Why Only Seven Notes In the Ladder of Fifths?

Discussions on the theoretical basis of the LCC

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Why Only Seven Notes In the Ladder of Fifths?

Postby chespernevins » Wed Jan 09, 2013 7:34 pm

Why is the Ladder of Fifths only seven notes, thus forming the Lydian scale? Why doesn't the Ladder go on to eight, nine, ten fifths, etc?

I am re-posting this here, having posted it a few days ago at another forum. The post assumes we are operating within the frame of reference of the Ladder of Fifths, and not looking for other organizational principles of tonality. I don't see this as much fact as an excursion in imagination following a certain line of logic. :D However, as far as I've heard, the popularly offered answer is usually along the lines of "tradition", or "there is no logic", so this may be an improvement...

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Why isn't the Ladder of Fifths (here built on Ab) eight notes such as:

A > D > G > C > F > Bb > Eb > Ab
#I > IV# > VII > III > VI > II > V > I

I am purposefully including the A, which is outside of the 7 note Ab Lydian scale.

===

My thoughts on this are based on the following:

1) imagine that this chain is on the cycle of fifths
2) the idea of interval tonics based on a fifth, and by extension, the chain/ladder of fifths (see the definition of the ladder of fifths and tonal gravity in the LCC)

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First example:

Almost anyone, I think, would agree that the tonic of the interval Ab-Eb is Ab, but what if we wanted to test this idea using the chain/ladder of fifths idea?

To test if Eb is the tonic, we can ask if Ab is in a chain of fifths built on Eb.

Here's what that would look like:

Ab > Db > Gb > B > E > A > D > G > C > F > Bb > Eb
IV > bVII > bIII > #V > #I > IV# > VII > III > VI > II > V > I

Ab is 11 fifths around the cycle from Eb. Ab is very distantly related to Eb in the chain of fifths.

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

Here's what that looks like:

Eb > Ab
V > I

Eb is one fifth around the cycle from Ab. Eb is very closely related to Ab based on the chain of fifths idea.

The conclusion drawn here is that Ab is the tonic of the Ab-Eb P5 interval. Based on the number of fifths, we find Eb is more closely tied to a
root of Ab than Ab is to a root of Eb, and therefore Ab is the tonic of the Ab-Eb interval.


===

Let's try Ab-C, to pick a another random interval which is still within the first seven notes of the chain.

C is four fifths around the cycle from Ab.

C > F> Bb > Eb > Ab
III > VI > II > V > I

Ab is eight fifths around the cycle from C.

Ab > Db > Gb > B > E > A > D > G > C
#V > #I > IV# > VII > III > VI > II > V > I

Ab is the tonic of the Ab-C interval.

===

What about Ab-D.

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

D > G > C > F > Bb > Eb > Ab
IV# > VII > III > VI > II > V > I

G# > C# > F# > B > E > A > D
IV# > VII > III > VI > II > V > I

===

Here's the turning point: the interval Ab-A.

A > D > G > C > F > Bb > Eb > Ab
#I > IV# > VII > III > VI > II > V > I

A is 7 fifths above Ab.

However, Ab(G#) is only 5 fifths up from A.

G# > C# > F# > B > E > A
VII > III > VI > II > V > I

A has more pull on Ab(G#) than Ab does on A.

A is the tonic of the A-Ab interval.

Ab no longer "owns" this level of the ladder because it is no longer the tonic of the interval.

Ab no longer "owns" ANY of the notes above D. Therefore, that's the end of the "chain/ladder".

This limiting factor creates a ladder of fifths of exactly 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.”
chespernevins
 
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Re: Why Only Seven Notes In the Ladder of Fifths?

Postby chespernevins » Sat Jan 12, 2013 9:57 am

You know, the ladder of fifths and interval tonics are mentioned in chapter one of the "new lcc" book, but I had to read between the lines to come up with this.

All the 6 fifths of the ladder are owned by the lydian tonic, according to the idea of "interval tonics based on the ladder of fifths".

But the 5 remaining tones - the ones "on the curve" - "own" their interval with the Lydian Tonic. (for example, in C Lydian, Ab is the tonic of the Ab-C interval, even though C is the overall Lydian Tonic).

I imagine that that is why these 5 notes are "dissonant" to the prevailing Lydian scale - because they challenge the authority of the Lydian Tonic.
Last edited by chespernevins on Sat Jan 12, 2013 2:29 pm, edited 1 time in total.
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Re: Why Only Seven Notes In the Ladder of Fifths?

Postby chespernevins » Sat Jan 12, 2013 2:30 pm

Yes. :)

The Unique Thelonious Monk is one of my favorite albums of all time. Oscar Pettiford is great.
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Re: Why Only Seven Notes In the Ladder of Fifths?

Postby FiveHundo500 » Sat Aug 08, 2015 10:12 am

Because that's what the Lydian Scale is, seven consecutive fifths. The Lydian Chromatic Scale is seven fifths, then a perfect 2nd, then three fifths, then a minor sixth. George Russell says that the reason for the Lydian Chromatic Scale being arranged in this way is historical, namely the order of development of Western harmony.
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