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

Discussions on the theoretical basis of the LCC

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Postby strachs » Fri Feb 13, 2009 11:11 am

A very clarifying paragraph (for me, anyway, because I was lost on this until now) on the issue of vertical vs. horizontal is found on page 197 (second paragraph).

It is helpful because it expresses that there are MATERIALS that are essentially horizontal or vertical (scale types with inherent characteristics), and there is BEHAVIOR that is vertical or horizontal.

Vertical principal scales are primarily used in a vertical fashion (a melody that conveys one MG of one vertical scale), but can be used in a horizontal fashion (tonic stations which yield to resolving tendencies). Russell calls this HORIZONTALIZED VERTICAL MELODIES.

Horizontal scales are primarily used in a horizontal fashion, but can be used in a vertical fashion. Russell calls this VERTICALIZED HORIZONTAL MELODIES.

I was getting frustrated sometimes about the terms, not realizing that they have multiple meanings; one referring to the actual properties of a pitch-set (scale), and the other referring to the way a melody behaves (which reveals whether the musician/composer is relating to isolated tonal areas, or the piece as a whole).


One thing that also helps to simplify things is realizing the implications of CMGs when applied to various scales. They imply that MG V, III, II, and VII, while having PRIMARY vertical (chord producing) significance, have a SECONDARY horizontal (resolving) function.

This helps me reduce the number of scales I need to work with, since the major scale can be recognized as MGV (of the Lydian scale), in it's horizontal/conceptual mode of operation.

Similarly, the harmonic minor scale can be recognized as MGIII (of the Lydian #2 scale), in it's horizontal/conceptual mode of operation.

In light of this, I wonder if the Lydian b7 parent scale is really just a conceptual/horizontal manifestation of Lydian Augmented MGII? Or is there a good reason to consider it as itself an 11TO vertical scale?

It would seem consistent with the the treatment of the Major and Harmonic Minor scales, to consider vertical application of the Lydian b7 scale, not as a vertical principal scale, but as VERTICALIZED HORIZONTAL MELODY.

Does this sound reasonable? Or would some tonal resources be lost this way?
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Postby chespernevins » Fri Feb 13, 2009 1:07 pm

I think George came to see the Maj b7 chord as a part of the I Major / Altered Major chord family since 7th chords are used as I chords in so many pieces.
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Postby strachs » Fri Feb 13, 2009 2:27 pm

It is true that the Maj b7 chord is treated as the I chord in much music. But that could be said of major chords in a major scale context, as well. This does not qualify the major scale to be a Primary Parent scale, though.

My angle, I guess, is to arrive at a consistent manner of treating structures that can occur as a result of MG or as a result of scale. I'm being anal, I know.
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Postby chespernevins » Tue Feb 17, 2009 12:59 pm

Hi strachs,

I’m going to throw this out there because I’m not understanding your point here.

It is true that the Maj b7 chord is treated as the I chord in much music. But that could be said of major chords in a major scale context, as well. This does not qualify the major scale to be a Primary Parent scale, though.


I'm not fully understanding an analogy between a major scale manifesting as CMGIh and a Lydian b7 scale on PMG I. Here's why:

For example, take C LYD CMGVh (Ionian) (The most fundamental appearance of the Ionian scale in the LCC):

G A B C D E F# (over G Maj triad)

This mode is horizontal in relation to a G Maj (C Lyd Vh) chord - by virtue of the note C in relation to the G chord.

Let’s transpose it to a C Ionian scale, and place it on the C LYD I Maj chord:

C D E F G A B over a C Maj triad (C LYD I)

You get a mode that is considered horizontal in relation to its I Chord (C Maj) - by virtue of the note F in relation to the C chord.

Now let’s compare that to your idea quoted here:

I wonder if the Lydian b7 parent scale is really just a conceptual/horizontal manifestation of Lydian Augmented MGII?


If you take a C Lyd Aug II mode:

D E F# G# A B C

This is not horizontal in relation to chord built on C LA II (D Maj/D Maj b7), given the G# in the mode.

Transpose it to a C Lydian b7 scale and place it on the C LYD I Maj chord:

C D E F# G A Bb

With the F#, you get a mode that is vertical with relation to the C LA I chord.

The behavior of the mode is dependant on the context.

It would seem consistent with the the treatment of the Major and Harmonic Minor scales, to consider vertical application of the Lydian b7 scale, not as a vertical principal scale, but as VERTICALIZED HORIZONTAL MELODY.


The Major and Harmonic Minor scales are horizontal scales, so they can be applied as Verticalized Horizontal Melodies in certain cases.

But the C LA II mode is not horizontal to begin with, so it can't be applied as a Verticalized Horizontal Melody.

If I have not understood your ideas, perhaps you can clarify?
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Postby strachs » Tue Feb 17, 2009 2:03 pm

Hey Ches,

thanks for replying. The answer, of course, was staring me right in the face the whole time, but I didn't see it until you pointed it out - the absence of the natural fourth in Lb7 is the strongest clue that this is not a horizontal scale.

