31edo: Difference between revisions

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Approximation to JI: -zeta peak index
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=== Consistent circles ===
=== Consistent circles ===
31edo is close to a circle made by stacking 31 pure [[17/13]] subfourths. A circle of 31 pure 17/13's closes with an error of only 2.74 cents ([[relative error]] 7.1%). Remarkably, 31edo tempers out [[83521/83486]], the 0.7-cent difference between a stack of four 17/13's and a stack of one 19/13 and one 2/1, giving 31edo's [[oneirotonic]] (5L 3s) [[mos]] accurate 13:17:19 chords.
31edo is close to a circle made by stacking 31 pure [[17/13]] subfourths. A circle of 31 pure 17/13's closes with an error of only 2.74 cents ([[relative error]] 7.1%). Remarkably, 31edo tempers out [[83521/83486]], the 0.7-cent difference between a stack of four 17/13's and a stack of one 19/13 and one 2/1, giving 31edo's [[oneirotonic]] (5L 3s) [[mos]] accurate 13:17:19 chords.
=== Zeta peak index ===
{{ZPI
| zpi = 127
| steps = 30.9783816349790
| step size = 38.7366910944446
| tempered height = 7.003472
| pure height = 6.809916
| integral = 1.403777
| gap = 17.739476
| octave = 1200.83742392778
| consistent = 12
| distinct = 9
}}


== Regular temperament properties ==
== Regular temperament properties ==