72edo: Difference between revisions

{{Infobox ET

| Prime factorization = 2³ × 3²

| Consistency = 17

| Monotonicity = 29

}}

The '''72 equal divisions of the octave''' ('''72edo'''), or '''72-tone equal temperament''' ('''72tet''', '''72et''') when viewed from a [[regular temperament]] perspective, 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 [[12edo]]. 72edo is also a superset of [[24edo]], a common and standard tuning of [[Arabic, Turkish, Persian|Arabic]] music, and has itself been used to tune Turkish music.

== Theory ==

72edo 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 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo 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.

72edo is an excellent tuning for the [[miracle]] temperament, especially the 11-limit version, and the related rank-3 temperament [[prodigy]], and is a good tuning for other temperaments and scales, including [[wizard]], [[harry]], [[catakleismic]], [[compton]], [[unidec]] and [[tritikleismic]].

== Intervals ==

== Notations ==

=== Sagittal ===

[[File:72edo Sagittal.png|800px]]

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=== Commas ===

Commas tempered out by 72edo include…

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