Olivier Messiaen’s 3rd Mode. Used by Coltrane, Holdsworth and Zappa!!!

First place the notes into a seven-note scale,
with the following intervals: 1,2,b3,b4,b5,bb6,bbb7.
Starting on C:
C,D,Eb,Fb,Gb,Abb,Bbbb. Abb sounds like G. Bbbb is
The same frequency as Ab.

The same intervals are played from the note E;
which is the same frequency as Fb in the scale above,
which started on C.
Starting on the note E:
E,F#,G,Ab,Bb,Cb,Dbb.
The intervals are: 1,2,b3,b4,b5,bb6,bbb7.

The same Intervals are played from G#; which is
notated as Ab in the scale above.

1, 2, b3,b4,b5,bb6,bbb7 are the intervals.
G#,A#,B,C,D,Eb,Fb are the notes.

Overlapping two scales gives the following triads:
Minor, Major, Augmented, and both Major and Minor
with b5’s. In addition, all triads have access to both Major
and Minor 7ths.

This scale uses nine of a possible 12 frequencies.
Interestingly, the three remaining notes are:
F, which is the fourth of C.
A, which is the fourth of E.
C#, which is the fourth of G#. These three notes are also an
Augmented Triangle, or Triad. So, all the same things apply
As the C,E,G# Triangle, or Triad above.