The Diminished Scale in Jazz is mostly used as an expression of a dominant chord with b9, #9, #11 and natural 13. The exception being its use over diminished chords, which don't show up that much these days.

The first things that become apparent when studying the Diminished Scale is that it consists of alternating half steps and whole steps, and that there are eight notes in the scale. This symmetrical construction means that there are only three Diminished Scales. If you play: C Db Eb E, F#, G, A, Bb Ñ then start on Eb: Eb, E, F#, G, etc., you quickly realize that you're playing the same scale. This has lots of implications for you as an improvisor, and they're all good. For instance, this scale contains four major triads: C, Eb, Gb, and A. It also has four 7th-chord arpeggios (spelled enharmonically):