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Symmetrical Scales

Diminished, Wholetone & Symmetrical Major

by David Valdez

I'd like to expand on this topic since it is such an important element inimprovisation. In modern western music we use a system of tuning that divideseach octave into twelve equal semi-tones. Using this system we find that thereare only a certain number of possible ways to create symmetrical scales. Theear hears these scales differently than other scales because they are expressions of pure relationships of wholenumber intervals. We pick them out immediately and can easily predict the nextnote. The system that I outline here is found in Nicolas Slonimsky's classicbook "The Thesaurus of Scales and Melodic Patterns". This book has influenced generations of classical composers and Jazz improvisers alike. The puredefinition of a symmetrical scale is a scale that covers one or more octaveswith equal intervallic scales between each note. The first symmetrical scalehappens when you divide one octave equally into two parts (or the 1:2 scale). This is a scale that consists of just two differentnotes, in the key of C -C & F#. The next one is the 1:3 scale,or the augmented triad- C, E, Ab. Next is the 1:4 scaleor the diminished 7th chord- C, Eb, Gb, A. {Again, remember that scales canhave any number of notes}. If we divide one octave equally into six parts weget the whole-tone scale or 1:6 scale. There are twosymmetrical scales that we think of in Jazz improvisation are the whole tonescale and the diminished scale. The diminished scale is really just two 1:4scales (augmented chords) a whole-step apart. Let's dealwith these in more detail since they are used the most in Jazz improvisation. Adiminished scale fits over a dominant seventh b9 and/or #9 chord (see notesfrom my workshop). So over a C7b9 you would play the diminished scale ahalf-step up- C# diminished. There are many common diminished licks that everyyoung jazzer thinks are great when they first discover them. These are reallycool until you realize that just about every jazz player on the planetover-uses them at the beginning of their careers. They are as cliché as you canpossibly get! As a matter of fact, it is hard not to sound cliché when usingthis scale. Because they are symmetrical you must play them UNSYMMETRICALLY inorder to sound interesting. The Slonimsky book is a great place to findinteresting non-cliché diminished and whole tone patterns.

You can also use diminished scales to create delayed resolutions. Justplay a diminished scale a half-step down for the root of the chord that youwant to resolve to. It isn’t important what the quality of the chord thatyou’re resolving to is, it could be major, minor, whatever. This is just aquick and simple way to calculate a V7b9 to I resolution on the fly.

Here is a simple iii-/vi-/ii-/V7/I:

C-7 / F-7 / Bb-7/ Eb7/Abmaj7/
C-7 /Edim F-7/Adim Bb-7/Ddim Eb7 /GdimAbmaj7/

Some ideas for hipper diminished patterns (#1-3 can also be applied towhole-tone scales)
  1. play patterns with intervals that contain widerintervals
  2. add leading tones/approach notes that are outsidethe scale
  3. instead of 4 note repeating patterns (like usualcliché patterns) use 5
    or 7 note patterns, so they shift around in the bar.
  4. Think of the diminished scale as two diminished chords a whole-step apart,alternate between the two chords. This creates the effect of two alternating tonalities.
  5. Another way to open up diminished scale is by breaking it up into fourdifferent symmetrical two-note tri-tone scales (1:2 scales according to NicolasSlonimsky). So over a B7b9 chord you would get these four simple symmetricalscales (yes, they are still considered scales even though they only havetwo notes.)-
    C F#
    D G#
    Eb A
    F B
  6. Alternate between diminished scale and the diminished scale a half-step up.Remember to keep in mind that diminished scales resolve down in half-steps. Diminished scales moving down in half-steps is like Dominantseventh flat ninth chords moving around the circle of fifths. So if you'replaying over a dominant seventh flat-ninth chord you can play the diminishedscale up a whole step from the root, then the diminished scale a half-stepbelow that (up a half-step from the root of the dominant chord). This implies aV7b9 of V7 to V7b9.

Original chords:
D-7 / G7b9 / Cmaj7

You play:
Adim /Ab dim / C maj7

Implying this:
D7b9 /G7b9 / Cmaj7

Each diminished chord is exactly the same notes as THREE other diminishedchords. Each dominant 7th b9 chord is therefore almost exactly the same asthree other dominant 7th b9 chords:
C7b9 is related to: Eb7b9, F#7b9 and A7b9- these chords are the sameexcept for ONE NOTE difference.

So here's where things get interesting.........

You may substitute any of these chords for any other chord AND THEIR RELATEDii-7s!!!!!!!

So put in to practice it looks like this:

/D-7 /G7b9 /Cmaj7 /

You may substitute:
/F-7 /Bb7b9 /Cmaj7 /
/Ab-7 /Db7b9 /Cmaj7 /
/B-7 /E7b9 /Cmaj7 /
Or even hipper:
/D-7 /F-7 Ab-7/Cmaj7/ (Thanks Mover!)

Bob Mover reminded me that when you're adding substitutions you can use therelated ii-7s rather than the V7s. Bob says that Phil Wood's does this a lot. This seems fairly obvious yetmost players don't do this very often.
For example here is a two-five in various stages of substitution:
D-7 /G7 /Cmaj7 /
D-7 /C#7 /Cmaj7 /
G#7 /C#7 /Cmaj7 /
Eb-7/Ab-7 /Cmaj7 /

We know that Trane was very deep into the Slonimsky book. His 'sheets of sound'period was just this very type of substitution. You could call this
type of substitution a 'Four Tonic System'. Later he started exploring 1:3 and2:3 substitutions, these are the classic Giant Steps (Countdown, Fifth House, etc.) 'Three Tonic System' subs. Thissystem spawned a school that is sometimes called the 'Jewish Tenor School'.The key exponents of this school are Brecker, Grossman, Liebman and the lategreat Bob Berg. There are other players, like saxophonists Rick Margitza andthe Northwest's Burt Wilson who have thoroughly incorporated this system intotheir playing . This is a modern 'New York' sound. The three tonic system is being used not only over ii7 - V7s but over almostanything and everything! It has so much internal momentum that it can be usedas a way to go outside without losing forward motion. Personally I find itreally hard to use the three tonic system withoutsounding too much like I'm playing patterns. I find the four tonic system a biteasier to use without sounding stiff. Bob Mover once told me that he thoughtthat the three tonic system had ruined the course ofmodern Jazz. I do see his point. Back at Berklee a horn player I knew hadT-shirts made with one of the most famous Grossman licks on it, the one thatsounds like this: weeee-ba-da-ba-doo-be-ahh. Any Steve Grossman fan knows justthe one I'm talking about......

One more symmetrical type scale is called the'Symmetrical Major' scale. This exotic sounding scale is made up of three majortriads major thirds apart.


This is nice over a Cmaj7, Emaj7, and Abmaj7 chords since it has leading tonesto each note of the major triad, just keep it moving.[/QUOTE]

There are other symmetrical scales in Slonimsky's book just waiting to be applied to Jazz improvisation!
Created: May 22, 2006.
©2006, HarriRautiainen and respectiveauthors

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