say to me, he can say it directly to me.


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## Woodduck

millionrainbows said:


> :
> It worked, didn't it?


"It," meaning your mind-games, your manipulating and toying with people for your own amusement and self-aggrandizement? Yeah, "it" worked just fine. It's good that you finally admit this. It would be better if you didn't do things that needed admitting.



> See the friction you've created? It proves that it's nearly impossible for me to start a thread without you derailing it, then overly-dramatically slinging around a lot of blame and laying guilt-trips on people.


The "friction" in this thread is trivial, really, given that it wasn't created to inspire discussion but to impress others with your knowledge, brilliance and insight, all of which you overestimate. Threads may be started for different reasons, not all of them respectable. You create threads destined for friction. But this thread wasn't derailed. It simply bogged down under the weight of its own annoyingness.



> I was just testing the waters, and it has turned out as I predicted.


Yes, you've admitted your motivations several times now.



> I don't think you should speak for others. You're always telling me not to. If TalkingHead has something to say to me, he can say it directly to me.


He did say it directly to you, and you have no good answer to what he said. I'm not speaking for TalkingHead. I haven't put any words in his mouth, paraphrased him, summarized him, or characterized him, as you do constantly to other people. I've simply quoted him. That you can't understand the difference is a problem that calls for introspection and clearer thinking on your part.


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## millionrainbows

Woodduck said:


> "It," meaning your mind-games, your manipulating and toying with people for your own amusement and self-aggrandizement? Yeah, "it" worked just fine. It's good that you finally admit this. It would be better if you didn't do things that needed admitting. The "friction" in this thread is trivial, really, given that it wasn't created to inspire discussion but to impress others with your knowledge, brilliance and insight, all of which you overestimate. Threads may be started for different reasons, not all of them respectable. You create threads destined for friction. But this thread wasn't derailed. It simply bogged down under the weight of its own annoyingness. Yes, you've admitted your motivations several times now. He did say it directly to you, and you have no good answer to what he said. I'm not speaking for TalkingHead. I haven't put any words in his mouth, paraphrased him, summarized him, or characterized him, as you do constantly to other people. I've simply quoted him. That you can't understand the difference is a problem that calls for introspection and clearer thinking on your part.


Gee, what can I say? Would you like to give me fifty lashes?


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## Wes Lachot

I would would like to suggest that there is a secondary dominant #IV7 that easily resolves to VII, as long as you relax the rules just a tiny bit to include contemporary voicings, and as long as you let go of the idea that a secondary dominant must "tonicize" the diatonic chord it proceeds. Sure, sometimes a secondary dominant does tonicize the next chord, but secondary dominants are also used quite frequently to introduce a chain of cycle 5 chords, or in situations where the changes are moving too quickly to talk about tonicization. If in the key of C an A7 precedes a Dm, when the tune stays on Dm for a while we say it's "tonicized", but if it quickly moves on from Dm to G7 it's just a secondary dominant introducing an S, D, T chain. In the exact same way an F# chord can introduce the S, D, T chain VIIm, III7, VI. 

Before moving on I'd like to question the notion that the VII tonality itself is somehow always necessarily "ugly". I mean, it's the 2nd chord of "Yesterday", the most covered song of the 20th century. McCartney loved that tonality so much he stole it from "Moon River", another exquisite use of the tonality, the chord that makes the tune in his estimable estimation. Carole King even had the guts to use the chord as the very first chord of the verse of "You've Got A Friend". And so on. You don't have to put the b5 in the voicing if it makes it too dark--just leave it out or substitute a 4 like King does (it's the melody note in that case, and is heartrendingly beautiful note against the VII tonality). McCartney changes the flat 5 note to a regular 5, by taking the melody up the ascending melodic minor scale of the relative minor target tonality, thereby circumventing the "too dark" problem. But then the flatted 5th shows up in the string quartet arrangement, so it works either way, somehow even simultaneously. 

In these cases above the VII tonality is approached from the I chord itself, a sort of "tritone substitution" for the secondary dominant in question, the #IV7. But it works just as well from the #IV7; you can try it for yourself at the piano. 

