Nine-Tone Order
Posted: Wed Dec 10, 2008 2:20 pm
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:
PMG +IV
AMG VI
Two possible 7b9 chords:
PMG II
AMG VII
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):
http://www.4shared.com/file/75372563/5e ... 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?
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:
PMG +IV
AMG VI
Two possible 7b9 chords:
PMG II
AMG VII
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):
http://www.4shared.com/file/75372563/5e ... 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?