72edo: Difference between revisions
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'''72-tone equal temperament''', or '''72-edo''', divides the octave into 72 steps or ''moria''. This produces a twelfth-tone tuning, with the whole tone measuring 200 cents, the same as in 12-tone equal temperament. 72-tone is also a superset of [[24edo|24-tone equal temperament]], a common and standard tuning of [[Arabic,_Turkish,_Persian|Arabic]] music, and has itself been used to tune Turkish music. | '''72-tone equal temperament''', or '''72-edo''', divides the octave into 72 steps or ''moria''. This produces a twelfth-tone tuning, with the whole tone measuring 200 cents, the same as in 12-tone equal temperament. 72-tone is also a superset of [[24edo|24-tone equal temperament]], a common and standard tuning of [[Arabic,_Turkish,_Persian|Arabic]] music, and has itself been used to tune Turkish music. | ||
Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with [[96edo]]), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri. | Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with [[96edo]]), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri. | ||
== Theory == | |||
{{Primes in edo|72|columns=11}} | |||
72-tone equal temperament approximates [[11-limit]] [[just intonation]] exceptionally well, is consistent in the [[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-tone equal temperament approximates [[11-limit]] [[just intonation]] exceptionally well, is consistent in the [[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. | ||
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* [[JuneGloom]] | * [[JuneGloom]] | ||
=== Harmonic | === Harmonic scale === | ||
Mode 8 of the harmonic series – [[overtone scale|overtones 8 through 16]], octave repeating – is well-represented in 72edo. Note that all the different step sizes are distinguished, except for 13:12 and 14:13 (conflated to 8\72edo, 133.3 cents) and 15:14 and 16:15 (conflated to 7\72edo, 116.7 cents, the generator for miracle temperament). | Mode 8 of the harmonic series – [[overtone scale|overtones 8 through 16]], octave repeating – is well-represented in 72edo. Note that all the different step sizes are distinguished, except for 13:12 and 14:13 (conflated to 8\72edo, 133.3 cents) and 15:14 and 16:15 (conflated to 7\72edo, 116.7 cents, the generator for miracle temperament). | ||