72 equal temperament

"Third tone" redirects here. For the Chinese third tone, see Standard Chinese phonology § Tones.

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). Playⓘ Each step represents a frequency ratio of 72√2, or ⁠16 + 2 / 3 ⁠ cents, which divides the 100 cent 12 EDO "halftone" into 6 equal parts (100 cents ÷ ⁠16 + 2 / 3 ⁠ = 6 steps, exactly) and is thus a "twelfth-tone" (Playⓘ). 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[1] and Ivan Wyschnegradsky,[2][3][4] 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 (96 EDO) as an approximation to continuous sound in discontinuous scales.

  1. ^ Hába, A. (1978) [1927]. Harmonické základy ctvrttónové soustavy [ German translation Neue Harmonielehre des diatonischen, chromatischen Viertel-, Drittel-, Sechstel- und Zwölftel-tonsystems   English translation Harmonic Fundamentals of the Quarter-Tone System] (in Czech and German). Translated by Kistner, Fr. Leipzig (1927) / Wien, 1978: C.F.W. Siegel (1927) / Universal (1978).{{cite book}}: CS1 maint: location (link)
    Revised German edition:
    Hába, A. (2001) [1927, 1978]. Steinhard, Erich (ed.). Grundfragen der mikrotonalen Musik [Foundations of Microtonal Music] (in German). Vol. 3. Kistner, Fr. (original translation) (rev. ed.). München, DE: Musikedition Nymphenburg Filmkunst-Musikverlag.
  2. ^ Wyschnegradsky, I. (1972). "L'ultrachromatisme et les espaces non octaviants". La Revue Musicale (290–291): 71–141.
  3. ^ Jedrzejewski, Franck, ed. (1996) [1953]. La Loi de la Pansonorité [The Laws of Multitonal Music] (manuscript) (in French). Criton, Pascale (preface). Geneva, CH: Ed. Contrechamps. ISBN 978-2-940068-09-8.
  4. ^ Jedrzejewski, Franck, ed. (2005) [1936]. Une philosophie dialectique de l'art musical [A Dialectical Philosophy of Musical Art] (manuscript) (in French). Paris, FR: Ed. L'Harmattan. ISBN 978-2-7475-8578-1.