935edo - Revision history

FloraC: /* Regular temperament properties */ sorting

2026-06-04T12:07:03Z

Regular temperament properties: sorting

← Older revision		Revision as of 12:07, 4 June 2026
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	\| {{Monzo\| -38 5 13 }}		\| {{Monzo\| -38 5 13 }}
	\| [[Astro]]		\| [[Astro]]
			\|-
			\| 1
			\| 339\935
			\| 435.08
			\| 9/7
			\| [[Supermajor (temperament)\|Supermajor]]
	\|-		\|-
	\| 1		\| 1
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	\| 104/75		\| 104/75
	\| [[Alphatrillium]]		\| [[Alphatrillium]]
	\|-
	~~\| 1~~
	~~\| 339\935~~
	~~\| 435.08~~
	~~\| 9/7~~
	~~\| [[Supermajor (temperament)\|Supermajor]]~~
	\|-		\|-
	\| 17		\| 17

FloraC: /* Regular temperament properties */ + table of rank-2 temps

2026-06-04T12:06:27Z

Regular temperament properties: + table of rank-2 temps

← Older revision		Revision as of 12:06, 4 June 2026
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	\|}		\|}
	* 935et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19- and 23-limit. It is the first to beat [[764edo\|764]] in the 13-limit, [[814edo\|814]] in the 17- and 23-limit, and [[742edo\|742]] in the 19-limit, only to be bettered by [[954edo\|954h]] in all of those subgroups.		* 935et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19- and 23-limit. It is the first to beat [[764edo\|764]] in the 13-limit, [[814edo\|814]] in the 17- and 23-limit, and [[742edo\|742]] in the 19-limit, only to be bettered by [[954edo\|954h]] in all of those subgroups.

			=== Rank-2 temperaments ===
			{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br>per 8ve
			! Generator*
			! Cents*
			! Associated<br>ratio*
			! Temperaments
			\|-
			\| 1
			\| 103\935
			\| 132.19
			\| {{Monzo\| -38 5 13 }}
			\| [[Astro]]
			\|-
			\| 1
			\| 442\935
			\| 567.27
			\| 104/75
			\| [[Alphatrillium]]
			\|-
			\| 1
			\| 339\935
			\| 435.08
			\| 9/7
			\| [[Supermajor (temperament)\|Supermajor]]
			\|-
			\| 17
			\| 194\935<br>(26\935)
			\| 248.98<br>(33.37)
			\| {{Monzo\| -23 5 9 -2 }}<br>(100352/98415)
			\| [[Chlorine]]
			\|}
			<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms\|minimal form]] in parentheses if distinct

FloraC: Expand

2026-06-04T11:24:49Z

Expand

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is a very strong 23-limit system, and is [[consistency|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. It [[tempering out|tempers out]] the {{monzo| 39 -29 3 }} ([[alphatricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.
+edo is a very strong [[23-limit]] system, and is [[consistent]] through to the [[27-odd-limit]]. It does reasonably well in the higher limits, though the sharply tuned [[11/1|11]] and [[23/1|23]] and the flatly tuned [[29/1|29]] and [[31/1|31]] create inconsistencies together, those being [[29/22]], [[29/23]], [[31/22]], [[31/23]] and their [[octave complement]]s; it is otherwise consistent to the [[39-odd-limit]]. It is a [[zeta peak edo]].
 === Prime harmonics ===
-{{Harmonics in equal|935}}
+{{Harmonics in equal|935|columns=11}}
 === Subsets and supersets ===
-Since 935 factors into {{factorization|935}}, 935edo has subset edos {{EDOs| 5, 11, 17, 55, 85, and 187 }}.
+Since 935 factors into primes as {{nowrap| 5 × 11 × 17 }}, 935edo has subset edos {{EDOs| 5, 11, 17, 55, 85, and 187 }}.
 == Regular temperament properties ==
-et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19- and 23-limit. It is the first to beat [[764edo|764]] in the 13-limit, [[814edo|814]] in the 17- and 23-limit, and [[742edo|742]] in the 19-limit, only to be bettered by [[954edo|954h]] in all of those subgroups.
+{| class="wikitable center-4 center-5 center-6"

Lériendil: /* Theory */tricot -> alphatricot

2025-06-12T17:38:26Z

Theory: tricot -> alphatricot

← Older revision		Revision as of 17:38, 12 June 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	935edo is a very strong 23-limit system, and is [[consistency\|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. It [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[~~tricot~~ comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.		935edo is a very strong 23-limit system, and is [[consistency\|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. It [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[alphatricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

ArrowHead294 at 16:25, 20 February 2025

2025-02-20T16:25:14Z

← Older revision		Revision as of 16:25, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|935~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	935edo is a very strong 23-limit system, and is [[consistency\|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. ~~The equal temperament~~ [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.		935edo is a very strong 23-limit system, and is [[consistency\|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. It [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: As a record ET in the 13- to 23-limit.

