Thoughts on Horizontal Tonal Gravity, CMG’s, And Duality

Discussions on the theoretical basis of the LCC

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Thoughts on Horizontal Tonal Gravity, CMG’s, And Duality

Postby strachs » Fri Mar 28, 2008 12:21 pm

The following is just some "thinking out loud" based on pgs 208-215 of LCCOTO. It's as much for my own sake as for discussion by anyone who finds it interesting. So file under G if this stuff is obvious or superfluous to you.........

Four of the modal genres (V, II, VII and III) are described as “dual-stateâ€
Last edited by strachs on Thu Feb 19, 2009 10:22 am, edited 1 time in total.
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Postby strachs » Fri Mar 28, 2008 12:40 pm

Definitely not claiming any special insight or understanding on the topic. Just seeking to understand it better than I currently do by putting it into words and rewording it over and over.

I certainly invite any corrections that you folks can offer before I get too attached to a wrong interpretation of things.
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Postby Bob » Sat Mar 29, 2008 7:58 am

In the morning fog of the first cup of coffee, your post and the reference (pgs 208-215 of LCCOTO) are a lot to chew on. In my 'pre-close read' state of coming to terms with CMGs, a few hypotheses:

CMG is a bridge to Vol 2 and in a sense an initial rapprochement with traditional major/minor theory of harmonic movement and as such, a prelude to Vol 2. It takes into account the traditional modes and allows that III V II and VII, can function as more than inversions, noting that they are also major and minor triads.

Chord substitution is discussed in the 1959 edition but not in the 4th edition, perhaps because a full exposition might best be saved for Vol 2, because it concerns HTG primarily.

A few approaches to chord substitution are
1. Substitute more 'outgoing' chordmodes, i.e., going down the column in Chart A. This produces more 'alteration' of color than different root movement, but does have subtle implications for resolving the chord, especially when using the symmetrical scales.
2. As noted in the '59 edition, the chords of the parent Lydian scale are interchangeable. As such the CMG major and minor triads may be heard as 'tonic stations' representing a 'transitory modulation' an effect that is enhanced by preceding the CMG with its own 'dominant 7th,' or 'ii-V7.'
3. It opens the door to 'modal substitution' and 'bi-chordal' strategies.
4. I don't know if Vol 1 gets us to tritone substitution or 'Coltrane changes,' but this can be inferred by the symmetrical structures of the LYD, LA, LD and the AUX scales, and it would be a surprise if not fully addressed in Vol 2.

(I reserve the right to edit this post as the executive function of my left frontal lobe comes online.)
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Postby strachs » Mon Mar 31, 2008 8:35 am

An interesting apparent contradiction to my analysis above is found on pg 197. It states there that all four horizontal scales can function as "verticalized horizontal melodies" on the level of VTG. Not only that, but that any of the seven principal scales of the LC Scale can funtion as "horizontalized vertical melodies" on the level of HTG.

I'm not certain that this means that member scales CAN be imposed on Conceptual Modal Tonics, but it kind of weakens my assertion that they CAN'T.

Every time I think I've grasped some kind of certainty in my understanding, I find something that again calls that into question. I feel like a Lydian Chromatic Scale, whose tonic is being "cut off" by another LCS in a sharp direction. (try to get a visual to that - kind of like the carpet being pulled from under my feet).
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Postby Bob » Mon Mar 31, 2008 10:18 am

strachs wrote:Every time I think I've grasped some kind of certainty in my understanding, I find something that again calls that into question. I feel like a Lydian Chromatic Scale, whose tonic is being "cut off" by another LCS in a sharp direction. (try to get a visual to that - kind of like the carpet being pulled from under my feet).


I hear you. Reading the CMG section, in particular, is like unpacking Kierkegaard or viewing an Escher sketch. Toru Takemitsu says "... we might call it poetry." And so it seems.
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Postby strachs » Tue Apr 01, 2008 7:50 am

OK. Corrections. Upon a closer read of the BASIC material on CMG’s (pgs 116-126), I can see that some of my above assertions were not correct.

One is that modes I and VI are “purely verticalâ€
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Postby Bob » Tue Apr 01, 2008 2:03 pm

Here's a nice quote:

Conceptual chordmodes demonstrate that the lydian Scale, the seminal scale of VTG, sounds a horizontal relationship with its mode II minor, mode V major, mode II major and mode VII minor triads.


page 123.

(I could say that Bb Lydian sounds a horizontal relationship with most of the chords in Autumn Leaves in F/dmin, but I won't.) :wink:
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Postby strachs » Wed Apr 02, 2008 5:39 am

Bob-O:

Kind of like saying: "I have no opinion on the matter.... but if I did, this is what it would be." I think you can go ahead and make that assertion about Autumn Leaves - I'm going to re-analyze it to prove you right.

