72edo: Difference between revisions
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=== Ivan Wyschnegradsky's notation === | === Ivan Wyschnegradsky's notation === | ||
{{ | {{Sharpness-sharp6-iw}} | ||
== JI approximation == | == JI approximation == | ||
[[File:72ed2.svg|250px|thumb|right|none|alt=alt : Your browser has no SVG support.|Selected intervals approximated in 72edo]] | [[File:72ed2.svg|250px|thumb|right|none|alt=alt : Your browser has no SVG support.|Selected intervals approximated in 72edo]] | ||
=== | === Interval mappings === | ||
72edo is the ninth [[ | {{Q-odd-limit intervals|72}} | ||
=== Zeta properties === | |||
72edo is the ninth [[zeta integral edo]], as well as being a peak and gap edo, and the maximum value of the [[The Riemann Zeta Function and Tuning #The Z function|Z function]] in the region near 72 occurs at 71.9506, giving an octave of 1200.824 cents, the stretched octaves of the zeta tuning. Below is a plot of Z in the region around 72. | |||
[[File:plot72.png|alt=plot72.png|plot72.png]] | [[File:plot72.png|alt=plot72.png|plot72.png]] | ||
=== | ==== Zeta peak index ==== | ||
{ | {| class="wikitable center-all" | ||
|- | |||
! colspan="3" | Tuning | |||
! colspan="3" | Strength | |||
! colspan="2" | Closest edo | |||
! colspan="2" | Integer limit | |||
|- | |||
! ZPI | |||
! Steps per octave | |||
! Step size (cents) | |||
! Height | |||
! Integral | |||
! Gap | |||
! Edo | |||
! Octave (cents) | |||
! Consistent | |||
! Distinct | |||
|- | |||
| [[380zpi]] | |||
| 71.9506065993786 | |||
| 16.6781081733140 | |||
| 9.157547 | |||
| 1.625363 | |||
| 19.964746 | |||
| 72edo | |||
| 1200.82378847861 | |||
| 18 | |||
| 13 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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|} | |} | ||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||