Bb
F
Db
Ab
Bb
Cb
D
E
Cb
G
Bb
F
Db
Ab
E
Cb
Db
D
F
G
D
Bb
Db
Ab
E
Cb
G
D
E
F
Ab
Bb
F
Db
E
Cb
G
D
Bb
F
G
Ab
Cb
Db
Ab
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G
D
Bb
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Ab
Bb
Cb
D
E
Cb
G
Bb
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Ab
E
Cb
Db
D
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D
Bb
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Ab
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Cb
G
D
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Ab
Bb
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Cb
G
D
Bb
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G
Ab
Cb
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Ab
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Bb Half-Whole Diminished Scale notes: Bb Cb Db D E F G Ab. Formula: 1 b2 b3 3 #4 5 6 b7. Chords that fit it: Bb, Bbm, Bb7, Bbm7, Bbdim, Bbdim7, Bbm7b5, Bb5.
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.