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A model for hexatonic scales in 96-EDO Archived 2009-01-16 at the Wayback Machine, 96edo.com. Detailed Examination of Hexatonic Scales Originating in the Natural Scale/Harmonic Series; The origin of triads and musica ficta filling in hexatonic gaps in the diatonic scale
Euler's Tonnetz. The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a ...
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.
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.
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".
A major feature of the blues scale is the use of blue notes—notes that are played or sung microtonally, at a slightly higher or lower pitch than standard. [5] However, since blue notes are considered alternative inflections, a blues scale may be considered to not fit the traditional definition of a scale. [6]
Hexatonic (6 notes per octave): common in Western folk music; Pentatonic (5 notes per octave): the anhemitonic form (lacking semitones) is common in folk music, especially in Asian music; also known as the "black note" scale; Tetratonic (4 notes), tritonic (3 notes), and ditonic (2 notes): generally limited to prehistoric ("primitive") music