So why is there no such thing as a secondary dominant of the VII chord? I think it's just because everybody says so, possibly because the secondary dominant #IV7 has for its own root a nondiatonic note. But the definition of a secondary dominant is supposedly that it's a V of a diatonic note, not that it itself has a diatonic root, and so the exclusion of the V of VII seems arbitrary, or possibly the result of this weird predudice against the VII tonality, which is ironically one of music's greatest sounds. Subdominant chords always have a soulful sound to them, especially when they're made minor, and the VIImin7 chord sort of takes the cake in that department. The only way to go deeper into subdominant minor land is the bVI-7 (check out Bill Evans version of "If You Could See Me Now". In this S, D, T chain the bVImin7 resolves to the bII7 to the I.)


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## millionrainbows

Wes Lachot said:


> So why is there no such thing as a secondary dominant of the VII chord? I think it's just because everybody says so, possibly because *the secondary dominant #IV7 has for its own root a nondiatonic note.* But the definition of a secondary dominant is supposedly that it's a V of a diatonic note, *not that it itself has a diatonic root,* and so the exclusion of the V of VII seems arbitrary, or possibly the result of this weird predudice against the VII tonality, which is ironically one of music's greatest sounds. Subdominant chords always have a soulful sound to them, especially when they're made minor, and the VIImin7 chord sort of takes the cake in that department. The only way to go deeper into subdominant minor land is the bVI-7 (check out Bill Evans version of "If You Could See Me Now". In this S, D, T chain the bVImin7 resolves to the bII7 to the I.)


The only way out of this is to consider the viiº as being essentially 'rootless,' and as having an alternate assumed diatonic root, such as G. This opens up the whole "jazz" can of worms of diminished sevenths and tritone substitutes.

*To nominate #IV7 as a 'secondary dominant' is wishful harmonic thinking, *exposing the harmonic flaw of the major scale compared to the lydian scale.



mikeh375 said:


> Anyone want to take a bet on our gurus "real" secondary dominant of the dim. triad on b being a dim. triad on F sharp? ....yes... I know...F sharp in C major!!! The Lydian wins out. Or something like that.


No, I didn't propose F# as a secondary dominant, for the following reason:

Start generating your scales from fifths and you'll see:

C-D-G-A-E-B-------F#? No, F, which sounds bad.

Now try the lydian:

F-C-G-D-A-E-B-F#....it works, and sounds better. Go to any organ and try this.

So, the major scale is "missing" a fifth anyway! It's flawed already! You can't use a non-diatonic root for something as basic as this.


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## Wes Lachot

Yeah, I've never bought the rootless VII explanation, not from my amazing teachers at Berklee, and not from any of the several books (many of them invaluable rescources) where I've seen VII described that way. It just didn't make logical sense to me that Mother Nature would play such a clumsy trick on us. I mean, rootless voicings were still eons in the future when Mother Nature created sound ;-)

I was pretty sure it would be obvious from my post above, going on and on about the VII being Subdominant in essence, that I was unlikely to be convinced that the VII tonality is somehow a rootless version of the V. What next, if we allow this sort of non-rigorous thinking to take hold? Is the III really a rootless version of the I? Well, they tried to run that one up the proverbial flagpole at Berklee as well, and I guess you might say I failed to salute.

What I tried to illustrate in my post above, perhaps not as clearly as I had hoped, is that there is a "tonality" to the VII, even if it wants to pull away towards its common destination V of VI. (I mean, even the V itself possesses this restless character of not being a final destination, unless some very clever magic happen in the progression to make us forget the original tonality, like in some sonata form pieces.) By giving several musical examples I was trying to illustrate what seems to me to be the obvious fact that the VII has it's own identity, and that that basic identity is Subdominant in nature. Of course there will always be musical situations where the VII chord resolves up to the I, and I can see why folks would analyze those situations that way (although there is an alternative way, but I don't want to be too long-winded here). But when VII resolves to V of VI to VI, I think that the already contorted explanation "it's really a 1st inversion V chord with no root and an added 9" just cannot continue to bear up under the added scrutiny.


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## EdwardBast

Wes Lachot said:


