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A Thought Experiment on George Russell's Lydian Chromatic Order of Tonal Gravity

George Russell is considered to be one of the great composers of the 20th century, and he is certainly one of my favorites. Check out George's first album, entitled "The Jazz Workshop", with Art Farmer, Hal McKusick, Barry Galbraith, and Bill Evans, as an exciting introduction.

Mr. Russell is equally, or perhaps more, famous for his massive theoretical work, called "The Lydian Chromatic Concept of Tonal Organization"*. The Lydian Chromatic Concept, for better or worse, is a lightening rod of controversy. I was fortunate enough to study the LCC with George Russell, and encountered the first and most common controversial topic within the first few weeks.

Mr. Russell begins by asserting that the Lydian scale is fundamental to Western music. His model of the Lydian scale is based on the interval of the Perfect 5th. According to Russell, the structure of the Perfect 5th contains within it the very basis of the LCC, and tonality itself; Tonal Gravity.

Tonal Gravity is built into the P5 interval, because in the P5 interval, one note is primary, or the "Tonic" of the interval, and the other note is secondary. The bottom note of the P5th is called the Tonic of the P5 interval. This comes from nature. The overtone series structures sound such that when a tone sounds, we hear the tone as the primary note, and at the same time, contained within that note, are other frequencies which also sound. The P5 above the original tone is one of the most prominent of these secondary frequencies to be heard. Therefore, we hear the interval of a P5 as having the bottom note as primary and the top note, secondary.

Therefore, there is a certain amount of hierarchy built in to a P5, a certain sense that a C is primary to the C-G interval, for example.

G
C <- The note C is primary in the C-G interval. Therefore, we call C the Tonic of the C-G interval.

Mr. Russell goes on to stack another fifth on top:

D
G
C

G is the tonic of the G-D interval, and C the tonic of the C-G interval. Therefore, C is the tonic of the C-D interval as well.

If we carry that to four 5ths, notice that we get the Pentatonic scale [ C D E G A ]:

E
A
D
G
C

Russell carries this further, to six fifths (7 notes):

F#
B
E
A
D
G
C

This stack of 5ths built on C is also the C Lydian scale [ C D E F# G A B ]. The note C, being the Tonic of this entire "Ladder of Fifths", is called The Lydian Tonic.

The Lydian Chromatic Concept has "Chromatic" in the name because Mr. Russell orders all 12 notes of the chromatic scale, and doesn't end with the 7 notes of the Lydian scale. This ordering of all 12 notes is called, by Russell, The Lydian Chromatic Order of Tonal Gravity, also named by Russell the "Western Order of Tonal Gravity".

Here is that order:

C#
F
Bb
Eb
Ab <-
F#
B
E
A
D
G
C

Here comes the stumbling block.

Notice that the last 5 notes of the ladder starts with Ab. The interval between F# and Ab(G#), is a 9th(2nd), not a 5th! This is because the Db(C#) is skipped and placed at the end, or the top of the ladder.

Interestingly, Russell demonstrates how the first 9 notes: the 7 notes of the C Lydian scale + Ab and Eb, can account for Major, Minor, 7th, Augmented, and Diminished chords. However, the problem with this is that, after being instructed in the central role of the P5th and the ladder of 5ths to the LCC it seems, to most students, arbitrary to skip a fifth! Is this a "fudge factor" just to get the results that Russell wanted?

Unfortunately, I think this confusion is largely because of the way, and the sequence in which, this material is presented, but this topic comes up perennially, with every new generation of students.

Here is a recent post I made to the Lydian Chromatic Forum, addressing this question, as posed, understandably, for the umpteenth time. Of course, the "Ladder of Fifths" approach is not the only way to analyze music, but the following post takes the LCC as a point of departure, works within the logic of the LCC.

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Start post:

Unfortunately, the "skipping a fifth" example as an explanation of the WOTG often seems to generate more questions than it answers. I have my own thought process on this topic. The "ladder" of six fifths (seven notes), and therefore, the Lydian scale, is a finite, 7-note entity. There is a natural limiting factor that does not allow it to go beyond the 7th note. I will give my theory on that below. The order of the last five notes [9 tone order through 12 tone order] is really what is in question. In fact, it is so much in question that Russell himself changed the order of these last five notes sometime between his earlier books and the later book.*

First of all, why is the Lydian scale only 7 tones? If we are using the ladder of fifths to create the Lydian scale, why do we stop at 7 tones and not keep going up to 8, 9, 10, etc? My thoughts on this are based on the following:

1) Imagining that this ladder is not just a straight ladder, but is on the cycle of fifths
2) The idea of interval tonics

Let's use a ladder of fifths built on C (purposefully shown here with the C#, which is outside of the 7 note C Lydian scale). All ladders, or stacks, of fifths shown here are synonymous with the order of notes in the cycle of fifths. They are just a way to visualize the cycle of fifths.