2024-07-15T15:38:07Z

As a record ET in the 13- to 23-limit.

← Older revision		Revision as of 15:38, 15 July 2024
Line 2:		Line 2:
	{{EDO intro\|935}}		{{EDO intro\|935}}

	935edo is a very strong 23-limit system, and is [[consistency\|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. The equal temperament [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.		== Theory ==
			935edo is a very strong 23-limit system, and is [[consistency\|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. The equal temperament [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 10:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 935 factors into {{factorization\|935}}, 935edo has subset edos {{EDOs\| 5, 11, 17, 55, 85, and 187 }}.		Since 935 factors into {{factorization\|935}}, 935edo has subset edos {{EDOs\| 5, 11, 17, 55, 85, and 187 }}.

			== Regular temperament properties ==
			935et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19- and 23-limit. It is the first to beat [[764edo\|764]] in the 13-limit, [[814edo\|814]] in the 17- and 23-limit, and [[742edo\|742]] in the 19-limit, only to be bettered by [[954edo\|954h]] in all of those subgroups.

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T11:28:40Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 11:28, 2 November 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|935}}		{{EDO intro\|935}}
	935edo is a very strong 23-limit system, and ~~distinctly~~ [[consistent]] through to the [[27-odd-limit]]. It is also a [[~~The Riemann zeta function and tuning #Zeta EDO lists\|~~zeta peak ~~tuning~~]]. ~~In the 5-limit it~~ tempers out the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro)~~. In~~ the 7-limit ~~it tempers out~~ [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612~~, and~~ in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].
			935edo is a very strong 23-limit system, and is [[consistency\|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. The equal temperament [[tempering out\|tempers out]] the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|935}}		{{Harmonics in equal\|935}}

	=== ~~Divisors~~ ===		=== Subsets and supersets ===
	935 ~~= 5 × 11 × 17~~, ~~with~~ subset edos 5, 11, 17, 55, 85, and 187.		Since 935 factors into {{factorization\|935}}, 935edo has subset edos {{EDOs\| 5, 11, 17, 55, 85, and 187 }}.

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~

BudjarnLambeth at 06:47, 9 July 2023

2023-07-09T06:47:42Z

← Older revision		Revision as of 06:47, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|935}}		{{EDO intro\|935}}
	935edo is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak tuning]]. In the 5-limit it tempers out the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].		935edo is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak tuning]]. In the 5-limit it tempers out the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].

BudjarnLambeth at 05:27, 9 July 2023

2023-07-09T05:27:31Z

← Older revision		Revision as of 05:27, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|935}}		{{EDO intro\|935}}
	935edo is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak tuning]]. In the 5-limit it tempers out the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].		935edo is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak tuning]]. In the 5-limit it tempers out the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].

FloraC: Improve intro and sectioning

2022-12-29T15:30:48Z

Improve intro and sectioning

← Older revision		Revision as of 15:30, 29 December 2022
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~The '''~~935 ~~equal divisions of the octave''' ('''~~935edo~~''') divides the [[octave]] into 935 parts of 1.283 [[cent]]s each. It~~ is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak tuning]]. In the 5-limit it tempers out the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].		{{EDO intro\|935}}
			935edo is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak tuning]]. In the 5-limit it tempers out the {{monzo\| 39 -29 3 }} ([[tricot comma]]), {{monzo\| -52 -17 34 }} ([[septendecima]]), and {{monzo\| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]].
	~~935 = 5 × 11 × 17, with subset edos 5, 11, 17, 55, 85, and 187~~.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|935}}		{{Harmonics in equal\|935}}

			=== Divisors ===
			935 = 5 × 11 × 17, with subset edos 5, 11, 17, 55, 85, and 187.

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->