On Symmetry

I won’t speak directly to his ideas as I haven’t fully grasped them yet, but M-base has a great essay on this topic at his website. What I was reminded of, however, was how one aspect of symmetry was covered by Schillinger. Take for example a C major scale expressed in the numbers of its half-step intervals:

 2+2+1+2+2+1

That’s C major ascending but if we use that same interval sequence and descend from C it yields the notes:

C Bb Ab G F Eb Db C

In other words, the symmetrical inversion creates the C phyrigian mode or conceived another way, the key of Ab major as being the “symmetrical relative” of C major.

Similarly C harmonic minor:

2+1+2+2+1+3+1

When symmetrically inverted:

C Bb A G F E Db C

Reversed:

C Db E F G A Bb C

As a basis for creating new melodic material, using symmetry in this way yields some tasty results. The above scale, for example, being one that would form a colorful base for improvising around C7, Eb7, Gb7 or A7. In other words, the symmetric inversion of a harmonic scale generates a dominant scale for its parent note and the notes of a diminished 7th chord built on that note. Why? The new scale contains the tritone intervals of Db – G (hence Eb7 or A7) and E – Bb (hence C7 or Gb7)

I’m not sure how any of that relates to the Ancient Greek modes and their manipulation – more reading to do…