Interesting quote you made. This sentence, to me, is the book's biggest revelation of what will be the subject of Volume II - horizontal tonal gravity. Volume I has us learning to relate vertically to a chord by recoginzing it's parent LC scale.

However, the quote you made tells us that from any of these vertical situations, you can RESOLVE, or move naturally, to a major triad on II or V, or a minor triad on III or VII. Not only a triad, though - a LC scale. (In other words, Tonal Gravity describes not only the natural relationships that all chord tones have with one central tone, but the relationship these 12 tonal centres have with each other)

chespernevins revealed this in his "cycle of doom" thread. I am not sure that one can resolve, as chesper claimed to ANY sharp-lying scale, but you can for sure to the two sharp-lying scales implied by the CMG's.

For this reason, I am sure that you can successfully analyze just about ANY peice of music, by starting with the final chord of the peice, and relating much of the melodic and harmonic material to the LC scale one or two fifths in a flat-lying direction. Adding more outgoing tonal resources to that flat-lying LC scale will yeild a richer pallette of chords to sound, but will ultimately have exactly the same resolving tendency to that final chord or scale.

What a simple, but very hugely flexible and insightful approach the Concept gives us!
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Postby Bob » Wed Apr 02, 2008 6:45 am

strachs wrote:chespernevins revealed this in his "cycle of doom" thread. I am not sure that one can resolve, as chesper claimed to ANY sharp-lying scale, but you can for sure to the two sharp-lying scales implied by the CMG's.


I think this may get into the whole issue of chord substitution. The subs are related to the original changes more or less remotely (as SMGs?) but may themselves be dealt with on their own VTG or HTG level, but still resolve back to the PMG or parent LC of the tune. I carelessly dubbed this the level of VHTG, but I don't know what this level is referred to 'officially.'

Schoenberg sort of addresses something like this in his Structural Functions of Harmony. Someone somewhere referred to the LCC as Music's GPS.

I infer from your post that it's true that going out is one thing, but finding your way home is quite another. The alternative goes to the level of 'getting lost.'
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Postby strachs » Wed Apr 02, 2008 8:32 am

"Level of Getting Lost". Cute.

I did take a look at the LC scales given for Autumn Leaves (pg247), and out of 27 VTG alliances, 16 involve either Ab, Eb, (the two keys in a flat-lying direction) or Bb itself (the final lydian tonic that the peice resolves to).

So, you were on the money when you "didn't" say Bb has a horizontal relationship with most chords in the tune. I think what will be made clearer in Volume II is how to charachterize the other Lydian Tonics in the piece (C, Db, and D) and their relationship to Bb. There is probably a way to grade ALL horizontal relationships, even those beyond the reach of the CMG's.

It's interesting to speculate about what's in that next book, isn't it?
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Postby Bob » Wed Apr 02, 2008 9:26 am

We do Autumn Leaves in F/dmin. None the less, my earlier views on Autumn Leaves have been widely eviscerated. I slipped that in to be mischeivous.

Vol II indeed. Fortunately, I have a few loose ends to pull together with Vol I to keep me busy.

This whole series of threads and posts on CMGs certainly has been stimulating. Inertia can be deadly.
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Postby strachs » Wed Apr 02, 2008 10:35 am

Bob wrote:This whole series of threads and posts on CMGs certainly has been stimulating.


I'm flattered. I hope that I havn't thrown off any conclusions you have arrived at, only to send you down a blind alley. Please let me know if any of the above seems off track.

I know I tend to write novels, so sorry if it's a lot to digest at once. I just don't like to leave any doubt as to what I mean, so I err on the side of saying too much.
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Postby Bob » Thu Apr 03, 2008 5:20 am

The dialogue since to Ches' 'resolving tendencies, CMGs and Autumn Leaves has been quite productive IMO.
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Postby strachs » Thu Apr 03, 2008 5:34 am

Glad to hear that.
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Postby strachs » Fri Feb 06, 2009 4:57 pm

OK, if you read what I recently posted on this subject (last week - i have deleted it now), just ignore it. Some of the points are valid, but others, I can see now, are just wrong.

It turns out that where I thought I was at odds with Russell, I am actually not. Some experimenting demonstrated my objections to be false, and I can understand some of his ideas more clearly now.

Word to the wise... when you think something in the book does not make sense, take some time to really assimilate what he's saying. He does not always express himself comprehensively, but the ideas he's trying to convey are right on the money.

Sorry If I have thrown anyone off.....
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