Much has been posted across the internet - including this website - on the subject of the octatonic Diminished Scale, as it's one of the more commonly used synthetic scale systems.

A "synthetic scale" is one which is derived from outside of the Major Scale matrix (which is built on a series of Perfect 5ths - and includes the minor scale systems and their modes, as well). Like the hexatonic Whole Tone Scale (built exclusively on whole steps), it's also a symmetrical system, built on alternating half and whole steps (and vice versa).

Because of its symmetrical nature, much of the Diminished Scale's traditional usage has been pattern based, giving rise to many stock "licks" and cliches, which have embedded themselves into the contemporary vocabulary and can still sound hip. A less explored concept - raised here - is to approach the Diminished Scale starting from a common tone where possible, over a set of chord changes.