About half-whole scale
Half-whole diminished scale is an octatonic scale, meaning, it has 8 tones, or more accurate, notes. The name explains which notes they are – if you choose A half-whole scale, you go this way:
First note is A, next one is the half step higher, which is B flat, next one is two half-steps (whole step) higher, which is C, next one is again half step away, which is D flat, and so on.
The formula is 1, b2, #2, 3, #4, 5, 6, b7.