As a result, you are again correct that the term Verticalized Horizontal Melody is not applicable, since we are NOT verticalizing an essentially horizontal scale resource. It's already vertical in nature.

The original phrase you quoted simply summed up that I didn't think common usage for the chord was justification for placing it on PMGI, any more than common usage of the Major scale was justification for it being the true parent of a major triad. However, as you pointed out, there is much more than common usage to place this chord on PMGI.

This being true, I find it amazing the reciprocal relationship that the 8TO and 10TO have with each other. Much of the AMG possibilities come from these two orders and their scales.

Don't worry, I'm catching up. Thanks for your input as I continue to slowly connect these dots!
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Postby strachs » Thu Feb 19, 2009 1:16 pm

Rather than start a new topic, I'll just plug this question in here......

On page 126, under the subheading "Summation of Conceptual Modal Genres", there is a paragraph (beside the word "vertically") that confuses me a little. Up until this point, the CMG's are described as TRIADS on those modal tonics.

I'm not sure if this paragraph is teaching something new or, as the subheading suggests, summarizing the preceding few pages (which contrast the vertical function of the PMG's with the horizontal function of the CMG's on those same modal tonics).

It's hard to describe without stating a specific LCS. Let's say we're referring to the CMG's of the F LCS: CM, Am, GM, Em.


Does this description mean that the 11 member scales of F LC can be used with these triads, or the 11 member scales of C LC and G LC?

If it means the member scales of F, does that mean that the C major chord (triad, presumably) can be colored by more outgoing tones, starting with C#, then Ab, then Eb and so on?

If it means the member scales of C, then is it really still a CMG of F LC, or was it only a CMG up until the resolution took place, after which it is it's own PMG I chord?

Is this actually a summary, or is this a major twist to the previous idea that CMG's are triads on these MT's? If it is a summary, the wording here may be a contributor to some of the confusion around the issue.
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Postby sandywilliams » Fri Feb 20, 2009 10:43 pm

Great question. You are in the one of the most interesting parts of the book. I think if you look at the top of page 125 it answers most of your questions. Cmaj can exist as both a PMG I( C LT) and a CMG Vh (F LT).
"If it means the member scales of C, then is it really still a CMG of F LC, or was it only a CMG up until the resolution took place, after which it is it's own PMG I chord?"
Once again I believe the answer would be both. Bear in mind that we are really talking about triads here. I'm not sure these conditions work with extended chords.
I"ll do some more research and get back to you.
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Postby strachs » Mon Feb 23, 2009 10:01 am

I guess my confusion stems also from the second sentence under that heading

They function both vertically and horizontally.


The information on CMG's up until this part of the book seemed to be referring to the dual nature of the four MODAL TONICS V, III, II, and VII - that they could produce PMG structures that contain the Lydian Tonic, or triads that suggest PMG I/VI of sharp-lying Lydian Tonic Centers.

The above quote seems to be suggesting that even the TRIADS THEMSELVES on these Modal Tonics have a dual nature. One of chord/scale alliance (vertical application), and one of tonic stations to cadence towards (horizontal application).

My suspicion is that, similar to the great degree of nuance available for applying vertical tonal gravity (pages 165-167 describes 9 distinguishable types of VTG melody), these seemingly disparate descriptions of CMG's are a result of the great variety of applications of horizontal tonal gravity, to be explored in Volume II.

My attempts to achieve a "black and white" understanding of the subject are always proving futile, and it's probably just because Vol I lacks a full-scale exposition of the level of horizontal tonal gravity.

That being said, what is stated in Vol I is extremely interesting and it's exciting to grapple with it to the extent possible with what IS said of it. I am grateful that Russell did not omit mention of it entirely in Vol. I. In the near future, I'd like to share some of my results of applying HTG. Who knows if it will prove to be in agreement with Vol II, but I've come up with a system anyway. Works for me. (stay tuned).

PS- Thanks sandy for assisting in this research - by all means continue to look for relevant quotes - since the subject is developed on different tangents throughout the book, it's sometimes hard to find the crucial sentence that clarifies things.
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Postby chespernevins » Tue Feb 24, 2009 8:05 am

Hey. I tried going back to this section. It is not very easy to penetrate, for sure. Perhaps a dictionary of terms and phrases would be the most powerful way to decipher the thornier parts of this book. The ideas can’t be SO very difficult to understand. It must be the wording.

I tried to decipher this paragraph on its own merits by trying to flesh out the terminology with examples.

By all means, let me know where I’ve gone wrong. I realize that the conclusions drawn here kind of contradict what some of us generally agreed upon - that is, limiting the CMG tonic chords to triads.

Quote from p. 126

The four conceptual modal genre triads of the Lydian [LC] Scale are V major, III minor, II major, and VII minor. They function both vertically and horizontally.


The four conceptual modal genre triads of the F Lydian [LC] Scale:
C maj, A min, G maj, E min

Vertically: each of the four CMG of a LC Scale may function as the prevailing chord of a VTG Alliance formed between it and any of the eleven member scales of its designated parent [LC] scale.


The paragraph says “each of the four CMGâ€
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Postby strachs » Tue Feb 24, 2009 8:55 am

I think you're right, Ches. I appreciate you weighing in on this.

