Symmetrical scales are those that have an even number of degrees. This would include whole tone and diminished. First, lets talk about the whole tone scale. As you can see, it is a six note scale. It is made up of intervals of whole steps. It has a floating, ethereal quality to the sound. It’s direct application would be on augmented chords, That is, any chord with a raised fifth degree. For example, a C augmented chord, C – E – G#, would take the C whole tone scale.
A C# augmented chord, C# – F – A, would take the C# whole tone scale.
You will discover that there are only two whole tone fingering patterns to learn. The only difference is where you start them and how you apply them. A well known example is the beginning of “You Are the Sunshine of My Life” by Stevie Wonder. The pattern right before he starts singing is a whole tone scale in thirds. In “Take the ‘A’ Train” the second chord is a II7 chord, try playing a whole tone scale that starts on the same note as the root of the chord.
Now lets move on to diminished scales. There are two types of diminished scales, half-step/whole-step and whole-step/half-step. I will deal with half-step/whole-step scales because you will see that they are the same scales, just started on a different note.
C half step/whole step diminished scale.
C# half step/whole step diminished scale.
D half step/whole step diminished scale.
There are only three fingering patterns to get under your fingers. Because of the configuration of these scales, they have an ambiguous quality to them. They apply to four different tonalities at the same time. Their direct application is over altered dominant chords. That is, dominant chords with sharp 9, 11 or 13 and/or flat 9 and 13. The C half-step/whole-step diminished scale would be used with C7alt, Eb7alt, F#7alt and A7alt chords. The C# half-step/whole-step diminished scale would be used with C#7alt, E7alt, G7alt and Bb7alt chords. The D half-step/whole-step diminished scale would be used with D7alt, F7alt, Ab7alt and B7alt chords.
Whole step/half step diminished scales are the same configuration of notes except that you start the scale with a whole step rather than a half step. A whole step/half step diminished scale applies to diminished chords. In other words, for a Cdim7 chord, C – Eb – F# – A, you would use a C whole step/half step diminished scale.
Here is one of many diminished patterns. If you listen to John Coltrane then you may have heard him playing these sorts of patterns. He discovered them in the book “Thesaurus of Scales and Melodic Patterns” by Nicolas Slonimsky.