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15 equal temperament information


Easley Blackwood's[1] notation system for 15 equal temperament: intervals are notated similarly to those they approximate and there are different enharmonic equivalents (e.g., up-G = up-A-flat). Play
Downmajor scale on C in 15 equal temperament. Play
Major chord (parsimonious trichord[2]) on C in 15 equal temperament: all notes within 18 cents of just intonation (rather than 14 for 12 equal temperament). Play 15-et, Play just, or Play 12-et

In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is a tempered scale derived by dividing the octave into 15 equal steps (equal frequency ratios). Each step represents a frequency ratio of 152 (=2(1/15)), or 80 cents (Play). Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave, each of which resembles the Slendro scale in Indonesian gamelan. 15 equal temperament is not a meantone system.

  1. ^ Myles Leigh Skinner (2007). Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky, p.52. ISBN 9780542998478.
  2. ^ Skinner (2007), p.58n11. Cites Cohn, Richard (1997). "Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations", Journal of Music Theory 41/1.

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15 equal temperament

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In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is a tempered scale derived by dividing the octave into 15 equal steps (equal frequency...

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Equal temperament

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An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such...

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12 equal temperament

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12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic...

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31 equal temperament

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In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET (31 tone ET) or 31-EDO (equal division of the octave), also known as tricesimoprimal...

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19 equal temperament

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In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 ET, is the tempered scale...

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53 equal temperament

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music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps (equal frequency...

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17 equal temperament

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In music, 17 equal temperament is the tempered scale derived by dividing the octave into 17 equal steps (equal frequency ratios). Each step represents...

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72 equal temperament

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In music, 72 equal temperament, called twelfth-tone, 72-TET, 72-EDO, or 72-ET, is the tempered scale derived by dividing the octave into twelfth-tones...

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22 equal temperament

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music, 22 equal temperament, called 22-TET, 22-EDO, or 22-ET, is the tempered scale derived by dividing the octave into 22 equal steps (equal frequency...

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41 equal temperament

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41 equal temperament, abbreviated 41-TET, 41-EDO, or 41-ET, is the tempered scale derived by dividing the octave into 41 equally sized steps (equal frequency...

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96 equal temperament

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In music, 96 equal temperament, called 96-TET, 96-EDO ("Equal Division of the Octave"), or 96-ET, is the tempered scale derived by dividing the octave...

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Quarter tone

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evidenced proposal of the equally-tempered quarter tone scale, or 24 equal temperament, was made by 19th-century music theorists Heinrich Richter in 1823...

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34 equal temperament

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theory, 34 equal temperament, also referred to as 34-TET, 34-EDO or 34-ET, is the tempered tuning derived by dividing the octave into 34 equal-sized steps...

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Musical temperament

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requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval...

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Meantone temperament

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to pure. Meantone temperaments are constructed similarly to Pythagorean tuning, as a stack of equal fifths, but they are temperaments in that the fifths...

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58 equal temperament

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In music, 58 equal temperament (also called 58-ET or 58-EDO) divides the octave into 58 equal parts of approximately 20.69 cents each. It is notable as...

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Mode of limited transposition

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prime equal division of the octave, such as 19 equal temperament or 31 equal temperament. Composite divisions, such as 15 equal temperament or 22 equal temperament...

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Circle of fifths

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and using the standard system of tuning for Western music (12-tone equal temperament), the sequence is: C, G, D, A, E, B, F♯ (G♭), C♯ (D♭), G♯ (A♭), D♯...

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Semitone

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equivalent if and only if twelve-tone equal temperament is used; for example, they are not the same thing in meantone temperament, where the diatonic semitone...

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List of quarter tone pieces

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[page needed]. Benson 2007, p. 228. Brotbeck 2004, pp. 56–57. Stockhausen 1964, p. 15, "Konträr-Klangräume: 6 Pauken, deren Stimmung ganztönig, und zur Klavierstimmung...

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List of musical scales and modes

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unusual 15 equal temperament Play — — — 15 — — — 16 equal temperament Play — — — 16 — — 17 equal temperament Play — — — 17 — — 19 equal temperament Play...

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Regular diatonic tuning

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tone equal temperament. As the semitones get larger, eventually the steps are all the same size, and the result is in seven tone equal temperament (s =...

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Just intonation

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of fixed pitch, such as electric pianos, are commonly tuned using equal temperament, in which all intervals other than octaves consist of irrational-number...

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Bach Temperament

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have applied the equal temperament. Herbert Kelletat (1960) suggests that Kirnberger III, or a similar temperament, was Bach's temperament. A. Sparschuh...

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Musical tuning

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Thirteenth Sound 19 equal temperament 22 equal temperament 31 equal temperament 53 equal temperament Schismatic temperament Miracle temperament Hexany Music...

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Octatonic scale

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removed, while the Romanian major scale has the ♭3 degree removed. 15 equal temperament has a ten-note analogue Complexe sonore Alpha scale Beta scale Delta...

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Index of music articles

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tuning 15 equal temperament 17 equal temperament 19 equal temperament 22 equal temperament 23 equal temperament 31 equal temperament 34 equal temperament 41...

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Young temperament

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Young's first temperament C major chord in Young's first temperament Problems playing this file? See media help. "Young temperament" may refer to either...

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Pythagorean tuning

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harmonics. The major scale based on C, obtained from this tuning is: In equal temperament, pairs of enharmonic notes such as A♭ and G♯ are thought of as being...

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