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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 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.
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 ...
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
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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".
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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]