692edo - Revision history

FloraC: /* Regular temperament properties */ + semidi

2026-03-27T15:03:24Z

Regular temperament properties: + semidi

← Older revision		Revision as of 15:03, 27 March 2026
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	! Associated<br>ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
			\|-
			\| 1
			\| 259\692
			\| 449.13
			\| 35/27
			\| [[Semidimi]]
	\|-		\|-
	\| 2		\| 2

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:30:09Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:30, 13 March 2026
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	\| [[Vishnu]] / [[acyuta]]		\| [[Vishnu]] / [[acyuta]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	[[Category:Vishnu]]		[[Category:Vishnu]]

FloraC: Expand a little

2025-10-24T10:43:43Z

Expand a little

← Older revision		Revision as of 10:43, 24 October 2025
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	== Theory ==		== Theory ==
	692edo is [[consistent]] to the [[19-odd-limit]], and has a sharp tendency, with odd [[harmonic]]s 3 through 19 all tuned sharp.		692edo is [[consistent]] to the [[19-odd-limit]] and almost the [[21-odd-limit]]; the only inconsistently mapped intervals in the 21-odd-limit are [[21/16]] and its [[octave complement]]. It has a sharp tendency, with odd [[harmonic]]s 3 through 19 all tuned sharp.

	As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 23 6 -14 }} ([[vishnuzma]]) in the [[5-limit]]; 4375/4374 ([[ragisma]]) and 29360128/29296875 ([[quasiorwellisma]]) in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], and [[6656/6655]] in the [[13-limit]]; [[2431/2430]], [[2500/2499]], and [[4914/4913]] in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], [[2432/2431]], [[2926/2925]], [[3136/3135]], and [[3250/3249]] in the [[19-limit]]. It [[support]]s and provides a good tuning for [[vishnu]] and its 13-limit extension [[acyuta]].		As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 23 6 -14 }} ([[vishnuzma]]) in the [[5-limit]]; 4375/4374 ([[ragisma]]) and 29360128/29296875 ([[quasiorwellisma]]) in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], and [[6656/6655]] in the [[13-limit]]; [[2431/2430]], [[2500/2499]], and [[4914/4913]] in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], [[2432/2431]], [[2926/2925]], [[3136/3135]], and [[3250/3249]] in the [[19-limit]]. It [[support]]s and provides a good tuning for [[vishnu]] and its 13-limit extension [[acyuta]].

FloraC: Bugfix

2025-10-23T09:10:18Z

Bugfix

← Older revision		Revision as of 09:10, 23 October 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 692 factors into primes as {{~~factorization~~\| 2<sup>2</sup> × 173 }}, 692edo has subset edos {{EDOs\| 2, 4, 173, and 346 }}.		Since 692 factors into primes as {{nowrap\| 2<sup>2</sup> × 173 }}, 692edo has subset edos {{EDOs\| 2, 4, 173, and 346 }}.

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

FloraC: Created page with "{{Infobox ET}} {{ED intro}} == Theory == 692edo is consistent to the 19-odd-limit, and has a sharp tendency, with odd harmonics 3 through 19 all tuned sharp. As an equal temperament, it tempers out {{monzo| 23 6 -14 }} (vishnuzma) in the 5-limit; 4375/4374 (ragisma) and 29360128/29296875 (quasiorwellisma) in the 7-limit; 3025/3024, 5632/5625, 9801/9800, and 19712/19683 in the 11-limit; 1716/1715..."

2025-09-15T17:10:42Z

Created page with "{{Infobox ET}} {{ED intro}} == Theory == 692edo is consistent to the 19-odd-limit, and has a sharp tendency, with odd harmonics 3 through 19 all tuned sharp. As an equal temperament, it tempers out {{monzo| 23 6 -14 }} (vishnuzma) in the 5-limit; 4375/4374 (ragisma) and 29360128/29296875 (quasiorwellisma) in the 7-limit; 3025/3024, 5632/5625, 9801/9800, and 19712/19683 in the 11-limit; 1716/1715..."

New page

{{Infobox ET}}
{{ED intro}}

== Theory ==
692edo is [[consistent]] to the [[19-odd-limit]], and has a sharp tendency, with odd [[harmonic]]s 3 through 19 all tuned sharp.

As an equal temperament, it [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnuzma]]) in the [[5-limit]]; 4375/4374 ([[ragisma]]) and 29360128/29296875 ([[quasiorwellisma]]) in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], and [[6656/6655]] in the [[13-limit]]; [[2431/2430]], [[2500/2499]], and [[4914/4913]] in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], [[2432/2431]], [[2926/2925]], [[3136/3135]], and [[3250/3249]] in the [[19-limit]]. It [[support]]s and provides a good tuning for [[vishnu]] and its 13-limit extension [[acyuta]].

=== Prime harmonics ===
{{Harmonics in equal|692|intervals=prime}}

=== Subsets and supersets ===
Since 692 factors into primes as {{factorization| 22 × 173 }}, 692edo has subset edos {{EDOs| 2, 4, 173, and 346 }}.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal 8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 1097 -692 }}
| {{Mapping| 692 1097 }}
| −0.1127
| 0.1127
| 6.50
|-
| 2.3.5
| {{Monzo| 23 6 -14 }}, {{monzo| 80 -49 1 }}
| {{Mapping| 692 1097 1607 }}
| −0.1313
| 0.0957
| 5.52
|-
| 2.3.5.7
| 4375/4374, 29360128/29296875, 283115520/282475249
| {{Mapping| 692 1097 1607 1943 }}
| −0.1464
| 0.0869
| 5.01
|-
| 2.3.5.7.11
| 3025/3024, 4375/4374, 5632/5625, 283115520/282475249
| {{Mapping| 692 1097 1607 1943 2394 }}
| −0.1245
| 0.0892
| 5.15
|-
| 2.3.5.7.11.13
| 1716/1715, 2080/2079, 3025/3024, 5632/5625, 200000/199927
| {{Mapping| 692 1097 1607 1943 2394 2561 }}
| −0.1268
| 0.0816
| 4.71
|-
| 2.3.5.7.11.13.17
| 1716/1715, 2080/2079, 2431/2430, 2500/2499, 4914/4913, 5632/5625
| {{Mapping| 692 1097 1607 1943 2394 2561 2829 }}
| −0.1375
| 0.0800
| 4.61
|-
| 2.3.5.7.11.13.17.19
| 1216/1215, 1331/1330, 1540/1539, 1716/1715, 2431/2430, 2500/2499, 4914/4913
| {{Mapping| 692 1097 1607 1943 2394 2561 2829 2940 }}
| −0.1425
| 0.0760
| 4.38
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods per 8ve
! Generator*
! Cents*
! Associated ratio*
! Temperaments
|-
| 2
| 41\692
| 71.10
| 25/24
| [[Vishnu]] / [[acyuta]]
|}
<nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[normal forms|minimal form]] in parentheses if distinct

[[Category:Vishnu]]