87edo: Difference between revisions
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87edo contains [[3edo]] and [[29edo]] as subset edos. | 87edo contains [[3edo]] and [[29edo]] as subset edos. | ||
[[348edo]], which slices the edostep in four, provides a good correction of the 7th harmonic. | [[348edo]], which slices the edostep in four, provides a good correction of the 7th harmonic. Multiples like [[696edo]] and [[783edo]] are also of theoretical interest. | ||
One step of 87edo is ''extremely'' close to [[126/125]], with the associated comma, 87-126/125-comma ({{monzo|86 174 -261 87}}) being tempered in equal temperaments well over 100,000 and with less than 0.001{{c}} error, with the [[optimal patent val]] for the 7-limit temperament being an enormous [[425082edo]]. But more notably, 87edo itself does the mapping consistently, making it a true circle of 126/125's. | |||
See also [[87th-octave temperaments]]. | |||
== Intervals == | == Intervals == | ||
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== Scales == | == Scales == | ||
=== Harmonic scales === | === Harmonic scales === | ||
87edo very accurately approximates | 87edo very accurately approximates [[Overtone scale|modes]] up to 8 of the [[harmonic series]], and the only interval pair not distinct is 14/13 and 15/14. It can also do mode 12 decently. | ||
==== (Mode 6) ==== | ==== (Mode 6) ==== | ||