Generally the two modes of the Symmetrical Diminished Scale are regarded by improvisors as producing a series of dominant seventh and diminished seventh chords.
With C Symmetrical Diminished, from the first mode which is C Half Step/Whole Step, we get:
C7,Dbº7,Eb7,Eº7,F#7,Gº7,A7,Bbº7
From the second mode, Whole step/Half Step:
Dbº7,Eb7,Eº7,F#7,Gº7,A7,Bbº7,C7
In all cases with the dominant seventh chords (C7, etc.) the upper voices are b9,#9,#11(or b5) and 13. The upper voices for the diminished seventh chords (Dbº7, etc.) are 9,b11(or natural 3),11,b13(or#5) and a maj7.
This is excellent material for improvising over the standard jazz repertoire but for new compositions there is a wealth of harmonic possibilities inherent in the patterns that emerge. A source for these possibilities is the same source that master improvisor John Coltrane was directed to by his teacher John Sandole, Slonimsky's Thesaurus of Scales and Melodic Patterns.
In the chapter that Slomonsky calls Sesquitone Progression/ Equal Division of One Octave into Four Parts, he shows via melodic patterns that we can have, among other things, multiple chord qualities from the same root.
From C Half Step/Whole Step the triads are:
C,Cm,Cº,Dbº,Eb,Ebm,Ebº,Eº,F#,F#m,F#º,Gº,A,Am,Aº and Bbº
Besides added notes, sevenths and upper voices, each triad can have any note from the scale as a bass note, creating a slash chord.
C/Db,C/Eb(or C/D#),C/E,C/F#(or C/Gb),C/G,C/A,C/Bb
Dbº/Eb, etc., etc.
An Application of Bartok's Pole Theory
"Every art has a right to strike it's roots in the art of a previous age; it not only has a right but must stem from it." - Bela Bartok
Erno Lendvai, in his book Bela Bartok - An Anaysis of His Music, describes Bartok's Axis System. We will look at this in detail in relation to composing for improvisors in the future in this blog, but for now will look at the part that puts the symmetrical diminished scale in perspective so that its possibilities don't seem so unwieldy. This is the Pole Theory.
According to Bartok, the Tonic Axis creates two poles that cross each other at a 90º angle. Imagine this as a clock face. The root of the scale or chord resides at 12:00, we will use C. At its polar opposite, 6:00, is F#. This is the primary pole. The secondary pole goes from 9:00 to 3:00 and vice versa. At 3:00 is Eb and at 9:00 is A.
What this means is that at equidistant points in the scale we have parallel identical chord types. Tritone substitutions are common for improvisors which is the primary pole but now we see that the addition of the secondary pole gives us a circle of chords a distance of a minor third, a tritone and a major sixth from each other that are substitutable for each other.
This also explains why there are only two modes from an eight-tone scale. The exact pattern repeats every minor third.
This is why all tones in the symmetrical diminished scale can be seen as aspects of the root. If the root is C, then an A major triad is the 13th,b9 and 5 of C. An F# triad is #11,b7 and b9 of C and an Eb triad is #9(or b3),5 and b7 of C and so on.
So when a more traditional C7 chord may be used it is possible, depending on context, to instead use A/D# or F#/A, etc.
Next: Deeper into the Symmetrical Augmented Scale.
Copyright © 1993-2010 Jack DeSalvo
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