negative scales

A favorite technique of mine is to devise my own scales. Usually it
involves working out a series of steps on the keyboard, counting &
numbering.

This process isn’t unusual since there is a mathematical component to
music. And the very basis of math is counting & the idea of a number
line.

There is also a correlation between the visual arts & music. Terms
such as density, color, proportion & composition come to mind. In the
“Essentials of Music” thread, Steve Latham’s ideas led to the
proposition of their visual equivalent: 3 planes of depth in
perspective, a foreground, middle ground, background.

I’ve realized that recently I, too, have taken a concept from the
visual arts & applied it to my scale designs (I am a visual artist,
having shows of my works & sketching almost daily).

The term “negative space” is the empty space left over in a drawing
once all the fore & middle ground shapes are blocked in. In the same
way, lately I’ve been considering the “left over” notes of any scale I
design, the notes not in the scale itself.

I recognize the value of this when applied to the hexatonic scales I
spoke of in a prior post. The “negative” of any hexatonic scale would
be the remaining 6 notes of the octave, meaning these scales & their
negative scales lend themselves readily to dodecaphony & the 12-tone
technique. (Two weeks ago I recorded a piano improvisation that used
a hexatonic scale & its negative scale, as two tonal centers.)

Similarly, the scale I devised of increasing half steps

C - Db - Eb - F# - Bb - C

when continued past the interior octave, gives an unexpected result:

C - Db - Eb - E - F# - G - A - Bb - C

This is a jazz scale I learned 20 years ago from an artist friend Ray
DiCecco. As such, it made it plain to me that there was some rational
explanation - - the mathematics behind this scale - - other than
simply being someone’s whimsy of creation.

I was surprised to see these increasing half steps formulate a
definite scale since I assumed at some point ALL the 12 notes would be
touched upon as I proceeded up the keyboard. Instead, after 24 steps
the entire sequence started again, always missing 4 notes:

D - F - G# - B

This is where the negative scale kicks into view: those 4 left over
notes are of course one of the 3 diminished 7th chords (diminished
7ths are built on successive 3rds and so start over on fourth half
step).

Since there are only 3 diminished 7th chord patterns, their negative
(this 8 note jazz scale) also would only have 3 positions before
repeating. (The Eb position yields the same notes as the C position.)

Furthermore, the jazz scale already incorporates 2 known diminished
7th chord patterns, so including the scale’s negative, facilitates the
3rd diminished chord & completes the cycle.

These interrelations of positive & negative scales & how they
correlate to known chords seem to be fertile ground for composition.
Anytime we recognize correlations & see how previously disparate
elements interrelate, creativity is sparked. And as we explore these
areas & our brains map out new connections between territories, we
tend to gain a deeper insight into our practice.

After envisioning positive & negative scales, I’m wondering what would
be a good musical indicator for the concept of zero? Besides
silence, of course.














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Relevant Pages

  • Re: Just do a Diminished Scale over Dm7flat5 to G7flat9??
    ... You'll notice that it sounds best if you use enclosures to setup a note in the chord you're approaching. ... Most people hear it as a fairly exotic sound on Dm7b5, ... The harmonic minor scale, although often referred to as a "diatonic scale" really isn't a diatonic scale. ... But the way you've phrased it it appears to be a logically skewed way of representing the relationship between the phrygian scale and min7 chords. ...
    (rec.music.makers.guitar.jazz)
  • Re: Note function
    ... Its called exotic scales - New horizons for jazz improve by Befumo. ... Although the more standardized way to do the scale name would be "locrian ... But when we use B superlocrian melodically on a B7alt chord (as the B ...
    (rec.music.theory)
  • Re: Improvising on mi ii V i
    ... In most classical analysis texts ii means a minor triad built on scale ... I (a C chord in C major). ... C nat min C harm min C nat min ... If you play it in 1/8 notes and start on C Eb G or Bb then you'll always have strong notes on strong beats when playing over Cm7 or Eb6. ...
    (rec.music.makers.jazz)
  • Re: Improvising on mi ii V i
    ... In most classical analysis texts ii means a minor triad built on scale ... I (a C chord in C major). ... C nat min C harm min C nat min ... If you play it in 1/8 notes and start on C Eb G or Bb then you'll always have strong notes on strong beats when playing over Cm7 or Eb6. ...
    (rec.music.makers.jazz)
  • Re: Am I missing something?
    ... the chord for that scale? ... The intervals are the same for the major scale starting with any note. ... It uses chord notes and scale notes. ... that no sharps or flats at the beginning of the staff meant the key of C. ...
    (alt.guitar.bass)