> Yeah, I've never bought the rootless VII explanation, not from my amazing teachers at Berklee, and not from any of the several books (many of them invaluable rescources) where I've seen VII described that way. It just didn't make logical sense to me that Mother Nature would play such a clumsy trick on us. I mean, rootless voicings were still eons in the future when Mother Nature created sound ;-)
> 
> I was pretty sure it would be obvious from my post above, going on and on about the VII being Subdominant in essence, that *I was unlikely to be convinced that the VII tonality is somehow a rootless version of the V. What next, if we allow this sort of non-rigorous thinking to take hold? Is the III really a rootless version of the I?* Well, they tried to run that one up the proverbial flagpole at Berklee as well, and I guess you might say I failed to salute.
> 
> What I tried to illustrate in my post above, perhaps not as clearly as I had hoped, is that there is a "tonality" to the VII, even if it wants to pull away towards its common destination V of VI. (I mean, even the V itself possesses this restless character of not being a final destination, unless some very clever magic happen in the progression to make us forget the original tonality, like in some sonata form pieces.) By giving several musical examples I was trying to illustrate what seems to me to be the obvious fact that the VII has it's own identity, and that that basic identity is Subdominant in nature. Of course there will always be musical situations where the VII chord resolves up to the I, and I can see why folks would analyze those situations that way (although there is an alternative way, but I don't want to be too long-winded here). But when VII resolves to V of VI to VI, I think that the already contorted explanation "it's really a 1st inversion V chord with no root and an added 9" just cannot continue to bear up under the added scrutiny.


Oh good. MR has been saying for years that the Vii° is a rootless V7 and the VII°7 is a rootless dominant b9th chord. Although it feels strange to say it, there are instances where I think MR has a point. But I've never felt strongly enough about it to argue one way or another.


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## millionrainbows

Wes Lachot said:


> Yeah, I've never bought the rootless VII explanation, not from my amazing teachers at Berklee, and not from any of the several books (many of them invaluable rescources) where I've seen VII described that way. It just didn't make logical sense to me that Mother Nature would play such a clumsy trick on us. I mean, rootless voicings were still eons in the future when Mother Nature created sound ;-)


What 'convinced' me was my ear; I never heard vii (B) as a root, but as a third going to I, as a V-I.



> I was pretty sure it would be obvious from my post above, going on and on about the VII being Subdominant in essence, that I was unlikely to be convinced that the VII tonality is somehow a rootless version of the V. What next, if we allow this sort of non-rigorous thinking to take hold? *Is the III really a rootless version of the I? *Well, they tried to run that one up the proverbial flagpole at Berklee as well, and I guess you might say I failed to salute.


Are you a guitar player? This is the whole basis of chord substitution.


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## millionrainbows

EdwardBast said:


> Oh good. MR has been saying for years that the Vii° is a rootless V7 and the VII°7 is a rootless dominant b9th chord. Although it feels strange to say it, there are instances where I think MR has a point. But I've never felt strongly enough about it to argue one way or another.


Walter Piston (in his Harmony book) and Arnold Schoenberg (in his Harmonielehre) both agree, so who should I believe, them, or some guy on the internet in his underwear? :lol:

Also, I'd like to say (for years to come) that the major scale is harmonically flawed, in that it does not consist of stacked fifths (like the lydian does), because of the tritone F-B.

If you can't get 7 fifths, one for each degree, then something is bound to go wrong, and to be 'off.'


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## Wes Lachot

MR: I'm aware of Piston's and Schoenberg's views on this. There is another school of thought as first proposed by Lendvai, and I figured you may be aware of this school of thought judging from a couple of your posts, but in any case if you are not yet familiar with it or are interested, the book is "The Workshop of Bartok and Kodaly" by Erno Lendvai. There's another one, a little easier to come by, titled "Bela Bartok: An Analysis of His Music" by the same author. As I pointed out in another thread, this system supports some of the statements you've made about tritone substitutions, which is why I surmised that you may already be familiar with the system.


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## millionrainbows

Wes Lachot said:


> MR: I'm aware of Piston's and Schoenberg's views on this. There is another school of thought as first proposed by Lendvai, and I figured you may be aware of this school of thought judging from a couple of your posts, but in any case if you are not yet familiar with it or are interested, the book is "The Workshop of Bartok and Kodaly" by Erno Lendvai. There's another one, a little easier to come by, titled "Bela Bartok: An Analysis of His Music" by the same author. As I pointed out in another thread, this system supports some of the statements you've made about tritone substitutions, which is why I surmised that you may already be familiar with the system.


The book I have by Lendval is this one, which I've mentioned in this forum before in discussions on Bartok. There seemed to be universal resistance to it, since it purports that Bartok used the golden mean. It is plausible to me, but here it met with resistance.

Since Bartok was using the diminished and half-whole scales, which contain tritones, it seems obvious that he was using some sort of tritone-relation ideas, although I might hesitate to call them tritone substitutions.

Bartok was using such a hybrid approach, and changing it, that I'm not sure if he is the best way to illuminate the idea of secondary dominants.


