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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 ...
The multiplication of two complex numbers can be expressed most easily in polar coordinates — the magnitude or modulus of the product is the product of the two absolute values, or moduli, and the angle or argument of the product is the sum of the two angles, or arguments. In particular, multiplication by a complex number of modulus 1 acts as ...
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 pitch collection is related to the octatonic scale, the whole tone scale, and the French sixth, all of which are capable of a different number of transpositions. [4] For example, the chord is a whole tone scale with one note raised a semitone (the "almost whole-tone" hexachord , sometimes identified as "whole tone-plus"), and this ...
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 "Ode-to-Napoleon" hexa chord is the six-member set-class with the highest number of interval classes 3 and 4 [8] yet lacks 2s and 6s. [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 ...
By comparison, in a square grid map, the distance from the center of each square cell to the center of the four diagonal adjacent cells it shares a corner with is √ 2 times that of the distance to the center of the four adjacent cells it shares an edge with. This equidistant property of all adjacent hexes is desirable for games in which the ...
The bebop major scale is derived from the Ionian mode (major scale) and has a chromatic passing note added (a ♯ 5) between the 5th and 6th degrees of the major scale. . Adding the ♯ 5 note to the seven-note major scale allows the chord tones 1, 3, 5 and 6 (a major 6th chord) to land on on-beats when the scale is played sequen