31edo - Revision history

Ground at 01:48, 14 August 2026

2026-08-14T01:48:16Z

← Older revision		Revision as of 01:48, 14 August 2026
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	62edo uses flat approximations of harmonics 13, 17, and 19 instead of sharp ones, and is arguably usable as a full 23-limit Meantone system with an overall flat tendency.		62edo uses flat approximations of harmonics 13, 17, and 19 instead of sharp ones, and is arguably usable as a full 23-limit Meantone system with an overall flat tendency.
	{{Harmonics in ED\|62\|37\|0}}		{{Harmonics in ED\|62\|37\|0}}

			=== 93edo ===
			93edo is a notable [[Monarch]] tuning.
			{{Harmonics in ED\|93\|37\|0}}

	=== 217edo ===		=== 217edo ===

2026-06-09T03:57:10Z

Multiples: add 62edo

← Older revision		Revision as of 03:57, 9 June 2026
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	== Multiples ==		== Multiples ==
			=== 62edo ===
			62edo uses flat approximations of harmonics 13, 17, and 19 instead of sharp ones, and is arguably usable as a full 23-limit Meantone system with an overall flat tendency.
			{{Harmonics in ED\|62\|37\|0}}

	=== 217edo ===		=== 217edo ===
	217edo is a theoretically strong system which keeps 31edo's tuning of 2.5.7.(13:17:19). 217edo is strong in the 19-limit and the smallest edo distinctly consistent in the 19-odd-limit.		217edo is a theoretically strong system which keeps 31edo's tuning of 2.5.7.(13:17:19). 217edo is strong in the 19-limit and the smallest edo distinctly consistent in the 19-odd-limit.
			{{Harmonics in ED\|217\|37\|0}}

	{{~~Harmonics in ED\|217\|37\|0~~}}		{{Navbox EDO}}
	{{Cat\|Edos~~}}{{Navbox EDO~~}}		{{Cat\|Edos}}

2026-05-25T03:07:17Z

JI approximation

← Older revision		Revision as of 03:07, 25 May 2026
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	Diatonic thirds are bolded.		Diatonic thirds are bolded.

	If one wants to stretch the octave to improve ~~all-around~~ JI approximation, the [https://en.xen.wiki/w/Zeta_peak_index zeta peak] octave stretch and the CWE optimization of 7-limit 31tet give an octave of 1200.8 cents, while the CWE optimization of 11-limit 31tet gives an octave of 1201.2 cents.		If one wants to stretch the octave to improve JI approximation, the [https://en.xen.wiki/w/Zeta_peak_index zeta peak] octave stretch and the CWE optimization of 7-limit 31tet give an octave of 1200.8 cents, while the CWE optimization of 11-limit 31tet gives an octave of 1201.2 cents.

	=== Chords ===		=== Chords ===

2026-05-20T19:07:09Z

← Older revision		Revision as of 19:07, 20 May 2026
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	\|}		\|}
	Diatonic thirds are bolded.		Diatonic thirds are bolded.

			If one wants to stretch the octave to improve all-around JI approximation, the [https://en.xen.wiki/w/Zeta_peak_index zeta peak] octave stretch and the CWE optimization of 7-limit 31tet give an octave of 1200.8 cents, while the CWE optimization of 11-limit 31tet gives an octave of 1201.2 cents.

	=== Chords ===		=== Chords ===

2026-05-18T17:03:11Z

← Older revision		Revision as of 17:03, 18 May 2026
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	\|}		\|}
	<nowiki>*</nowiki>Aligned with the consensus agreed upon by various 31edo resources. ADIN in specific clarifies the unspecified "major" and "minor" qualities found in these resources as "nearmajor" and "nearminor" to distinguish them from supermajor/subminor.		<nowiki>*</nowiki>Aligned with the consensus agreed upon by various 31edo resources. ADIN in specific clarifies the unspecified "major" and "minor" qualities found in these resources as "nearmajor" and "nearminor" to distinguish them from supermajor/subminor.

			== SCL files ==
			See [[31edo/SCL files]].

	== Multiples ==		== Multiples ==

2026-05-15T13:08:54Z

MOS scales

2026-04-22T09:41:11Z

← Older revision		Revision as of 09:41, 22 April 2026
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	!Step		!Step
	!Cents		!Cents
	!ADIN		!ADIN*
	!Neutral diatonic		!Neutral diatonic
	!Notation		!Notation
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	\|2/1		\|2/1
	\|}		\|}
			<nowiki>*</nowiki>Aligned with the consensus agreed upon by various 31edo resources. ADIN in specific clarifies the unspecified "major" and "minor" qualities found in these resources as "nearmajor" and "nearminor" to distinguish them from supermajor/subminor.

	== Multiples ==		== Multiples ==

2026-04-06T20:35:25Z

Scales: proper reasoning

← Older revision		Revision as of 20:35, 6 April 2026
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	== Scales ==		== Scales ==
	31edo does not temper out 64/63, meaning that it can be used to tune [[Diasem]] while representing some simpler 5-limit intervals. 31edo's step is called a [[diesis]], and can function as an [[aberrisma]]. Due to being a prime number, 31edo has a large number of ~~full-period MOS scales that exist in the edo~~. Orwell[9] ([[gramitonic]]) is one example, so is Mohajira[7] ([[mosh]]).		31edo does not temper out 64/63, meaning that it can be used to tune [[Diasem]] while representing some simpler 5-limit intervals. 31edo's step is called a [[diesis]], and can function as an [[aberrisma]]. Due to being a prime number, every MOS scale in 31edo has a full-octave period, and 31edo has a large number of them. Orwell[9] ([[gramitonic]]) is one example, so is Mohajira[7] ([[mosh]]).

	31edo also has a usable 12-note chromatic scale, approximating [[Golden sequences and tuning\|golden]] Meantone/monocot.		31edo also has a usable 12-note chromatic scale, approximating [[Golden sequences and tuning\|golden]] Meantone/monocot.

2026-04-06T20:32:58Z

JI approximation: use 1 decimal place for cents

2026-04-06T05:10:27Z

MOS scales: reduce table width

← Older revision		Revision as of 05:10, 6 April 2026
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	\|-		\|-
	!Scale (albitonic)		!Scale (albitonic)
	\| - (11-note scale has >10 steps interval)		\| - (11-note scale has<br>>10 steps interval)
	\| - (11-note scale has >10 steps interval)		\| - (11-note scale has<br>>10 steps interval)
	\|4-4-4-4-4-4-4-3		\|4-4-4-4-4-4-4-3
	\|1-1-6-1-1-6-1-1-6-1-6		\|1-1-6-1-1-6-1-1-6-1-6
	\| - (11-note scale has >10 steps interval)		\| - (11-note scale has<br>>10 steps interval)
	\|-		\|-
	!Generator		!Generator