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Ab Half-Whole Diminished Scale notes: Ab Bbb Cb C D Eb F Gb. Formula: 1 b2 b3 3 #4 5 6 b7. Chords that fit it: Ab, Abm, Ab7, Abm7, Abdim, Abdim7, Abm7b5, Ab5.
The half-whole diminished scale alternates half and whole steps: 1 b2 b3 3 #4 5 6 b7. It fits dominant chords with b9 and #9, so it is a jazz and fusion staple over 7b9 chords. It is symmetric: the pattern repeats every three frets, so there are only three different ones.