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Nine-Tone Order

PostPosted: Wed Dec 10, 2008 2:20 pm
by strachs
If you've read any of the "Close-To-Distant Revisited" thread, where I go on and on about the Lydian Chromatic Scale versus the Pythagorean ladder of fifths, you'll know that I am in favor of laying out the 12 tones of Equal Temperament in fifths for the purpose of analysis, writing out a row like this:

F C G D A E B F#/Gb C#/Db G#/Ab D#/Eb A#/Bb

Doing so provides a kind of birds-eye view of the tones being used, and their relationship to the Lydian Tonic. Looking from this viewpoint, some interesting things become apparent. I'm still not fully settled in what I'm seeing, so I invite comments from others to tell me if this makes sense.

Observation #1:
The well-known phenenomenon of "relative major/minor" can be observed from this view. (Interesting because theorists can easily explain why the major triad sounds final, but have always been a little dumbfounded about why the minor triad should sound so final, when it does not express the overtone series like major does)
The triad F major is formed using the first, second, and fifth tones of the P5 ladder.
The triad D minor (relative minor of F major) contains the first, fourth, and fifth tones of the P5 ladder.
The distance between the two related tones is four fifths (half the span of the seven-tone order).
This is also the distance from the relative minor to the last tone in the seven-tone order (Lydian scale).
This is also the distance from the last tone in that seven-tone order to the most common of the five "distant" tones (the tenth tone, or Russel's 9-tone order).

Observation #2:
In Russell's book, the term "consonant nucleus" caught my attention (page 14, with reference to the 9-tone order). I began wondering why this tonal level is seemingly so useful, so "consonant". These are some of my observations, aided by the row of perfect fifths, above:

The seven -tone order is framed in a tritone (F-B, eg.). Exactly in the middle is the relative minor of the Lydian Tonic (D, eg.).
Exactly in the middle of the "unused" notes (orders 8-12) is perhaps the most important higher-than-7 tone. Russell calls it the 9th tone, I call the 10th. Whatever.
It is the tone that gives us the Harmonic Minor Scale (because it's the leading tone of the IIIh CMG, or Aeolian Mode).
It is also the tone that gives us the Lydian Diminished Scale (allowing two m7b5 chords a minor third apart, as well as two 7b9 chords, also a minor third apart.)

Two possible m7b5 chords:

Two possible 7b9 chords:

In both cases, the alternate version is a minor third away.
This allows the same harmonic device to be used in a major key and it's relative minor key.
Example is "The Gentle Waltz" by Oscar Peterson.
The first four measures employ the F Lydian Diminished scale to provide the m7b5 and 7b9 of a ii-V7-I cadence in C Major.
The next four measures employ the same F Lydian Dminished scale to provide the m7b5 and 7b9 of a ii-V7-i cadence in A Minor.

Here's a Finale score of the piece - excuse the occasional eighth rest in your way - I'm still having trouble with layers (I hope this is legal, since I "Finale'd" it myself): ... d=f916286f

Especially for those not extremely harmonically adventurous, the nine-tone order (Russel's, not mine) provides the tools to reach beyond, without going too far beyond and getting lost. It's also the tonal order that was (probably unknowingly) employed by Bach, Mozart, Chopin, and others; extremely useful in analyzing their music's harmonic language.

It seems to me that even some of the most chromatically-rich compositions of the Classical and Romantic era do not stray beyond this tonal level. For example, Chopin's famous Prelude in E Minor (Op. 28 No. 4), a highly chromatic and seemingly rule-breaking piece of music, derives almost all of it's chords from three Lydian Chromatic scales (F, C, and G), all within the span of CMG-relation, all using the seven- and nine- tone orders. If this interests you, I'll post my analysis of this Prelude.

Anyway, I wanted to post this stuff in hopes that you'll all reciprocate and give me your observations of both the uniqueness of the 9-tone universe, and the relative major/minor phenomenon. Are they related? Does the minor third interval really possess the power both to "relate" major and minor keys, and at the same time provide some of the more useful vertical structures? Am I just reading way too much into this?

PostPosted: Wed Dec 10, 2008 10:43 pm
by dds1234
Guys I am about to rant so... I totally recommend ignoring this.

I love the minor third! If you move it anywhere... Where does it go?

Since you mentioned it, this is the only interval that has sparked my interest for some time.

I have a view on it. It might seem like an odd one, but I do.
-In question form I might add.

T.G. 7 T.O.
1 2 3 -(4)- 5 6 7

Four equals - The center of the seven tonal order.
The center of the ingoing order. Why Is that? What is its function? Why is it so appealing to me? It is separated from the others by a center - a middle location. Disregard all that and - It's still a complex interval.

I am getting at nothing. It's not really a view, just an observation. You are not reading too much into it. It does have this mysterious movement to it... It makes absolutly no sense to me.

Do you mean your nine tone order or his? Did I ignore you questions? If so then my apologies.

P.S. Finale is bleh! (IMO) I just adore Photoscore and Sibelius.

PostPosted: Thu Dec 11, 2008 10:14 am
by strachs
I edited the above to clarify that I meant Russell's 9-tone order (sorry for confusing things).

And you're right, Finale is BLEH - but as a mere hobbyist, my musical budget is also BLEH. Notepad it is.

Glad to see I'm not the only one who is interested in the minor third phenomenon.

As a side note, the precise reason for many minor-key Baroque works ending on a major triad is because the minor triad was seen to lack the finality of the major, on account of not mirroring the overtone series as exactly.

I certainly haven't solved the mystery of the minor third, but I do feel that the equal distance between the Lydian tonic, the relative minor degree, the outer tone of the 7-tone order, and the tone of the most widely used "higher-than-seven" tonal order, has to signify something.

Not to mention the MG ambiguity of the diminished 7th chord (composed of all four minor sevenths) noted over in the "Diminished vs. m7b5" thread.

Not to mention that the "critical bandwidth" (Helmholtz), within which beating and "rouphness" are felt/heard, is approximately a minor third.

There's definitely some special property to this interval. Studying relationships using Pythagorean fifths just makes this all the plainer.