C#
F#
B
E
A
D
G
C

I'm sure we agree that the tonic of the interval C-G is C, but what if we wanted to test this idea using the ladder of fifths?

To test if G is the tonic of the C-G interval, we can ask if C is in a ladder of fifths built on G.

Here's what that would look like:

C <-
F
Bb
Eb
Ab
Db
F#
B
E
A
D
G <-

C is 11 fifths up the ladder, or around the cycle, from G. C is very distantly related to G in G's ladder of fifths.

To test if C is the tonic of the C-G interval, we can ask if G is in the chain of fifths built on C.

Here's what that looks like:

E
A
D
G <-
C <-

G is one fifth around the cycle from C. G is very closely related to C in the context of C's ladder of fifths.

Based on the number of fifths, we find G is more closely tied to a root of C than C is to a root of G, and therefore, the conclusion that we draw here is that C is the tonic of the C-G interval.

===

Let's try the same procedure with the interval of C-E.

E is four fifths around the cycle from C.

E <-
A
D
G
C <-

C is eight fifths around the cycle from E.

C <-
F
Bb
Eb
Ab
Db
F#
B
E <-

Therefore, C is the tonic of the C-E interval.

===

What about C-F#.

They are exactly opposite on the cycle, so either one could be the tonic.

F# <-
B
E
A
D
G
C <-

C <-
F
Bb
Eb
Ab
Db
F# <-

===

Up until now, C has been the tonic of all intervals in the Ladder, as formed with the note C and the 6 notes above C. However, here's the turning point: the interval C-C#.

C# <-
F#
B
E
A
D
G
C <-

C# is 7 fifths above C.

C is only 5 fifths up from C#.

C <-
F
A#
D#
G#
C# <-

Therefore, C# has more pull on C than C does on C#. C# is the tonic of the C#-C interval.

C no longer "owns" the notes beyond six fifths away because, beyond this, the gravity of the intervals is inverted.

In the same way, Ab owns the Ab-C interval, Eb owns the Eb-C interval, Bb owns the Bb-C interval, and F owns the F-C interval.

This limiting factor creates a ladder of fifths of exactly 7 notes because C no longer "owns" ANY of the notes above F#. Therefore, F# is the end of the C ladder of fifths, and the C Lydian scale is defined as 7 notes.

I imagine that this is what G. Russell means by the statement:

"an order of six fifths represents a self-organized GRAVITY FIELD."

===

Let's build on this idea of interval tonics and the 7-note ladder as a "self-organized GRAVITY FIELD" to imagine the function of the last 5 notes of the chromatic scale.

Here is our 7-note ladder of fifths on C

F# <-
B <-
E <-
A <-
D <-
G <-
C <-

This is an organized set of notes with a very clear hierarchy.

Now let's introduce the first of the chromatic notes, Ab (G#)

C#
F# <-
B <-
E <-
A <-
D <-
G <-
C <-
F
Bb
Eb
Ab <=!

In the context of C Lydian, the note Ab is a challenge to the authority of the C. Why? Because Ab is the tonic of the Ab-C interval, and Ab also owns TWO other intervals as well: Ab-G, and Ab-D.

Ab is disruptive in the context of C Lydian - it challenges the authority of C - and is therefore felt to be dissonant.

Now let's look at Eb:

C#
F# <-
B <-
E <-
A <-
D <-
G <-
C <-
F
Bb
Eb <=!!
Ab

The note Eb is even more of a challenge to the authority of C. After all, Eb is the tonic of the Eb-C interval, and THREE other intervals as well: Eb-G, Eb-D and Eb-A.

Apply the same concept to Bb, which is even more disruptive:

C#
F# <-
B <-
E <-
A <-
D <-
G <-
C <-
F
Bb <=!!!
Eb
Ab

Bb owns the Bb-C interval, and FOUR other intervals as well: Bb-G, Bb-D, Bb-A, Bb-E. Bb really asserts its own power in the context of C Lydian.

You get the idea.

