The diminished scale is an eight-note symmetric scale that alternates half steps and whole steps. It sounds tense, angular and jazzy: the sound of a dominant 7th with a b9, or of a diminished 7th chord.
Formula
The reference key is A, the key all four diagrams use. There are two forms. Half-whole starts with a half step:
| Degrees | 1 | b2 | #2 | 3 | #4 | 5 | 6 | b7 |
|---|---|---|---|---|---|---|---|---|
| Notes | A | Bb | C | C# | D# | E | F# | G |
Steps: H W H W H W H W.
Whole-half starts with a whole step:
| Degrees | 1 | 2 | b3 | 4 | b5 | #5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Notes | A | B | C | D | Eb | F | F# | G# |
Steps: W H W H W H W H.
Sound and character
Half-whole has a 3 and a b7, so it's dominant, but with every tension at once: b9, #9, #11 and 13. Whole-half outlines a diminished 7th chord (A C Eb F#) with a note a whole step above each chord tone. Both sound restless and modern.
Where it's used
Jazz, bebop, fusion and metal. Use half-whole over dominant 7th chords with altered tensions: A7b9, A13b9, A7#9. Use whole-half over diminished 7th chords: Adim7. Half-whole A is two dim7 chords interlocked: A C D# F# and Bb C# E G. The second one is A7b9 without its root, which is why A7b9 and C#dim7 sound so alike.
The symmetry
The pattern repeats every minor 3rd. Compare each pattern with its copy three frets higher: same shape, same notes. So there are only three diminished scales, and A half-whole is also C, Eb and F# half-whole.
How to move it
The root is the amber dot. Slide the pattern so the amber dot lands on the new root: up two frets for B half-whole (over B7b9), down one fret for Ab whole-half (over Abdim7). Moving it three frets keeps the same notes.
Related: half-whole is whole-half starting on its second note.