Although the term triad is used extensively in discussing CMG's, the diagrams in examples VI:14-VI:17 show triads, and also list some extended chords below, thus allowing for the entire mode to provide extended chord tones over and above the triad.

This certainly opens things up a lot, since a C major (Ionian) chordmode can be colored by the tonal orders and scales of FLC.

It's actually an important piece of info you've unlocked by clarifying this, because I was always wondering where those CM11 chords (stuff without the raised 11th) fit in, but it's as a CMG alliance with a flat-lying Lydian Scale.

Probably the reason for speaking of triads is because its the TRIAD'S existence within the Lydian scale that creates the close relationship between neighboring Tonal Centres. (The Lydian scale's own construction implies a relationship with the two sharp-lying Lydian scales, since it can produce the PMG I triad of them both). Once that relationship is recognized, the upper tones can freely be used to color the chord, even beyond the triad.

Even more interesting, and mind-boggling, is that you can even impose horizontal scales over the CMG triad!

To demonstrate why this is so freaky, Let's say we're dealing with F Lydian Chromatic as the parent scale in our VTG chord/scale alliance. We choose to sound CMG Vh (C maj), but color it with a horizontal member scale of F LCS: F maj b7. Essentially, we are now sounding C DORIAN MODE, even though we are supposedly dealing with a major-type tonic station chord.

Freaky indeed. But not wrong. There's nothing to say that a major-type tonality can only morph to other major-type tonalities, and that minors can only exist a minor third below a major.

For example, even though pentatonic-based blues scales are commonly treated as major type (C D Eb E G A) and minor type (A C D Eb E G), with the same relative-major/minor relationship as traditional tonality, the existence of the African-American Blues scale demonstrates the also common practice of choosing a tonic and relating to it at your whim with tones that practically ignore whether you're in a major or minor tonality. Blues is almost never strictly major or minor, but morphs freely as the feeling requires.

I go on, and on, and on, but it's basically to say, I'm picking up what you're putting down, and it's helping me along for sure. I hope some of what I put down helps at least as many as it confuses.
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Postby strachs » Tue Feb 24, 2009 9:20 am

Since you're all helpin' me out here, I have another question.

We know that the GRAVITY CENTERING ELEMENT (GCE) for VTG is the CHORD in a chord/scale alliance.

I haven't yet spotted what the GCE is for HTG (maybe it's not in there), have you?

Reason I ask, is because I know how to tell the difference between vertical materials and horizontal materials, but I'm less informed on how to exactly define horizontal behavior as opposed to vertical. The key is the GCE for that level of tonal gravity. It's probably the cadence, but who knows.
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Postby strachs » Tue Feb 24, 2009 10:02 am

Another point: although the CMG's can be used to express upper extensions of the chordmode, the distinction between the Primary and the Conceptual status is only clear when the chord is limited to a triad. As you progress into upper extensions, you are bridging the gap (picture the two hands in Michealangelo's Creation of Man painting) and blurring the distinction.

Eg.
FVv = Fmaj triad/C bass note
FVh = C maj triad/C bass note

Extensions:
FVv: E G B D
FVh: B D F A

Once all upper extensions are sounded, what is the difference between FVv and FVh? It's another intersect point, where two equally valid options exist, where the choice of the musician prevails, and may well affect his/her other decisions in the piece of music.
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Postby chespernevins » Tue Feb 24, 2009 12:43 pm

I haven't yet spotted what the GCE is for HTG (maybe it's not in there), have you?

Reason I ask, is because I know how to tell the difference between vertical materials and horizontal materials, but I'm less informed on how to exactly define horizontal behavior as opposed to vertical. The key is the GCE for that level of tonal gravity. It's probably the cadence, but who knows.


Yes, exactly, it's the cadence, as you say. Another way to say it is that the GCE of HTG behaviour is the tonic station to which the horizontal mode wants to resolve down the line (over the course of time).

This is in the 1950's book. (Do you have that one?)

So I suppose that our example above:

A
F
D
B
G
E
C

may be an example of verticalized horizontal gravity.

Whereas sounding a C Major scale over the chord progression:

| GLYD VI | GAuxDim II | FLydDim VI | BLydAug +V | CLYDI | CLYDI |

Would be an example of "regular" HTG.

==================

I like what your'e saying here:

This certainly opens things up a lot, since a C major (Ionian) chordmode can be colored by the tonal orders and scales of FLC.

It's actually an important piece of info you've unlocked by clarifying this, because I was always wondering where those CM11 chords (stuff without the raised 11th) fit in, but it's as a CMG alliance with a flat-lying Lydian Scale.


Like the very first example in the whole book!

And there are those cases later in the book where 9 tone order scales resolve to CMGs (Bach examples). I never knew what earlier part of the text these examples were predicated upon, but this may be it. Glad you pointed out this very difficult paragraph.

Give me some time to read your entire post thoroughly.
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Postby sandywilliams » Tue Feb 24, 2009 8:39 pm

The GCE(s) would be the tonic stations and the key.
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