Hearing the WOTG

[chespernevins]

I was playing this exercise this morning.

This exercise is based on altering the notes of the Lydian, one at a time, to keep a 7 note chord throughout. I am sure I am not the first to do this.

On a good piano, I played Eb Lydian VI in tertian order (C min 13 chord), and then altered the notes of Lydian VI in order of the WOTG. I chose C min/Eb Lyd because it seemed like a good register on the piano.

I played the following, playing the Lydian VI chord first each time to "cleanse the palette". Then I played the altered chord. I repeated the FULL altered chord, but for ease of notation here, I will just write the one note that is altered.

1) Lyd VI (C min 13) -> LA VI (Cmin Maj7 13)

A
F
D
Bb -> B
G
Eb
C

2) Lyd VI -> LD VI (Cmin7 b5 nat 9 13)

A
F
D
Bb
G -> Gb
Eb
C

3) Lyd VI -> Lyd b7 VI (Cmin b9 13)

A
F
D -> Db
Bb
G
Eb
C

4) Lyd VI -> Ionian VI (Cmin b13)

A -> Ab
F
D
Bb
G
Eb
C

5) Lyd VI -> Lyd b2 VI (Cmin b11? 13)

A
F -> Fb (E)
D
Bb
G
Eb
C

Exploring the relative minor seemed like an intuitive way to hear the WOTG. (I think guitarjazz mentioned this once or twice.)

I think this is pretty straight forward up through the 10 tone order. But interestingly, the LCC goes to symmetrical scales to provide the colors of the 11 and 12 tone orders.

For this type of exercise, am I missing something or creating confusion by using an altered Lydian scale in the 11 and 12 tone orders, instead of the symmetrical scales? That is, in terms of strictly attempting to hear the ingoing to outgoing progression of the 9 to 12 tone orders.

[chespernevins]

At first glance...regarding the ladder of fifths.

Is there reason why C# can't enter enharmonically as Db? This would allow Ab, Eb, & Bb to join the ladder; then consider their unique relationship to C?

You could see it this way, of course - if I understand your post.

In the experiment, I wanted to simply add, one at a time, each of the five outgoing notes to the C Lydian ladder to see what effect it seemed to have.

The question is, if we put Db on the "bottom" of this cycle of fifths, then why is F, Bb, Eb, and Ab gradually more and more consonant and then Db suddenly the most dissonant?

Why does Db break the pattern? Is there some different circumstance with Db?

If you look at the cycle of fifths, you notice that F and C#, the two most dissonant notes, are surrounding C Lydian.


Bb
Eb
Ab
C# <---------- 12 TO
F# -- C Lyd
B
E
A
D
G
C -- C Lyd
F <---------- 11 TO
Bb <---------- 10 TO
Eb <----------- 9 TO
Ab <----------- 9 TO
Db <---------- 12 TO


Does their dissonance have something to do with their close proximity to the limits of C Lydian on the cycle?

F is the second most dissonant note in the WOTG. It is also the quintessential horizontal tone because of its flat lying close proximity to C Lydian.

Introducing an F to C Lydian becomes a tension note because it suggests the tonic of a flat lying key.

Is there some link between this and the fact that C# is one fifth sharp to C Lydian and is also the most dissonant note in the WOTG?

Playing an F in a C Lyd environment introduces a shade of F Lyd into C Lyd. And sure, we could say that playing a Db introduces a shade of Db Lyd into C Lyd. But I'm suggesting that C# in a C Lyd environment could be seen/heard as introducing a shade of G Lydian into C Lyd.

For example, if we play a C# over an A min (C LYD VI) chord, it greatly challenges the very minor quality of that minor chord. This is the only outgoing note that actually threatens the minor quality of the VI chord.

If we view this C# as suggesting an A Maj (b7) chord, doesn't this suggest a shade of G Lydian?

===

The C-F# tritone suggests C Lyd. It could suggest F# Lydian as well, except that the notes {G,D,A,E,B} are between them on this view of the cycle, making it strongly C Lydian.

