December 16, 2010: The Symmetrical Augmented Scale, Giant Steps and The Whole Tone Scale

Symmetrical Augmented Scale

The symmetrical augmented scale is a hexatonic scales, meaning it has six tones. Like the symmetrical diminished scale, it only has two modes, which are repeated at equidistant points. Here is the structure of the first mode and the triads it produces with C as root:

R,#2(or b3),3,5,#5(or b6)and 7

Extended arpeggio:

R,3,#5,7,#9 and a natural 5

Triads:

C+,C,Cm,Eb+(or D#+),E+,E,Em,G+,Ab+,Ab,Abm and B+

What makes the symmetrical scale eccentric is that for seventh chords it colors three distinctive chord qualities from the same root and repeats it at equidistant intervals of a major third:

Cmaj7#5, Cmaj7 and Cm(maj7)

Emaj7#5, Emaj7 and Em(maj7)

Abmaj7#5, Abmaj7 and Abm(maj7)

If, as Slonimsky tells us, the symmetrical diminished scale separates the octave into four equal parts as represented by Bartok’s Pole Theory, the symmetrical augmented scale divides the octave into three equal sections. The three interchangeable points can be imagined as three points of a triangle. If C is the initial root then C is at the top point of the triangle, E is at the bottom left and Ab(G#) is at the bottom right.

It then becomes clear that this was the model for Coltrane’s Giant Steps where the three equidistant points are B, Eb and G. In fact, the same symmetrical diminished scale can be player over the Bmaj7, Ebmaj7 and Gmaj7 in that composition, though that is not what Coltrane does on his recording of the same name.

Whole Tone Scale

With the exception of the chromatic scale, the remaining symmetrical scale with no interval larger than a minor third and that repeats every octave is the whole tone scale. This scale was perhaps the first symmetrical scale to find its way into the ears of European listeners via the works of some of the Impressionist composers in the late 19th and early 20th centuries. Again, it was taken up by the innovators of the BeBop period in jazz.

This structure of the whole tone scale is:

R,2,3,#4(or b5), #5(orb6) and b7

Extended arpeggio:

R,3,#5,b7,9,#11

The whole tone scale divides the octave into six equal parts, so the chord qualities repeat at every chord tone.

Next: Modal Inexactitude and Superimposition

Copyright © 1993-2010 Jack DeSalvo