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## Wes Lachot

millionrainbows said:


> The book I have by Lendval is this one, which I've mentioned in this forum before in discussions on Bartok. There seemed to be universal resistance to it, since it purports that Bartok used the golden mean. It is plausible to me, but here it met with resistance.


Yes, this is the second book I referred to. The first one, "The Workshop of Bartok and Kodaly" goes into much more detail, but it does appear to be out of print, unfortunately. In any case, it is a very logical theory, and your statement about the resistance to it resulting from all the golden mean stuff resonates with what I said above in my post. So we are on the same page there. For those who are unfamiliar with the theory, it can be found, at least in summary, in the book pictured.

I'm not exactly sure what you mean by your statement: "Bartok was using such a hybrid approach, and changing it, that I'm not sure if he is the best way to illuminate the idea of secondary dominants." All I was doing was pointing out that there are views that differ from Piston's and Schoenberg's, and that these ideas may be worth considering by other readers of this thread.

Getting back to actual music, did you check out those musical examples I mentioned at the piano? I find that most musical rhetorical points are best conveyed by a combination of verbiage and listening to the musical example until the point sinks in. If you tried that, and the sound didn't fit my description to your ears, then that's cool too. This is certainly not a one-size-fit-all theory. Thanks for your contribution. As I said in another thread, I suspected that maybe you'd read Lendvai.


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## Wes Lachot

MR: One more thing. I did a theory forum search on the word "Lendvai", and all that came up was that one thread on Bartok, with only 8 replies or something like that. Now I am the first to admit to being tech-challenged, and I may not be using the search engine correctly, but if this is it for Lendvai on this forum then I think it's fair to say that his theory has not been thoroughly discussed, and there may indeed be some around here whose ears and minds perk up. If so, great. That's what I was going for. 

I'm certainly not finding any resistance to Lendvai's 12-tone functional harmony system in that thread. As I said, I'm tech-challenged when it comes to search engines and so forth, so please direct me if there are other threads.

Update: I see Lendvai discussed in another forum, but not the Music Theory forum, and you did bring up the 12-tone system of functional harmony, so good to know. If you ever need help defending or explaining the theory, I'm here. I use the theory in my own teaching and actually developed it independently over a number of decades, and was happy and surprised when I discovered Lendvai. I began developing my version of the axis system, which I call "Wild Theory", back in 1979, after my piano teacher conveyed to me a theory hint he'd gotten directly from Bill Evans, regarding "the system" as Evans referred to it. I am not attributing the system I use to Evans, only conveying to readers of this thread my inspiration for developing the system. Since I have yet to write a book on the system, I am directing those who are interested to Lendvai.


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## millionrainbows

I'll go ahead and post this, which came from the Composer's Datebook forum on Bartok.

Bartók can be hard to pin-down, because he used an arsenal of different techniques in composing. To some, his string quartets are the way in; to others, like me, the orchestral works such as "Music for Percussion..." that Sid James mentioned earlier are the key.

The "creepiness" that many listeners cite is due to the fact of Bartók's use of small intervals, as well as use of the diminished scale (symmetrical in nature & dividing the octave in half via the tritone).

Here is my long-winded explanation of Bartók, which you can take or leave, which I posted elsewhere: 

I'm skimming through "Bartok: An Analysis of his Music" by Elliott Antokoletz, and there's an interesting chapter called 'Basic Principles of Symmetrical Pitch Construction."

It states, basically, that traditional Western music was based on an uneven division of the octave, namely the perfect fourth and fifth.

Look at all the intervals: all of them have complementary intervals which add up to an octave (min. 3rd/maj. 6th, etc.), and the smaller of these two complements generates a cycle which divides the octave symmetrically: one cycle of m2, two cycles of M2, three of m3, four cycles of M3, and six cycles of tritones; except the p4 and p5: this complementary interval does not generate a cycle which divides the octave symmetrically, but must extend through many octaves in order to reach its initial starting point again. Thus, there is only one cycle of perfect fourths, or perfect fifths.
In terms of pure set theory, the reason that perfect fourths and fifths behave this way is that 5 (a perfect fourth is five half steps) and 7 (a perfect fifth is seven half steps) are not divisors of 12...neither 5 nor 7 go into 12; 
until:

5 goes into 60, a multiple of 12 (circle of fourths, five octaves: C F Bb Eb Ab Db Gb B E A D G)

7 goes into 84, a multiple of 12 (circle of fifths, seven octaves: C G D A E B Gb Db Ab Eb Bb F)..."

