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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, or in other words 72 equal steps (equal frequency ratios). Each step represents a frequency ratio of 72√2, or 16+2⁄3 cents, which divides the 100 cent "halftone" into 6 equal parts (100 ÷ 16+2⁄3 = 6) and is thus a "twelfth-tone". Since 72 is divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72, 72-EDO includes all those equal temperaments. Since it contains so many temperaments, 72-EDO contains at the same time tempered semitones, third-tones, quartertones and sixth-tones, which makes it a very versatile temperament. This division of the octave has attracted much attention from tuning theorists, since on the one hand it subdivides the standard 12 equal temperament and on the other hand it accurately represents overtones up to the twelfth partial tone, and hence can be used for 11-limit music. It was theoreticized in the form of twelfth-tones by Alois Hába and Ivan Wyschnegradsky, who considered it as a good approach to the continuum of sound. 72-EDO is also cited among the divisions of the tone by Julián Carrillo, who preferred the sixteenth-tone as an approximation to continuous sound in discontinuous scales. (en)
- Na teoria musical, uma escala em 72 temperamentos iguais, 72-EDO ou de doze avos de tom é uma que divide a oitava em 72 graus de temperamento igual, dividindo cada semitom em seis partes iguais, de forma que cada grau equivale a uma multiplicação por 12√2 (≈ 1,009673) da frequência do anterior. Há, portanto, seis graus para cada semitom, grau próprio dos 12 temperamentos iguais, sistema dominante da música ocidental desde o século XIX. (pt)
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- Na teoria musical, uma escala em 72 temperamentos iguais, 72-EDO ou de doze avos de tom é uma que divide a oitava em 72 graus de temperamento igual, dividindo cada semitom em seis partes iguais, de forma que cada grau equivale a uma multiplicação por 12√2 (≈ 1,009673) da frequência do anterior. Há, portanto, seis graus para cada semitom, grau próprio dos 12 temperamentos iguais, sistema dominante da música ocidental desde o século XIX. (pt)
- 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, or in other words 72 equal steps (equal frequency ratios). Each step represents a frequency ratio of 72√2, or 16+2⁄3 cents, which divides the 100 cent "halftone" into 6 equal parts (100 ÷ 16+2⁄3 = 6) and is thus a "twelfth-tone". Since 72 is divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72, 72-EDO includes all those equal temperaments. Since it contains so many temperaments, 72-EDO contains at the same time tempered semitones, third-tones, quartertones and sixth-tones, which makes it a very versatile temperament. (en)
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