If we add an F to the C Lydian Ladder {F,C,G,D,A,E,B,F#} the C-F# tritone is still there of course, but in addition, the secondary F-B tritone suggests F Lyd. In fact, we have all the notes of F Lyd present, making a full ladder of fifths on F.

If we add, for example, Eb to the C Lydian Ladder {Eb,C,G,D,A,E,B,F#}, our C-F# tritone is still present. We also have a secondary tritone of Eb-A. But unlike the F Lydian example, we do not have all the notes of Eb Lyd. We only have {Eb,C,G,D,A}. We don't have a ladder of fifths built on Eb.

If we add Db/C# to the C Lydian Ladder, we still have our C-F# tritone. We also have a Db-G tritone. This tritone could suggest Db Lydian, or it could suggest G Lydian. We don't have a full Lydian scale built on Db, however, with the notes {Db,C,G,D,A,E,B,F#}. We only have {Db,C,G}. But we do have a full G Lydian scale with this set of notes: {C,G,D,A,E,B,F#,C#}.

So we could say that a secondary tritone of G-C# in C Lydian more suggests G Lydian than it does Db Lydian.

[motherlode]

Ok. Let me follow along.

[motherlode]

I read the stated premise of your post and I'm just walking along following the logic.

But what has become obvious to me is that you appear to have uncovered a sort of 'parallel universe' that exist in the cycle of 5ths. In your example, built on C, the breaking point comes at C#/Db.

There's something unsettling that happens at C#/Db. I don't think it's to far fetched to conclude that George Russell found something unsettling at that point as well.

How else can we explain the reworking of the tonal gravity chart?
I didn't know that TG had been reworked until I posted a copy from the first edition ( I believe it was dogbite that pointed that out). Needless-to-say, I was taken aback.

You have already answered a NAGGING question for me...

There certainly seems to be a 'parallel universe' and the cycle of 5ths appears to be an attempt to achieve unity...Ummmm!

Like I said, this was not the intended premise of your post but it has helped to clarify this personal issue for me.

[chespernevins]

ML,

Thanks a lot for taking the time to look over my thoughts. I like your characterization of a parallel universe!

I can only imagine how weird that must have been when you heard tonal gravity had re-arranged itself! It must be strange to have to translate as you read posts like this.

Anyway, thanks for taking a look.

[guitarjazz]

Having heard George Russell play the Principal ChordModes at the piano I believe that his thinking was more based on his ears more than a slide rule. In the case of the troublesome bII, play an F major Principal ChordMode, now add a Gb. It certainly is a troublemaker. GR was concerned with vertical unity and the WOTG does as nice job of establishing a spectrum whereby all twelve tones can be utilized vertical over any PMG. If you sit at the piano and start playing all the chords starting on page 23 I think it will become more apparent what GR was after.
If you spend too much time on the floor of the woods with a microscope you might miss the tastiest morels.

[joegold]

Having heard George Russell play the Principal ChordModes at the piano I believe that his thinking was more based on his ears more than a slide rule. In the case of the troublesome bII, play an F major Principal ChordMode, now add a Gb. It certainly is a troublemaker. GR was concerned with vertical unity and the WOTG does as nice job of establishing a spectrum whereby all twelve tones can be utilized vertical over any PMG. If you sit at the piano and start playing all the chords starting on page 23 I think it will become more apparent what GR was after.
If you spend too much time on the floor of the woods with a microscope you might miss the tastiest morels.

On the contrary...
Play a Gb on an F maj triad and you get a very usable sound that could be symbolized as F(addb9).
Acoustically speaking, it's a partial voicing of F7b9, with the b7 (the 7th partial above F) omitted (and with a distorted version of the 9th partial sounding).
Please see my initial post to this forum where I discuss the theory of acoustical roots.
I.e. The ear interpolates the b7 as being implied by the presence of the b9.
Just looking at it statistically; the only chord type that regularly supports Tb9 is the dom7 chord type.
So when we hear a b9 above a root we expect it to be a dom7 chord.
On the other hand, context can affect how we hear this chord.
Eg. If we have an already firmly established key of F major happening, and we play a cadence that treats Fmaj as the I chord, when we arrive at the F chord having a b9 on it will be heard as a contextual non sequitur, even though vertically speaking there is *no* rub.

