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, , 3, , 5, 6, b7.
Here are a few of common fingerings for this scale (in key of E):
And the key of A:
Characteristic chords for this scale are: Half Diminished, Diminished, Minor 7, Diminished 7. You can play a progression of those chords following each note of the scale.
I see this scale as a tool to describe an atmosphere of danger and fear. Try to play around with a pedal tone (for example A), and improvise with notes of this scale, and you'll see what I'm talking about.
I will present some of my ideas for soloing in this scale, in the key of Am. First I'm gonna start with some one string runs. Example 1 (Fig 1) involves having E note as a pedal tone.
Example 2 (Fig 2) sounds pretty interesting if you play it right. You start from A note on 5th fret, first string, with index finger, and then hammer on with your ring or middle finger on higher note in the scale (Bb note), and then you slide with index finger from A to Bb note. Then continue the process all the way to higher A note on 17th fret.
Next example (Fig 3) is a slide/legato phrase on one string.
The following riff (Fig 4) requires usage of all four fingers of your left hand. Try to experiment with this kind of phrases, you might get to really groovy licks!
Next phrase (Fig 5) is a good way to experiment with using same notes in a row. Try playing this example in reverse, too!
You can also arpeggiate with notes of this scale.
The good thing about this scale is that you can use it almost any minor key, but you have to be carefull about that. If you play in A phrygian dominant, you can put this scale with no doubt, you can also hit it after natural minor, but you have to make sure you want this atmosphere in your solo. Try to combine all minor options with this, I ensure you it's worth it!