Another post of scale idientification: What scale has these notes : C D Eb F Gb Ab A B? It is a octotonic 8-note ascending scale .
It's Mode 2 of Messiaen's Modes of Limited Transposition. It's composed of four segments, each comprising the intervals of a tone and a semitone (or the reverse). Like the diminished seventh chord it can be transposed three times.
Messiaen never claimed to have invented it, and acknowledges its earlier use by Rimsky-Korsakov, Scriabin, Stravinsky and Ravel. In Russia it's known as the Rimsky-Korsakoff scale, partly perhaps because he documented his use of it. It is likely that most composers, when they are young, think they have invented it. Willem Pijper certainly did, and in the Netherlands it is called the Willem Pijper scale.
Mozart, Beethoven and Schubert used it, but only 'by accident' in the context of a diminished seventh harmony and always resolving to a common chord, which is inconsistent with the mode. Liszt seems to have been one of the first to have exploited the mode's tonal ambivalence.
It is often called 'the octatonic scale', but
C C# D# E F# G A Bb
has an equal claim to that name.
As user45266 says, you could write a book on it.
You can refer to my answer to your other scale ID question (lycrimic) for more specifics, but via the same sources and process, I dug up the name "diminished scale".
Really, I should have recognised it myself, because this scale is way less obscure in western music. It sees plenty of use under that specific name, often as a dominant scale, and it has many interesting properties. Other names include "octatonic" (generally context-specific), "Whole-half Diminished" (there's another scale called the Half-Whole Diminished that is very similar, though), etc.
You can do your own research on this one, because honestly someone could write a book on this scale.