It's only when you add Gb to an Fmaj7 chord that you get the vertical rub.
And that's because by also having the E nat present in the voicing the door is closed to hearing the b9 above it as being harmonically compatible with the chord, and there are at least 2 acoustically related reasons why we hear it that way.
1. The maj 7th of a maj7 chord is also experienced as a distorted partial, in this case a distorted 7th partial.
F A C E
4 5 6 7*
I use "*' to denote a distorted partial.
2. With the b9 also being experienced as a distorted partial we now have a vertical structure with two altered partials.
The more altered partials that a chord voicing possesses the more dissonant the chord will be experienced as.
F A C E Gb
4 5 6 7 *

And although b9's on maj7 chords are by no means everyday occurrences for most jazz musicians, there are notable instances of it actually being used.
Eg. The second melody note of Herbie's Tell Me A Bedtime Story.
Sometimes it's even notated that way in a chord symbol.
Maj7(b9)
There are two charts played in the big band that I am a regular member of that have maj7b9 chords and both instances sound beautiful.

One symmetrical structure in music that tends to help to justify the b9 on a maj7 chord is often called the super-arpeggio.
It's the sequence of maj 3rds followed by min 3rds that exists within (GR's favourite chord) the maj7(9,#11,13) chord.
F M3 A m3 C M3 E m3 G M3 B m3 D
If we continue that symmetrical pattern, the next note will be a maj 3rd above D, i.e. F#.
When the chord is actually voiced that way
1 3 5 7 9 #11 13 b16
it's really not all that dissonant sounding, although, admittedly, it's not nearly as consonant sounding as the same chord without the b9.

Likewise... The ladder of P5ths is also a symmetrically patterned structure and to my ear it totally supports F# as the 7th P5th above F.
F C G D A E B F#

I.e.
The symmetry involved in the construction of both these chords helps to cause the ear to actually expect the F# to be the 8th note in the sequence. Any tone other than F# would be a non sequitur.

And, for my money, adding a C# to an Fmaj triad is several more times annoying than adding a Gb to an Fmaj triad.
The first reason for this is because of the b9 interval formed between C, down in the main body of the chord, and the C# above.
b9's are the interval that is avoided most often within harmonic structures, i.e. chords, within straight-ahead music (i.e. music that is not relying heavily on atonal effects).
b9's, being the most complex interval of all the intervals, are, for the most part, anathema to the experience of harmony.
Of course there are some notable and very common exceptions to this "avoid b9's rule" too, the most common being the b9 interval within a dom7b9 chord.

Still, b9's are very nearly almost universally shunned in chord structures in most all of Tonal music.

Now, if the C# is voiced below the C then we have a whole other situation because there is no b9 interval.
Instead, we have a maj 7th, C#-C, which is several time more consonant and more usable harmonically than the b9 interval.
But if the chord is voiced that way then it's not an F chord anymore.
It'll be Dbmaj7#5.
I.e. F A C C# is an ugly sounding F chord.
But Db F A C is a vanilla sounding root position Dbmaj7#5 chord.
I haven't tried them all yet, but I suspect that any other voicing/permutation or inversion of these 4 tones that has the C# below the C will be experienced as a Db/C# chord rather than as an F chord.

The other reason why C# doesn't harmonize with an Fmaj triad is because the ear can't make sense of how it clouds the 3rd partial (the P5th) of the F fundamental.
I.e. We seem to be willing to hear an Faug triad as having a distorted 6th partial, but having both the un-distorted partial and the distorted partial together in the same voicing totally confuses the ear as to the consonance of the chord and it will be heard as a dissonance.

[guitarjazz]

I'm not surprised that you mentioned Tell Me A Bedtime Story. Interestingly enough, George discussed this piece and analysed it in terms of HTG. I guess that would be a good one to discuss with Ben at a lesson.
I think the bII is quite a rub, in a vertical sense, over PMG I Major.
Not sure what you are getting at about using C# in and F major chord. In the 9 tone order there could be an F major7#5 FAC#E. Having a C natural in the chord at the same time is possible under certain circumstances but I don't think it's what the author intended initially.

