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David Valdez grew up in Santa Cruz, Calif., USA, and currently lives in Portland, Oregon. He started on the alto at eight years old. David studied saxophone with Joseph Viola, Jimmy Mosher, George Garzone, Bob Mover and Paul Contos. Studied Jazz improvisation at Berklee College of Music from '86-'89. He has played the alto for thirty years and picked up the tenor sax just last year.
David has worked with Kurt Rosenwinkle, Charlie Hunter, Clark Terry, John Medeski, Dave Holland, Josh Roseman, The Either Orchestra, Eddie Henderson, Dave Fuiczynski.
Musical Influences: Bird, Cannonball, Trane, Charles Macpherson, Lee Konitz, Johnny Griffin, George Garzone, Phil Woods, Dick Oats, Frank Srozier, Gary Bartz, Joe Henderson, Warne Marsh, Stanley Turrentine, Bob Mover, Rich Perry, Sonny Rollins, Sonny Criss, Sonny Stitt, Steve Grossman, Jimmy Mosher, Johnny Hodges and Lenny Tristano.
David's web blog

Selected Related Books:

Thinking in Jazz
Thesaurus of Scales and Melodic Patterns
by Nicolas Slonimsky
Thinking in Jazz:
The Infinite Art of Improvisation by Paul F. Berliner
Jazz Improv: How to Play It and Teach It by Jimmy Amadie
Improvising Jazz by Jerry Coker
Jazz Piano & Harmony : An Advanced Guide (w/CD) by John M. Ferrara
Tonal and Rhythmic Principles : Jazz Improvisation by John Mehegan
Thinking in Jazz
Vol. 3, The II/V7/I Progression: A New Approach To Jazz Improvisation (Book & CD Set)
Jamey Aebersold Play-A-Long Series
A New Approach to Jazz Improvisation by Jamey Aebersold (Audio CD)
Jazz Improvisation by David Baker
Modern Jazz Piano : A Study in Harmony by Brian Waite

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Symmetrical Scales

Diminished, Wholetone & Symmetrical Major

by David Valdez

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I'd like to expand on this topic since it is such an important element in improvisation. In modern western music we use a system of tuning that divides each octave into twelve equal semi-tones. Using this system we find that there are only a certain number of possible ways to create symmetrical scales. The ear hears these scales differently than other scales because they are expressions of pure relationships of whole number intervals. We pick them out immediately and can easily predict the next note. The system that I outline here is found in Nicolas Slonimsky's classic book "The Thesaurus of Scales and Melodic Patterns". This book has influenced generations of classical composers and Jazz improvisers alike. The pure definition of a symmetrical scale is a scale that covers one or more octaves with equal intervallic scales between each note. The first symmetrical scale happens when you divide one octave equally into two parts (or the 1:2 scale). This is a scale that consists of just two different notes, 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 scale or the diminished 7th chord- C, Eb, Gb, A. {Again, remember that scales can have any number of notes}. If we divide one octave equally into six parts we get the whole-tone scale or 1:6 scale. There are two symmetrical scales that we think of in Jazz improvisation are the whole tone scale and the diminished scale. The diminished scale is really just two 1:4 scales (augmented chords) a whole-step apart. Let's deal with these in more detail since they are used the most in Jazz improvisation. A diminished scale fits over a dominant seventh b9 and/or #9 chord (see notes from my workshop). So over a C7b9 you would play the diminished scale a half-step up- C# diminished. There are many common diminished licks that every young jazzer thinks are great when they first discover them. These are really cool until you realize that just about every jazz player on the planet over-uses them at the beginning of their careers. They are as cliché as you can possibly get! As a matter of fact, it is hard not to sound cliché when using this scale. Because they are symmetrical you must play them UNSYMMETRICALLY in order to sound interesting. The Slonimsky book is a great place to find interesting non-cliché diminished and whole tone patterns.

You can also use diminished scales to create delayed resolutions. Just play a diminished scale a half-step down for the root of the chord that you want to resolve to. It isn’t important what the quality of the chord that you’re resolving to is, it could be major, minor, whatever. This is just a quick 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   /Gdim  Abmaj7/

Some ideas for hipper diminished patterns (#1-3 can also be applied to whole-tone scales)

  1. play patterns with intervals that contain wider intervals
  2. add leading tones/approach notes that are outside the scale
  3. instead of 4 note repeating patterns (like usual cliché 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 four different symmetrical two-note tri-tone scales (1:2 scales according to Nicolas Slonimsky). So over a B7b9 chord you would get these four simple symmetrical scales (yes, they are still considered scales even though they only have two 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 Dominant seventh flat ninth chords moving around the circle of fifths. So if you're playing over a dominant seventh flat-ninth chord you can play the diminished scale up a whole step from the root, then the diminished scale a half-step below that (up a half-step from the root of the dominant chord). This implies a V7b9 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 diminished chords. Each dominant 7th b9 chord is therefore almost exactly the same as three other dominant 7th b9 chords:
C7b9 is related to: Eb7b9, F#7b9 and A7b9- these chords are the same except for ONE NOTE difference.

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

You may substitute any of these chords for any other chord AND THEIR RELATED ii-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 the related ii-7s rather than the V7s. Bob says that Phil Wood's does this a lot. This seems fairly obvious yet most 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 and 2:3 substitutions, these are the classic Giant Steps (Countdown, Fifth House, etc.) 'Three Tonic System' subs. This system spawned a school that is sometimes called the 'Jewish Tenor School'. The key exponents of this school are Brecker, Grossman, Liebman and the late great Bob Berg. There are other players, like saxophonists Rick Margitza and the Northwest's Burt Wilson who have thoroughly incorporated this system into their playing . This is a modern 'New York' sound. The three tonic system is being used not only over ii7 - V7s but over almost anything and everything! It has so much internal momentum that it can be used as a way to go outside without losing forward motion. Personally I find it really hard to use the three tonic system without sounding too much like I'm playing patterns. I find the four tonic system a bit easier to use without sounding stiff. Bob Mover once told me that he thought that the three tonic system had ruined the course of modern Jazz. I do see his point. Back at Berklee a horn player I knew had T-shirts made with one of the most famous Grossman licks on it, the one that sounds like this: weeee-ba-da-ba-doo-be-ahh. Any Steve Grossman fan knows just the 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 major triads major thirds apart.
This is nice over a Cmaj7, Emaj7, and Abmaj7 chords since it has leading tones to each note of the major triad, just keep it moving.

There are other symmetrical scales in Slonimsky's book just waiting to be applied to Jazz improvisation!

Created: May 22, 2006.
© 2006, Harri Rautiainen and respective authors
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