In the previous post I wrote about Schoenberg’s presentation of the harmonic series as the foundation of Western tonality. I have been positively entranced by this concept.

I’ve been practicing just playing the harmonic series in the left hand.

Melodic minor scale

As I noted in the last post, the melodic minor scale built on the 5th above the fundamental exists (with allowance for discrepancy between the pure harmonics versus equal-temperament tuning, but I will just ignore this and proceed based on the evidence of the gut feeling of the power these consonances) within every harmonic series. That means that this scale has a special relationship with any root note, such as for example g melodic minor to C or e melodic minor to A.

Bill Evans and “crunchy” sounds

The “A” and “B” voicings popularized by Bill Evans are both transpositions of harmonics available in the “crunchy”-sounding 3rd and 4th octaves above the fundamental. This sound was present in Debussy, and ins Rachmaninoff to a lesser degree.

Chords that compose the melodic minor scale

Another interesting aspect of the harmonic series – chords available in the harmonic series:

  • Major I (e.g. A)
  • minor v (e.g. e)
  • Major II (e.g. B) – contains the #11, AKA the leading done of the harmonically-related melodic minor scale

These 3 chords – all a 5th apart, and which, again, are all available in a harmonic series – together compose the harmonically-related melodic minor scale.

Consonant-dissonant continuum

Guided by Schoenberg’s notion that “the expressions ‘consonance’ and ‘dissonance’ are false” (and are, instead, a continuum, based on how far away a tone is from the fundamental, I’ve experimented also with major chords around the circle of fifths in relation to the fundamental.

  • Dissonant? is very unscientific – just my gut reaction to playing the major chord in the middle register above the fundamental in the bass. Following Schoenberg, this could probably be quantified by measuring the total “harmonic distance” of each of the three notes in the chord from the fundamental. That would be interesting to see.
(T) # of 5ths away Quality (F=(R)oot) Quality (T=R) Dissonant?
6 down I don’t know haha M♯11 (F=♯11) 3
5 down M♭9sus(sus6); (T=♭9) M7 (F=M7) 2
4 down m(sus6) (T=sus6) M (F=3) 1
3 down m7 (T=m3) M6 (F=6) 1
2 down m7sus9 (T=m7) Madd9 (F=9) 1
1 down Msus6 (T=sus4) M (F=5) 1
(F)undamental M (T=R) M (F=R) 0
1 up M7add9 (T=5) M add4 (F=4) 1
2 up M69♯11 (T=9) dom7 (F=b7) 1
3 up M13♭9 (T=13) M♯9 (F=♯9) 2
4 up M7♯5 (T=3) Madd♯5 (F=♯5) 2
5 up dim, add M7(T=M7) M♭9 (F=♭9) 4
6 up (= 1st row) I don’t know haha M♯11 (F=♯11) 3

Practicing polyrhythms, left hand independence, and the harmonic series

Another interesting aspect to practice – polyrhythm of 3 against 4. The only way to start absorbing this is to go to the common denominator 12. I note that to play 3 over 4, if we subdivide each quarter into triplets, in the first triplet we play on the first note, in the second the second, in the third the third, and in the fourth not at all. And that is the basis of practicing. The goal is always to end up simply “feeling” this. At slow tempos the feeling is lost, but we have to build back up to the fast tempos.

# in measure # in triplet Part of the “3 against 4”?
1 1 yes
2 2  
3 3  
4 1  
5 2 yes
6 3  
7 1  
8 2  
9 3 yes
10 1  
11 2  
12 3  

It’s not easy to feel in your fingers, but once you feel it, it sounds very natural.

A practice method to tie polyrhythms, left hand independence, and the harmonic series is:

  • arpeggiate up and down the first 7 harmonics of the harmonic series
    • this forms a highly consonant voicing of a dominant 7th chord
    • adds up to 12 notes up and down, exactly forming a single measure
  • play the “3” against the first harmonic (the root of the 7th chord) and both instances of the 5th harmonic (the major third of the 7th chord)