[guitarjazz]

Joey, have you heard this?
http://www.youtube.com/watch?v=LCEw_04Ikuc

[joegold]

I'm not surprised that you mentioned Tell Me A Bedtime Story. Interestingly enough, George discussed this piece and analysed it in terms of HTG. I guess that would be a good one to discuss with Ben at a lesson.
I think the bII is quite a rub, in a vertical sense, over PMG I Major.
Not sure what you are getting at about using C# in and F major chord. In the 9 tone order there could be an F major7#5 FAC#E. Having a C natural in the chord at the same time is possible under certain circumstances but I don't think it's what the author intended initially.

Actually, about the maj(add#5) [or maj(addb6) or however you want to notate it] chord, I just realized that I was wrong earlier about the P5th and the #5 not being able to coexist within the same chord without destroying either the chord's harmoniousness or its root feeling.
F Db A C is a such a voicing.
It's still a highly harmonious sonority and it still has a root feeling on F.

The point I was trying to make is that adding bII to a maj chord is really not that big a deal either and I still can't see why GR decided that he had to skip it in his ordering of the tones of the vertical tonal gravity field.
I.e. I'm still trying to wrap my head around the "Western Order".
I just don't get it.
To me, with my present admittedly limited understanding of the LCC, that skip of the bII seems to bring the whole house of cards, i.e. the *theory* on which the Concept is actually based, tumbling down.

At the present time I'm not here in this forum as a LCC believer who is trying to get deeper into the Concept.
I'm here as someone who is intrigued by the Concept but who can not (yet?) reconcile the other things I'm convinced that I know about music with Russell's seminal ideas.
For the time being at least, until y'all happen to convince me of the Concept's theoretical truths it'd be a good idea to keep that in mind when talking to me.

Meanwhile, in the other thread here that I actually started, I asked whether there was another more objective order of tonal gravity that Russell discusses besides the "Western Order", but no-one has answered me about that yet.
Am I correct in thinking that the Horizontal Order Of Tonal Gravity consists of a different order of tones from the Western Order which is primarily a vertical concept?
Does the horizontal order just stick to the ladder of 5ths?

[joegold]

Joey, have you heard this?
http://www.youtube.com/watch?v=LCEw_04Ikuc

I have now. It was in the background as I was typing my immediately previous post.
Thanks.
It was nice.

Is this somehow relevant to our discussion or to this thread in general?
Or is it just a nice version of Herbie's tune that you wanted me to check out?
Strange, but I could have sworn that I heard him playing Maiden Voyage somehow within his solo on Bedtime Story.
Crafty.

[guitarjazz]

[quote="joegold"][quote="guitarjazz"]I'm not surprised that you mentioned Tell Me A Bedtime Story. Interestingly enough, George discussed this piece and analysed it in terms of HTG. I guess that would be a good one to discuss with Ben at a lesson.
I think the bII is quite a rub, in a vertical sense, over PMG I Major.
Not sure what you are getting at about using C# in and F major chord. In the 9 tone order there could be an F major7#5 FAC#E. Having a C natural in the chord at the same time is possible under certain circumstances but I don't think it's what the author intended initially.[/quote]

Actually, about the maj(add#5) [or maj(addb6) or however you want to notate it] chord, I just realized that I was wrong earlier about the P5th and the #5 not being able to coexist within the same chord without destroying either the chord's harmoniousness or its root feeling.
F Db A C is a such a voicing.
It's still a highly harmonious sonority and it still has a root feeling on F.

The point I was trying to make is that adding bII to a maj chord is really not that big a deal either and I still can't see why GR decided that he had to skip it in his ordering of the tones of the vertical tonal gravity field.
I.e. I'm still trying to wrap my head around the "Western Order".
I just don't get it.
To me, with my present admittedly limited understanding of the LCC, that skip of the bII seems to bring the whole house of cards, i.e. the *theory* on which the Concept is actually based, tumbling down.

