87edo - Revision history

Eliora: /* Subsets and supersets */

2026-10-03T02:46:56Z

Subsets and supersets

← Older revision		Revision as of 02:46, 3 October 2026
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	[[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.		[[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]].		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]].		See also [[87th-octave temperaments]].

2026-10-03T02:45:59Z

Subsets and supersets: tying it all together

← Older revision		Revision as of 02:45, 3 October 2026
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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]].

			See also [[87th-octave temperaments]].

	== Intervals ==		== Intervals ==

2026-10-03T00:58:41Z

Harmonic scales

← Older revision		Revision as of 00:58, 3 October 2026
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	== Scales ==		== Scales ==
	=== Harmonic scales ===		=== Harmonic scales ===
	87edo very accurately approximates ~~mode~~ 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.		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) ====

2026-10-03T00:55:05Z

Mos scales

2026-10-03T00:52:43Z

Harmonic scales

@@ Line 525: / Line 525: @@
 == Scales ==
 === Harmonic scales ===
-edo accurately approximates the mode 8 of [[harmonic series]], and the only interval pair not distinct is 14/13 and 15/14. It can also do mode 12 decently.
+edo very accurately approximates mode 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 8) ====

2026-10-03T00:45:08Z

Scales

@@ Line 524: / Line 524: @@
 == Scales ==
 === Harmonic scales ===
 edo accurately approximates the mode 8 of [[harmonic series]], and the only interval pair not distinct is 14/13 and 15/14. It can also do mode 12 decently.
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 and 21 are flat; 17, 19, and 23 are sharp. Still decent all things considered.
 === Other scales ===

2026-10-03T00:44:32Z

Scales: add luna

2026-10-03T00:30:19Z

Mos scales

2026-10-02T14:55:16Z

Harmonic scales

← Older revision		Revision as of 14:55, 2 October 2026
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	\|}		\|}

	The scale in adjacent steps is 15, 13, 12, 11, 10, 9, 9, 8.		The scale in adjacent steps is '''15 13 12 11 10 9 9 8'''.

	==== (Mode 12) ====		==== (Mode 12) ====
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	\|}		\|}

	The scale in adjacent steps is 10, 9, 9, 8, 7, 7, 6, 6, 6, 6, 5.		The scale in adjacent steps is '''10 9 9 8 7 7 6 6 6 6 5'''.

	13, 15, 16, 18, 20, and 22 are close matches.		13, 15, 16, 18, 20, and 22 are close matches.

2026-10-02T14:53:25Z

Scales