The reason why this 'difference' of fourths and fifths was brought up is because the author of the Bartok book is saying that Bartok based his music on an even division of the octave, namely, the tritone.

From a perspective of pure arithmetic, the octave can be seen as 'unity.' The octave, without regard to register, in terms of pitch identity and relation to a 'root,' can be called '1' or unity. On a number line, anything less than one, proceeding back to zero (infinity), is fractional. Anything larger than one proceeds forward, into the 'other' infinity of octaves.

Perhaps this is why the 4th & 5th are different; instead of dividing the octave fractionally, they are expansive by nature; they go 'outward' past one, past the octave, into other 'root' stations. Hence, the use of 4ths & 5ths to create root movement.

Every interval has its complement. All the intervals except perfect fourths & fifths have a smaller number which divides the octave (12) symmetrically;

So each interval has 2 numbers which add up to an octave.

The m2 has itself 1 and 11; 
M2 is 2 and 10; 
m3 is 3 and 9; 
M3 is 4 and 8;
p4 is 5 and 7;
tritone is 6 and 6;
p5 is 7 and 5;
m6 is 8 and 4;
M6 is 9 and 3;
m7 is 10 and 2;
and M7 is 11 and 1.

You can see the symmetry in this; and if we eliminate the redundancies, such as 10-2/2-10, we have 6 essential intervals.

Again, neither 5 nor 7 go into 12; until
5 goes into 60, a multiple of 12 (circle of fourths, five octaves: C F Bb Eb Ab Db Gb B E A D G)
7 goes into 84, a multiple of 12 (circle of fifths, seven octaves: C G D A E B Gb Db Ab Eb Bb F)"

The fourth and fifth, as pointed out, cannot be used as divisors of 12 (the octave); therefore, they can be seen as "expanding" in nature, as they generate cycles of 12 notes (outside the octave). Remember, 60 and 84 had to be used as the common denominators for 5 and 7. These large numbers can be seen as 'outside the octave' or as a 'greater referential point.' Hence, the reason the 4th and 5th are the basis of traditional Western music; this facilitates movement outside the octave, to a new reference point or new key.

This means that 'modern' music, like Bartok's, is 'inward-going' or 'introspective' if you like to indulge in metaphor (after all, this is art, not science). This is what Marshall McLuhan was getting at in his book "Through the Vanishing Point," in which he explains how our perspective on things is literally reversed in modern art, putting us at the other end of the 'vanishing point.' Like looking down the wrong end of a telescope, or rather a microscope, the 'inner' world now becomes our universe, heading towards the 'other infinity' towards zero; just like our number line, where anything less than one, proceeding back to zero (infinity), is fractional, and anything larger than one proceeds forward, into the 'other' infinity of octaves.

This is about music, and the nature of tonality. The ideas I put forth about intervals, although fairly simple in one sense, are laying the groundwork for a larger, more all-encompassing understanding of tonality and chromaticism. I see it as a necessary reference to the ideas which will follow. The 'simple arithmetic' of intervals is necessary, in case some of these ideas about intervals & reciprocals might not be fully 'grokked' by some readers.

It's simple, and it's complicated, all at the same time; but after a thorough pondering and practical application (in composition) of Howard Hanson's ideas of interval projection, I decided it was time to tackle the ideas of another musical giant: Bartók, and what a revelation it has been! Especially the little book by Ernö Lendvai, which I highly recommend, that is, IF you are sufficiently prepared to read it. Some knowledge of intervals & reciprocals is necessary.
The Ernö Lendvai book deals a lot with the 'meta-concepts' of Bartók's methods. It generalizes to a great extent, and is not a very lengthy book, but it states the case elegantly, and it is a beautiful book. It divides Bartók's ideas into two main categories: the 'GS' approach, which has to do with the "Golden Section" and the Fibonacci series, and is also called his 'chromatic system'; and Bartók's 'diatonic system,' which is based on acoustic principles.

The beauty of all this is that the two approaches reflect each other in an inverse relationship.


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## Wes Lachot

Thanks for moving the post over, MR. There is plenty more to discuss about the system as it regards concepts of functional harmony, of course. Beethoven may have been the first to intuit the logical musical conclusions regarding the geometrical connections between the keys (though Bach probably intuited just about everything, but I don't have the evidence in the case of Bach). I say this purely based on listening and studying the scores, not thinking about micro-tuning or even math for that matter. Just listening and studying the scores, oh yeah, and playing the piano, which can be a sort of simultaneous listening/studying experience to check the actual relevance of musical theories.

