Literally, a scale consisting of eight tones. Alternatively listed in E2 as the "
diminished scale." Forgive me the redundancy, but I thought I'd offer my own take, which is slightly but substantially different from the author of the other node. Here I will be speaking not of any scale which has eight tones (of which there are several), but of a specific arrangement of half and whole steps.
The octatonic scale is one of a set of scales, called generally synthetic scales for the reason that they came to be used in Western Art Music as an artificial and deliberate departure from traditional modes/scales (such as major/ minor). The scale can be generated by proceeding from a given note (for lack of a better term, the tonic) by alternating half and whole steps. For example (whole step = W, half step = H):
W H W H W H W
C D D# F F# G# A B
or
H W H W H W H
C C# D# E F# G A A#
Of course, either of these arrangements of half and whole steps can be transposed to generate a new scale. Only two arrangements of half/whole steps are considered technically "octatonic" in the sense I mean here, and these are usually named by whether the half step or the whole step begins the scale (thus, for example, an octatonic scale with the half step first would be the second of the two examples).
These two half/whole step sequences can be transposed to any "tonic," but there exist only three unique pitch collections as a result of such transpositions (as opposed to transpositions of the major scale, for example, which produce a unique pitch collection for every transposition). To illustrate my point, the octatonic scale given above with the whole step first can be transposed up by a minor third, the result being:
D# F F# G# A B C D
which, as can be seen by comparing the transposed scale to the original scale, is simply a re-arrangement of the tones of the original scale (a fact made relevant by the octatonic scale's apparent atonality, discussed later). As it turns out, only one transposition of the two given scales returns a unique pitch collection; that collection is:
C# D E F G G# A# B
which is a transposition of the second example scale, up by a minor second. The proof that these are the only unique pitch collections is certainly possible but would expand this node into perpetuity. Just take my word for it. (Unless I'm wrong.)
Now that we know what the octatonic scale is, we can discuss what it's for. The octatonic scale has the peculiar property that it doesn't establish a tonal center, unlike major, minor, or even other modal scales. This is because the scale has evenly distributed its "notes of inflection." In a major scale, for example, the seventh scale degree tends to the first, the second to the first, the fourth to the third, and so on. That is, the scale has a set of inflections which are based on common practice period usage and also, to a lesser extent, harmonics. In an octatonic scale, however, a C# could just as well be a Db -- we don't know where it's going.
This is how the first composers to use this scale intended it to be used. Impressionists such as Claude Debussy and Maurice Ravel used it to blur tonality and create "washes of sound." Russian composers of the late nineteenth century and early twentieth century, being so tied up with the French intelligentsia of the time, carried over the technique themselves, and the octatonic scale can be found in the works of Nikolai Rimsky-Korsakov, Igor Stravinsky, and Alexander Scriabin.
Another interesting aspect of the octatonic scale is that a chord of major, minor, or diminished quality can be built on some members of the scale "diatonically" -- that is, without the chromatic alteration of other members of the scale. For example, you can take the octatonic scale above, half step first, and pull out a major triad (C E G), a minor triad (C D# G), and a diminished triad (C D# F#). In the same way, some notes of any octatonic scale can be used to build dominant seventh chords -- which probably explains the octatonic scale's use to jazz musicians.