At the present time I'm not here in this forum as a LCC believer who is trying to get deeper into the Concept.
I'm here as someone who is intrigued by the Concept but who can not (yet?) reconcile the other things I'm convinced that I know about music with Russell's seminal ideas.
For the time being at least, until y'all happen to convince me of the Concept's theoretical truths it'd be a good idea to keep that in mind when talking to me.

Meanwhile, in the other thread here that I actually started, I asked whether there was another more objective order of tonal gravity that Russell discusses besides the "Western Order", but no-one has answered me about that yet.
Am I correct in thinking that the Horizontal Order Of Tonal Gravity consists of a different order of tones from the Western Order which is primarily a vertical concept?
Does the horizontal order just stick to the ladder of 5ths?[/quote]
That's a nice chord. F Db A C. What would the chord be called if you reordered the notes and say , started with Db in the bottom?
Yes , the Circle of Close to Distant Relationships sticks to the circle(not ladder) of fifths. That's in the last lesson of the 1959 edition which you might have.
If the bII thing is bothering you I guess I'll throw a question back to you: How would you personally create an inside outside continuum for an F major chord/scale( with all 12 tones available)?

[chespernevins]

If the bII thing is bothering you I guess I'll throw a question back to you: How would you personally create an inside outside continuum for an F major chord/scale( with all 12 tones available)?

I was going to ask the same thing, Joe.

[joegold]

That's a nice chord. F Db A C. What would the chord be called if you reordered the notes and say , started with Db in the bottom?

Db F A C is just Dbmaj7#5.

Yes , the Circle of Close to Distant Relationships sticks to the circle(not ladder) of fifths. That's in the last lesson of the 1959 edition which you might have.

Thanks. That's good to know.
I'll have to find some more time to look through the 1959 Ed again.
From what I've already read in the 4th Ed, there doesn't really seem to be *all that much* in the way of important new material, although obviously there are some important differences.

If the bII thing is bothering you I guess I'll throw a question back to you: How would you personally create an inside outside continuum for an F major chord/scale( with all 12 tones available)?

I'd look for extensions that I can add vertically to the Fmaj7 chord that don't create any b9 intervals with the chord tones:
G = T9
B = T#11
D = T13
Those are, of course, the usual suspects.

The more exotic extensions that can be added to this chord w/o creating any b9 intervals are:
T#9 (Ab) and T#13 (Eb) aka Tb7

Also Tb9, as has already been discussed, has been used on Maj7 chords too, vis a vis the so-called "super-arpeggio". But of course this does create a b9 with the chord's root.

The b6 (Db) aka #5 has a vertical role to play on this chord too, as long as it doesn't create a b9 with the C in the chord.

The remaining tone of the chromatic scale, Bb, can also be used vertically on a maj chord if it is voiced in such a way that it does not create a b9 interval with the 3rd (A).
But in traditional maj/min key-based music, inclusion of scale degree 4 within a voicing of the I chord will usually destroy the T function of that I chord.
But there are exceptions to this "rule" as well.
Imagine, for instance, a I IV V blues progression using maj7(add4) chords on I IV and V voiced 1 5 3 4 7 (bottom to top).
That Imaj7(add4) chord can still operate with T function if it's surrounded by that type of context. Other-wise it takes on the character of a SD func chord.
This blues sounds better though with Dom7(add4) chords than it does with Maj7(add4) chords.

There's also the fact that the root of a maj7 chord, when voiced above the 7th of the chord, creates a b9 interval too.
Standard practice, when the melody is the root on a maj7 chord, is to use a maj 6th chord instead, in order to avoid the b9.

So, if I had to order the 12 tones of the chromatic scale according to their vertical consonance with an Fmaj7 chord functioning as Imaj7 in the key of F major, from safest to least safe, my order would be this:
C A E G F D B Ab Eb Gb Db Bb

If the Fmaj7 chord had some other function in some other key, say the key of C major, then the D and B would change places:
C A E G F B D Ab Eb Gb Db Bb

Keep in mind also that vertical structures that contain more than one version of the 9th or the 11th or the 13th will be extremely unwieldy at best and completely dissonant at worst.