72edo: Difference between revisions

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Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with [[96edo|96-edo]]), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri.

72-tone equal temperament approximates [[11-limit|11-limit just intonation]] exceptionally well, is consistent in the [[17-limit|17-limit]], and is the ninth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|Zeta integral tuning]]. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33.

72-tone equal temperament approximates [[11-limit|11-limit just intonation]] exceptionally well, is consistent in the [[17-limit|17-limit]], and is the ninth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|Zeta integral tuning]]. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other 5-limit major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33.

72 is an excellent tuning for [[Gamelismic_clan|miracle temperament]], especially the 11-limit version, and the related rank three temperament [[Marvel_family#Prodigy|prodigy]], and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic.

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 Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with [[96edo|96-edo]]), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri.
--tone equal temperament approximates [[11-limit|11-limit just intonation]] exceptionally well, is consistent in the [[17-limit|17-limit]], and is the ninth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|Zeta integral tuning]]. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33.
+-tone equal temperament approximates [[11-limit|11-limit just intonation]] exceptionally well, is consistent in the [[17-limit|17-limit]], and is the ninth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|Zeta integral tuning]]. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other 5-limit major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33.
 is an excellent tuning for [[Gamelismic_clan|miracle temperament]], especially the 11-limit version, and the related rank three temperament [[Marvel_family#Prodigy|prodigy]], and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic.