The Half-Whole Scale (the diminished scale) is like any other scale, made up of notes that are a set distance away from each other.
Semi-Tone, Tone, Semi-Tone, Tone, Semi-Tone, Tone, Semi-Tone, Tone,
So we will end up with 7 notes. Each of these notes we will number...
1 b2 #2 3 b5 5 6 b7 1
This particular scale is also classed as a scale of limited transposition due to the nature of intervals within it. This means that it essentially repeats every 3 frets.