Try To Track The Tritones

The main body of the LCC and its practical application, including all 4 published versions of Book 1 with their inserts: the 1959 tan cover; the 1959 light green cover Japanese edition; the 1970‘s white cover, which adds an illustrated River Trip to the 1959 edition, and the currently available Fourth Edition, 2001.

The authorization code is the first word on Page 198 of the Fourth Edition of the LCCTO.

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Try To Track The Tritones

Postby strachs » Thu Apr 23, 2009 1:16 pm

One thing that the Concept has really brought to the fore for me, is the importance of tracking the presence of tritones, even when they're not being sounded.

For one thing, the number of simultaneous tritones is a charachteristic of the Tonal Orders, and is expressed by the various Scales and Chords that represent them.

When only one tritone is present, the Seven-Tone Order (7TO) is being expressed. Identifying the Lydian Tonic of the moment (a core skill in using the Concept) basically amounts to locating that tritone and getting your bearings based on it (much like using a compass to find North, after which you can go in any direction you like).

In this 7TO, chords that contain the tritone make this easy. MGII (7th), MGVI (m6), and MG+IV (m7b5) all sound the tritone, and therefore make it a simple matter to identify the Lydian Tonic, and therefore which Lydian Tonic Center you are in.

Some music remains in that Lydian Tonic Center, bouncing around between the various modes of it, sounding triads on it's modal tonics.

Other music goes a little further, and actually changes Lydian Tonic Centres, but remaining within the range established by the CMG phenomenon - one or two fifths away.

For example, a simple blues progression (I - IV - V ) using all 7th chords. It does not simultaneously sound more than one tritone, but each chord sounds a different Lydian Tonic Center - identifiable by the tritone in each 7th chord ( in D, the chords would be D7, G7, and A7, representing C Lydian, F Lydian, and G Lydian).

What actually characterizes this progression is the movement of the tritones. This can be demonstrated by duplicating the tritone movement in more of a "scale degree modulation" approach.

For example, play D7, then Dm6, then D7 again. You can hear the same tritone movement as you do when changing from D7 to G7 and back. It's the same parent scale relationship, therefore the same tritone movement, therefore a variation on the same sound.

Locating the tritone allows you to horizontally exploit vertically simple colors (within the 7TO).

Realizing this, one can use this knowledge to exploit the higher Tonal Orders horizontally as well. All you need to do is identify the tritones (in all Tonal Orders higher than 7, two or even three tritones occur together vertically).

A key factor is how far apart the secondary tritone(s) is (or are) from the primary one (Lydian tonic and 7th tone).

For example, both the Lydian Augmented scale (8TO), and the Lydian b7 scale (10TO) contain a secondary tritone located two semitones from the primary tritone. F Lydian Augmented has F-B plus G-C#. F Lydian b7 has F-B plus A-Eb.

In each case, the secondary tritone is responsible for the AMG (for 7th chords) available in that scale. In LA, the AMG 7th chord is on III, using the scale's secondary tritone instead of it's primary one. In Lb7, the AMG 7th chord is on I, again using the scale's secondary tritone instead of it's primary one.

The Lydian Diminished scale (9TO) contains a secondary tritone that is three semitones away from the primary tritone. This secondary tritone is also responsible for the AMG 7th chord, which is on VII.

Now, although this is just one of the ways to exploit this tritone awareness, notice the resolution possibilites that emerge when we combine our AMG 7th chords with the usual CMG resolutions:

F Lydian

PMG II resolves to CMG Vh
G7 - CM

F Lydian Augmented

AMG III resolves to CMG Vh
A7 - CM

F Lydian b7

AMG I resolves to CMG Vh
F7 - CM

F Lydian Diminished

AMG VII resolves to CMG Vh
E7 - CM

Add the tritone substitutions to these:

B Lydian
C#7 - CM

B Lydian Augmented
D#7 - CM

B Lydian b7
B7 - CM

B Lydian Diminished
Bb7 - CM

... the myriad of possible resolutions for 7th chords (and that's just focussing on ONE CMG resolution target) become apparent - but in a manageable, controllable framework. How different from the major-scale-based, roman-numeral-type explanations that traditional theory offers!

One of my points here is to add to the whole Substitution topic - that there are more possibilities than just tritone substitution, and that the Concept helps us to understand and manage the possibilities.

But my other can 'o worms to open is that a more complete picture of what's happening in the Tonal Orders is gained when we locate the secondary tritones and note their distance from the primary one - that's not really discussed in Russell's book as far as I can tell.

(I like Russell's idea that a basic practical skill that is needed to make use of the Concept is to quickly identify the Lydian Tonic. I think an equally practical skill would be quick identification of Secondary Tritones as well. I'm trying to think of exercises that could be done to acheive this (maybe flash cards or something). If you have any Ideas, please let me know.)

The next logical realization along this tangent is what happens when the simultaneous tritone is only a semitone apart from the primary one? This produces the final two tonal orders, the 11TO and the 12TO, noted for their "outgoing-ness" relative to the Lydian Tonic.

The scales representing these Tonal Orders are the Auxiliary Diminished and Auxiliary Diminished Blues. These scales have three tritones.

It seems to me that the reason these tonal orders are so "outgoing" vertically, is that they are so INGOING horizontally. When modulating, or resolving, from one Lydian Tonic Center to another, the most related, most horizontally ingoing tonal center to resolve to is the one that is one step in a sharp direction, as explored at the beginning of this post. Horizontal movement occurs most naturally and easily to this tonal centre. What is the distance between the two tritones? One semitone.

Tonal centres move or resolve easily to one whose tritone is a semitone away. But these same tritones resist sounding simultaneously. My theory is that this is what accounts for the outgoing-ness of the 11- and 12-tone orders, whose simultaneous tritones are a semitone apart.

