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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.
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.
An essentially nine-note blues scale is defined by Benward and Saker as a chromatic variation of the major scale featuring a flat third and seventh degrees (in effect substitutions from Dorian mode) which, "alternating with the normal third and seventh scale degrees are used to create the blues inflection. These 'blue notes' represent the ...
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.
This tritone relationship between possible resolutions is important to Scriabin's harmonic language, and it is a property shared by the French sixth (also prominent in his work) of which the synthetic chord can be seen as an extension. The example below shows the mystic chord rewritten as a French sixth with notes A and D as extensions:
Modes of limited transposition are musical modes or scales that fulfill specific criteria relating to their symmetry and the repetition of their interval groups. These scales may be transposed to all twelve notes of the chromatic scale, but at least two of these transpositions must result in the same pitch classes, thus their transpositions are "limited".
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.
[2] 6-20 maps onto itself under transposition three times (@0,4,8) and under inversion three times (@1,4,9) (six degrees of symmetry), allowing only four distinct forms, one form overlapping with another by way of an augmented triad or not at all, and two augmented triads exhaust the set as do six minor and major triads with roots along the ...
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