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This leads to scales with translational symmetry which include the octatonic scale (also known as the symmetric diminished scale; its mirror image is known as the inverse symmetric diminished scale [citation needed]) and the two-semitone tritone scale:
In classical theory (in contrast to jazz theory), this symmetrical scale is commonly called the octatonic scale (or the octatonic collection), although there are a total of 43 enharmonically inequivalent, transpositionally inequivalent eight-note sets.
The augmented scale: 0 3 4 7 8 11 (Root, minor 3rd, major 3rd, 5th, augmented 5th, major 7th, or minor 3rd, semitone, minor 3rd, semitone, minor 3rd, semitone) may appear to be an inexplicable omission on Messiaen's part. It is a symmetrical scale used frequently by modern jazz improvisers.
Because of the repetition of the interval pattern after only two notes, each note in the scale can be the root in another symmetric diminished scale. For example, the C diminished scale of the half-step-first type, has the same notes as the half-step-first E ♭ diminished scale as well as the whole-step-first D ♭ diminished scale.
List of musical scales and modes Name Image Sound Degrees Intervals Integer notation # of pitch classes Lower tetrachord Upper tetrachord Use of key signature usual or unusual ; 15 equal temperament
Symmetry is also an important consideration in the formation of scales and chords, traditional or tonal music being made up of non-symmetrical groups of pitches, such as the diatonic scale or the major chord. Symmetrical scales or chords, such as the whole tone scale, augmented chord, or diminished seventh chord (diminished-diminished seventh ...
These scales contain all three notes of a minor triad: the root, a minor third (rather than the major third, as in a major triad or major scale), and a perfect fifth (rather than the diminished fifth, as in a diminished scale or half diminished scale).
The augmented scale, also known in jazz theory as the symmetrical augmented scale, [3] is so called because it can be thought of as an interlocking combination of two augmented triads an augmented second or minor third apart: C E G ♯ and E ♭ G B. It may also be called the "minor-third half-step scale", owing to the series of intervals ...