The inverse is true as well. Tritones that have an ingoing vertical relationship (like the 9TO's tritone) with the primary tritone are considered distant or outgoing horizontally.

The tritone F-B coexists quite naturally with the tritone that is three semitones apart: Ab-D. The Lydian Diminished scale and it's chords demonstrate this. But resolution, or modulation from Tonal Centers that are this same distance apart, is not so natural (F Lydian to D Lydian or Ab Lydian).

Tritones that are two semitones apart are kind of a happy medium. They blend fairly naturally when sounded simultaneously, as with the 8TO's LA scale and the 10TO's Lb7 scale, but also are related somewhat by CMG-relation between tonal centres (resolving to CMG II and VII, representing I and VI in a Lydian Scale two steps sharp).

By now, you'll be wondering what all of this has to do with practical considerations. My point is simply this: Identifying the location of tritones in a structure, whether simple or complex, is vital to understanding both horizontal movement, and vertical structures sounding in one moment. It helps us see how the horizontal and the vertical are at odds and inversely related to each other. It also can help us to quickly identify what AMG choices are made available to us in different Tonal Orders and scales, if we know where the tritones exist in our Chords.

I'm not sure that any of this will be interesting, useful, or even understandable to those reading it, but then again, this can only be discussed with people familiar with Tonal Orders, Outgoingness, and other Concept-isms.
Last edited by strachs on Wed May 06, 2009 9:22 am, edited 1 time in total.
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Postby strachs » Wed May 06, 2009 1:10 pm

I did some experimenting with this and realized a few things.

For one thing, AMG's are not really intended to provide alternate resolution paths to the CMG's. They place a chord in a more outgoing tonal environment, which is primarily a vertical consideration. That being said, the resolution possibilities that arise from sounding 7th chords on AMT's still work, and create a variety of interesting-sounding resolutions.

The other thing is that, the very existence of tritone substitutions is quite mysterious. As the above resolutions show, tritone substitution suggests resolution from a LCS that is a tritone away from the original, to the same tonic station chord. That would mean that PMG's can resolve, not only to CMG Vh, but also to a tonic station a tritone away (F7, for example can resolve to Bb major or E major). You could almost say there is an imaginary CMG tonic station on bII if you wanted to.

Or maybe I'm just nuts, who knows?


_______________
BTW, some of those resolutions that don't sound so smooth resolving to C major, sound good resolving to it's relative, A minor (IIIh).
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Postby sandywilliams » Wed May 06, 2009 8:43 pm

Some of the AMGs, such as VII( as in say Ab Lydian environment over a G7) initially seem a bit remote from C major, yet ,Ab is only only one fifth away from the LT of C minor. Carrying this a little further I guess you could say that B Lydian (AMG +V for G7+5) is only one fifth away from Gb, the LT of C mi7b5. The only hitch is that a min7b5 doesn’t count as a tonic station, does it? Maybe as an AMG of the tonic minor?
Seems like there is an interchangeability of major and minor that must be considered in this or might be of use.
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Postby sandywilliams » Wed May 06, 2009 8:57 pm

[quote="strachs"] You could almost say there is an imaginary CMG tonic station on bII if you wanted to.

Or maybe I'm just nuts, who knows?
.[/quote]
After writing my last post I get what you are saying above. Yes, an imaginary CMG on bII. Or the modal genre I and +IV could be the ultimate( sorry, probably a bad choice of words) tritone sub.
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Postby strachs » Thu May 07, 2009 9:32 am

Thank you for trying to find some validity to my ideas.

I'm really impressed at your approach to finding some reason that a resolution to C would work, even if it's only the root, and not the chord quality that attracts a resolution.

Something similar happens with the Lydian Diminished scale, whose effect I like to think of as MG-morphing. Each of the purely vertical MG's (I, VI, and +IV) kind of interchange their identities. MG I becomes minor, MG VI becomes m7b5, and MG +IV becomes a diminished tetrachord (the flat seventh becomes a double-flat seventh if you will).

I kind of typed my point into oblivion by focusing so much on resolutions from AMG's to CMG's. My main idea (that I basically buried) was about the importance of recognizing that the higher tonal orders did not only introduce a new tone to the Lydian scale, but a new tritone as well. A secondary tritone having at least some correspondency with the primary tritone of another Lydian Chromatic Scale. The distance between the two tritones, whether one semitone, two, or three, determines the vertical charachter of the scale, as well as how close or distant the scale is to other scales.

For example, the F Lydian scale is three steps away from the D Lydian scale, right? The tritone in F Lydian is F-B, the tritone in D Lydian is D-Ab. The F Lydian Diminished scale contains both of those tritones, creating at least some unity or correspondency between the two LCS's.

Similarly, the F Lydian scale is two steps away from G Lydian. The tritone in F Lydian is F-B, the tritone in G Lydian is G-C#. The F Lydian Augmented Scale contains both of those tritones, creating some correspondency between the two LCS's. (not to mention that G Lb7 is F LA)

One final example: F Lydian is two steps (in the opposite direction) from Eb Lydian. The tritone in F Lydian is F-B, the tritone in Eb Lydian is Eb-A. The Lydian Flat Seventh scale contains both of those tritones, creating some correspondency between the two LCS's. (not to mention that Eb LA is F Lb7)

I'm not saying I understand entirely the full implications of this, but it's a notable observation, I think, and I have a feeling this will be of some great usefulness as I explore it further (AMG's were just one example of how to apply the recognition of secondary tritones, but there are sure to be other uses for this feature.)

One thing that comes to light in this investigation: fifths and semitones are interchangeable in measuring the distance between tritones.

I'll definitely keep you posted as I discover further uses for this, but in the meantime, thank you Sandy for giving such careful thought to my seemingly useless ramblings.
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