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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 produced.
The two whole-tone scales as a symmetrical partitioning of the chromatic scale; [1] if C=0 then the top stave has even (02468t) and the bottom has odd (13579e) pitches. In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone.
The size of an interval between two notes may be measured by the ratio of their frequencies.When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (), 2:1 (), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third).
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Example of Hauer's tropes. [8] Play ⓘ. Allen Forte in The Structure of Atonal Music [9] redefines the term hexachord to mean what other theorists (notably Howard Hanson in his Harmonic Materials of Modern Music: Resources of the Tempered Scale [10]) mean by the term hexad, a six-note pitch collection which is not necessarily a contiguous segment of a scale or a tone row.
The H relation (LPL) exchanges a triad for its hexatonic pole (C major and A ♭ minor) [5] Any combination of the L, P, and R transformations will act inversely on major and minor triads: for instance, R-then-P transposes C major down a minor third, to A major via A minor, whilst transposing C minor to E ♭ minor up a minor 3rd via E ♭ major.
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