Symmetrical Scales-Diminished, Wholetone & Symetrical Major

This is an important topic relating to material that I recently covered in my class. Blogger seach engine
sucks, making this hard to find so I am re-posting this article:

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 Nicholas 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 UNSYMETRICALLY in order to sound interesting. The Slonimsky book is a great place to find interesting non-cliche diminished and whole tone patterns.

Some ideas for hipper diminished (and WT:#1-3) patterns-
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, alternate between the two chords.

5. 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 /

Implying this:

D7b9 /G7b9 /

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!)

Mover reminded me that when you're adding substitions you can use the related ii-7s rather than the V7s. Bob says that Phil Woods does this. 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, ect) '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 ii-7 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 symetrical type scale is called the 'Symetrical 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.

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


Brian Berge said...

This is enlightening to me.

I'm reminded of a question I have that may or may be related to multiple tonics: The ascent of the root of Melodic Minor scales by a 3rd while the chords continue their usual descent in 5ths, e.g. (according to "The Jazz Theory Book") the minor ii-V-i goes:

D½° (F melodic minor)
G7alt (Ab melodic minor)
CmM (C melodic minor)

Is this related to multiple tonics? or are multiple tonics actually more...simultaneous?


David Valdez said...

The case you mention is not really a three tonic system. Over a minor two-five in C you may play F, Ab and C melodic scales. These melodic minor scales move up first by a minor third interval then by a major third interval. A three or four tonic system is based first of all on the 1:3 and 1:4 symetrical scales, so the tonics are all EQUALLY spaced. Secondly, even though you are playing three different melodics they are not really functioning as three different tonics. For example- the Ab melodic is still functioning as a V7 of the key of C minor, not as an Ab minor tonic. Check out the link to the David Baker article on my 'Extended Coltrane Changes' post for a complete description of the use of the three tonic system over ii-7 V7 I s.

Brian Berge said...

That makes sense! Thank you! :)

Dan said...

This one again. It's good to look at. I have an idea related to it, so more food for thought. This idea starts with the progression that Bob Mover reminded you of: Gmin / Bbmin Dbmin / F

This progression is strong because it moves from the dominant to the backdoor to the tritone sub. dominant, which is why you'd use it sooner than you might go: Gmin Bbmin / Dbmin Emin / F

However (and this is my little idea), you could go down from the dominant to the tritone sub in a similar way:

Gmin Emin / Dbmin (Gb7) / F

And of course mixing and matching these from the perspective of a tritone sub can yield some other strong choices:
Dbmin Emin / Gmin / F
Dbmin Bbmin / Gmin / F

josh said...

the scale you mention as symmetrical major can also be calle the augmented scale. It also can be looked at as two augmented triads a minor third apart. There is a nine note scale consisted of 3 augmented triads minor thirds apart: C+, Eb+, Gb+. This scale is listed in Messiaen's modes of limited transposition and is used by Allan Holdsworth a lot.

David Carlos Valdez said...

Calling it an Augmented scale may confuse it with the Whole-tone scale.

It is three augmented triads minor thirds apart, also three Major triads major thirds apart.

I really like this scale and actually use it quite a bit.

Pat Tucker said...

Awesome! You mentioned the Grossman Lick T-shirt. We were all transcribing Fancy Free and other Live at the Light House solos at that time. Dave Barraza wrote the lick out, I had it printed out on shirts for Dave, myself, Sam Burton, Marc Fendel, Rudresh Mahanthappa, George Garzone and Ed Tomassi. It was funny to watch other sax players around Berklee staring at our shirts.