Readers may have already guessed that I am referring to Beethoven's frequent use of simple diminished chords expanding outwardly (contrary motion of soprano and bass voices) to produce either a major triad, if the soprano voice moves up a whole step and the bass voice moves down a half step, or a minor triad, if the soprano moves a half step up and the bass moves a whole step down. This in and of itself may have been nothing new when he began employing it, but he would use them serially from time to time in a way that really began to exploit the enherant symmetry later expored so thoroughly by Bartok and Kodaly.


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## millionrainbows

When I think of Beethoven and diminished chords turning into dominant flat 9s, I think of String Quartet No. 16 in F, Op. 135, last movement.


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## Wes Lachot

millionrainbows said:


> When I think of Beethoven and diminished chords turning into dominant flat 9s, I think of String Quartet No. 16 in F, Op. 135, last movement.


Alright, cool, let's talk about Beethoven!

I feel as though my assertion that the axis system can shed new light on classical functional harmony could use some actual meat on the musical bones. So here's an example for those who are interested in this sort of thing:

Charles Rosen, on pp 382 and 383 of "The Classical Style", sheds considerable light on the subject of "substitute dominants" (his words) and yet in my view doesn't fully explain Beethoven's tendency of modulating to alternate keys in sonata form situations where historically composers usually modulated to the key of the V. But he makes a stab at it. Rosen refers to these alternate keys (usually mediant or submediant) as "substitute dominants", and contrasts the effects Beethoven obtained ("greater tension and imperative need for resolution") with the Romantic composers' use of "subdominant" key areas in these same musical situations.

Specifically, on page 382 Rosen refers to op. 31 where LVB goes from the home key of G to the key of B, as one of his examples. I can't explain why Rosen would refer to either the submediant or the flat submediant as "dominant", so I'll just have to let that lie. But by my listening experience--by no means a scientific study--LVB is likely to choose the key of the III where he's looking for an alternative to the I, and that is a Dominant key area in the axis system. I welcome other perspectives on this, as I am by no means the last word on LVB. I just have an eye and ear for pattern, that's all.

This does resonate with Lendvai's observations, and my own ears, meaning that the key of the III (in major) sounds and feels dominant. Viewed through the lens of the axis system this move to the key of the III rather than the V is a pretty logical alternative for a composer with a restless imagination and a bent for pattern and symmetry, which I think it's fair to say pretty accurately describes LVB. Since in the axis system the III is one of the Dominant tonal areas, it is a perfectly logical and valid alternate Dominant tonal area, and as I mentioned earlier (possibly in another thread?) I believe Beethoven had an innate sense of these geometric relationships, if anybody ever did.

If anyone who reads this thread is aware of any writings where Rosen discusses Lendvai, I would appreciate a heads up, as I am always looking to expand my research.


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## millionrainbows

Wes Lachot said:


> ...But by my listening experience--by no means a scientific study--LVB is likely to choose the key of the III where he's looking for an alternative to the I, and that is a Dominant key area in the axis system. I welcome other perspectives on this, as I am by no means the last word on LVB. I just have an eye and ear for pattern, that's all.
> 
> This does resonate with Lendvai's observations, and my own ears, meaning that the key of the III (in major) sounds and feels dominant. Viewed through the lens of the axis system this move to the key of the III rather than the V is a pretty logical alternative for a composer with a restless imagination and a bent for pattern and symmetry, which I think it's fair to say pretty accurately describes LVB. Since in the axis system the III is one of the Dominant tonal areas, it is a perfectly logical and valid alternate Dominant tonal area, and as I mentioned earlier (possibly in another thread?) I believe Beethoven had an innate sense of these geometric relationships, if anybody ever did.


Since a "III in a major key" does not exist in CP tonality, then it's "function" is up for grabs.

I'm not sure what the point is here, but I also consider a MAJOR chord on III as being dominant, since diatonically it would include D (the flat seventh), not D#.

But usually a *bIII* would be in relation to its relative minor, vi, which would diatonically make it a I. So we know it's not a I.

As far as Beethoven, he used root movements in thirds to get to distant key areas quickly, because by fourths/fifths it takes 5 or 7 cycles, and with M3 or m3, which are recursive, it only takes 3 or 4 cycles; and depending on chord quality, it could be an even closer relative minor relationship.

Also, root movements in thirds outline "triads" as well as being root movements. See Beethoven's Ninth.


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