The Octatonic Scale
The octatonic scale is a hybrid scale that differs from symmetrical scales like the chromatic, whole tone and diminished.
Symmetrical scale depend on one interval, chromatic--half step, whole tone-whole step and diminished-minor third. For this reason, the structure of the chords really aren't chords since a chord has a major and a minor third from note to note depending on the quality. Diminished chords are called chords, augmented as well, but the matrix with which you construct chords is limited to one-interval sizes that are compounded.
The octatonic scale is a hybrid kind of scale that most resembles a diminished scale and can be used as a replacement for a diminished chord. I will use the term chord to describe any vertical structure in this article but as referred to before, multiple intervallic distances make a chord.
Although there is a diminished quality to the octatonic scale and the outside interval is a minor third as in a diminished set interval, the octatonic scale's first interval is a half step. The pattern of the octatonic scale is half step-whole step, which added is a minor third.
The resemblance of the octatonic and diminished scale is only when using the scale in linear fashion, there is a bit of added non-chord tone tension in the octatonic when against the diminished chord but that is the final resemblance since the diminished chord is just a collection of minor thirds and the octatonic has a tremendous amount of possibilities when adding the basic intervallic steps of half and whole.
For instance, if we start an octatonic scale on "E," we get mixed "thirds." I use the term "thirds" to examine the G and G# in a chord respect. In counting from E G# is the forth tone.

The pattern being half step-whole step allows for every interval. Major and minor thirds are most notable. The tonal matrix of the diminished scale allows for only a minor third; a whole tone allows for only a major third.

Chord progressions in the octatonic realm yield mysterious settings. The scale itself is a mysterious setting. The beginning of Igor Stravinsky's Firebird congers the path of beast that is obscured.

Stravinsky's most extensive use of the octatonic scale is the complete Rite of Spring. Slice it anywhere and it conforms to the octatonic scale. As well, Toru Takamitzu's To the Edge of Dream is another octatonic piece. Both uses of the scale and its permutations is towards the edginess of the scale, the great dissonances that sound almost like a unsuspended dominant composition, but this is a primitive way of looking at it from simple tonal structures. Scriabin's Prometheus was called "unresolved dominant harmony," and that is really a useless analysis even if the piece does seem to have a tonic at the end the intention is to make this crux of the piece "home." It is correct that you could resolve most of it to a compatible "home" chord, but we are not dealing with tonal music in the traditional way.
The octatonic scale was one of the earliest methods, besides symmetrical scales, of obtaining a non-tonal feel. To say it is an a-tonal scale and setting might be correct. To say that the scale we are dealing with in the first example is "in" e would be incorrect. More correctly stated, it is "on" e as e is the starting note. As in symmetrical scales the octatonic does have the effect of repeating itself every minor third but the real gold in the scale is the whole step within the minor third.
The octatonic has provided the Jazz Music label ECM with what I used to call their signature chord. The scale has been a staple of jazz musicians for quite a long time.

Taking the above example and treating it as a diminished chord, repeating itself every minor third, the octatonic makes for a more dissonant and tense setting.

The octatonic scale is also a matrix for simple chords. Take for instance the E-major, G-major, Bb major, C# major, as well their minor equivalents. Notice that the progression of major chords is in minor thirds so the resemblance to the diminished scale is apparent, but in this case the chords are major and have their perfect fifths, as well the minor equivalents do as well.
But the chords are not constructed in the same way as a diatonic scale. The octatonic scale has eight pitches and in these types of matrixes, chord building does not have to follow the same procedure and if it does, the yield of chords is the same as the diminished scale in quality. As seen in this example, it is easy to understand why some people in Jazz call this the double-diminished scale.
Nomenclature aside, the octatonic scale contains enough intervallic differentiation to yield some really dizzy chords. It will yield many of the diatonic and tonal chords but will give some collections that have little tonal gravity.
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