Up until now, we haven't really produced a full, unbroken, competing 7-note ladder of fifths. Ab, Eb, and Bb were kind of stand-alone disruptors (or magnets, or competing gravity sources) entering into the field of gravity that is C Lydian.

But with F, we introduce a competing, unbroken, 7-note ladder of fifths:

F#
B <=
E
A
D
G
C <-
F <=!!!!

This is almost as dissonant as it can get, with a fully formed ladder of fifths based on a competing tonic. This situation represents two keys being sounded at once (F and C).

However, notice that this competing ladder on F still supports the note C, as C is in the ladder of fifths built on F. F doesn't banish C to outsider status, it just usurps the authority of C.

In fact, notice that all of the competing tonics: Ab, Eb, Bb, and F, while presenting a challenge to C, also still *support* C by forming consonant intervals with C. (C is within the imaginary ladder of fifths built upon any of these notes).

A ladder of fifths built on any of these notes is in a *flat-lying* direction from C.

However, enter C#, the worst kind of villain. The addition of C# forms another full competing ladder of fifths, built on G.

C# <=!!!!!
F#
B
E
A
D
G <=!!!!!
C XX

The G ladder of fifths forms a competing gravity field (G Lydian) that is *sharp-lying* from C Lydian, and in fact excludes the note C. If the listener (or reader) accepts G as the new Lydian Tonic, C has very little place in this new order.

Remember how dissonant the F is, in the context of C Lydian?

Well, the C, our original Lydian Tonic, is equally as dissonant in the new context of G Lydian!

The note G could never have done this to C on its own! It needed C# to yank the cycle into a new order.

Contemplate this quote from p.15 of the modern LCC book, and apply it to the two examples above: "As the strongest of the Lydian Chromatic Scale's vertical tones, the raised fourth degree has a neutralizing effect upon the strongest of its horizontal tones, the fourth degree."

According to this statement of Russell's, in C Lydian, F is the strongest horizontal tone. Meanwhile, F# is the strongest vertical tone, and it has the capability to have a neutralizing effect upon F.

Apply this logic then, to the G ladder of fifths. Does the C# have a similar effect upon the C (in the key of G) as the F# does upon the F (in the key of C)?

Therefore, does the b9 (C#) have a neutralizing effect upon the Lydian Tonic (C) in the key of C?

To conclude, in this fairy tale, C# is the rift in the C Lydian universe. C# is the note that excludes C the most, by completing a ladder of fifths on G, a sharp lying key. C# forms a gateway into an alternate universe! (Much as if you played C# over A minor).

Hope you enjoyed the story! :D

==

Anyway, feet back on the ground now, the "Western Order of Tonal Gravity" is the title of the modified ladder of fifths, and causes the b9 to be skipped, as mentioned. The "Western Order" part of the title tells us that we are taking history into account in the organization of these notes. Why do we skip the b9 (the C#, in C Lydian)? Because we accept the sound of minor (A minor/dorian) as another facet of tonality.

Here is the start of page 231, in summary*:

Let's make intervals - combinations of two notes.

We will combine C (the Lyd Tonic) with G, then with D, and then A.

Each note includes, by default, a harmonic series. Take the first few harmonics in the overtone series, for example [C C G C E] and simplify it to a triad on each note [C E G].

Combine the C Triad, with the next note in the ladder of fifths, G, and its triad G B D.

The notes C E G and G B D are all very consonant with C Lydian.

Next, let's combine a C triad and a D Triad:

C E G | D F# A. All very consonant with C Lydian.

In these three triads, we already have all the notes of C Lydian.

Next. What about a C triad and an A triad. C E G | A C# E. This gives us a bitonal sound. However, our Western history (This is where The Western Order title comes into play) allows us to bend the A triad to be minor, which is a stable sound in itself. The Minor is another aspect, or facet, of its "relative Lydian mode". This is the first instance where we reject a note, C# - in favor of staying in the original mode of C and choosing C to represent a part of A minor.

So, on the one hand we have an unbending ladder of fifths. But on the other hand, we have a 7-note mode that has multiple facets, or various forms (Major, Minor, etc.)

Something has to give to accommodate both of these organizations.

So the ladder of fifths/cycle of fifths is still used as an organizing structure within tonality. But the ladder can't be maintained in its objective form of perfectly regular chromaticism (in P5ths) and still represent all the facets of each individual key without bending.

*This article references the book: Lydian Chromatic Concept of Tonal Organization, Volume One: The Art and Science of Tonal Gravity. George Russell. Fourth Edition, 2001. Concept Publishing Co., Brookline MA.