Jazz

A.  the ‘secret’ dominant scale which is 5th mode of harmonic minor plus a #9, or:

1 b2 b3 3 4 5 6 b7

Note, by way of contrast, that both the half-whole diminished and the altered scale have the first 4 notes, and the mixolydian scale has the last 4:

1 b2 b3 3 #4 5 6 b7 = half-whole diminished

1 b2 b3 3 #4 #5 b7  = altered scale

1   2  3  4  5   6  b7 = mixolydian

B. broken 9th chord arpeggios (i.e. 3, 5, 7, 9 where any voice can be displaced by an octave)

* also note in bar 21, the two a notes should be natural, not ab