354edo - Revision history

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"

2026-03-13T13:33:09Z

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 13:33, 13 March 2026
Line 105:		Line 105:
	\| [[Oganesson]]		\| [[Oganesson]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|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:Stearnscape]]		[[Category:Stearnscape]]

ArrowHead294 at 22:57, 20 February 2025

2025-02-20T22:57:14Z

← Older revision		Revision as of 22:57, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|354~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 14:10, 16 January 2025

2025-01-16T14:10:01Z

← Older revision		Revision as of 14:10, 16 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	354edo is [[~~enfactoring\|~~enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by [[tempering out]] the [[schisma]] and the [[parakleisma]], but the approximation to higher [[harmonic]]s are much improved.		354edo is [[enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by [[tempering out]] the [[schisma]] and the [[parakleisma]], but the approximation to higher [[harmonic]]s are much improved.

	In the 7-limit, ~~the equal temperament~~ tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. In the 13-limit, particularly 2.3.5.13 subgroup, one should consider [[peithoian]], as it preserves 5-limit tuning of 118edo while also improving the first harmonic 118edo tunes inconsistently.		In the 7-limit, it tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. In the 13-limit, particularly 2.3.5.13 subgroup, one should consider [[peithoian]], as it preserves 5-limit tuning of 118edo while also improving the first harmonic 118edo tunes inconsistently.

	354edo provides the [[optimal patent val]] for [[stearnscape]], the 72 & 282 temperament, and 13- and 17-limit [[terminator]], the 171 & 183 temperament.		354edo provides the [[optimal patent val]] for [[stearnscape]], the {{nowrap\|72 & 282}} temperament, and 13- and 17-limit [[terminator]], the {{nowrap\|171 & 183}} temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 30:		Line 30:
	\| 32805/32768, 118098/117649, 250047/250000		\| 32805/32768, 118098/117649, 250047/250000
	\| {{mapping\| 354 561 822 994 }}		\| {{mapping\| 354 561 822 994 }}
	\| ~~−0~~.0319		\| −0.0319
	\| 0.1432		\| 0.1432
	\| 4.23		\| 4.23
Line 37:		Line 37:
	\| 540/539, 4000/3993, 32805/32768, 137781/137500		\| 540/539, 4000/3993, 32805/32768, 137781/137500
	\| {{mapping\| 354 561 822 994 1225 }}		\| {{mapping\| 354 561 822 994 1225 }}
	\| ~~−0~~.0963		\| −0.0963
	\| 0.1817		\| 0.1817
	\| 5.36		\| 5.36
Line 44:		Line 44:
	\| 540/539, 729/728, 1575/1573, 4096/4095, 31250/31213		\| 540/539, 729/728, 1575/1573, 4096/4095, 31250/31213
	\| {{mapping\| 354 561 822 994 1225 1310 }}		\| {{mapping\| 354 561 822 994 1225 1310 }}
	\| ~~−0~~.0871		\| −0.0871
	\| 0.1671		\| 0.1671
	\| 4.93		\| 4.93
Line 51:		Line 51:
	\| 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 4096/4095		\| 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 4096/4095
	\| {{mapping\| 354 561 822 994 1225 1310 1447 }}		\| {{mapping\| 354 561 822 994 1225 1310 1447 }}
	\| ~~−0~~.0791		\| −0.0791
	\| 0.1559		\| 0.1559
	\| 4.60		\| 4.60
Line 58:		Line 58:
	\| 540/539, 729/728, 936/935, 969/968, 1156/1155, 1445/1444, 1521/1520		\| 540/539, 729/728, 936/935, 969/968, 1156/1155, 1445/1444, 1521/1520
	\| {{mapping\| 354 561 822 994 1225 1310 1447 1504 }}		\| {{mapping\| 354 561 822 994 1225 1310 1447 1504 }}
	\| ~~−0~~.0926		\| −0.0926
	\| 0.1509		\| 0.1509
	\| 4.43		\| 4.43
Line 105:		Line 105:
	\| [[Oganesson]]		\| [[Oganesson]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	[[Category:Stearnscape]]		[[Category:Stearnscape]]

ArrowHead294: Partial undo

2024-11-16T12:27:14Z

Partial undo

← Older revision		Revision as of 12:27, 16 November 2024
Line 16:		Line 16:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
Line 52:		Line 61:
	\| 0.1509		\| 0.1509
	\| 4.43		\| 4.43
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 5-limit temperaments supported by [[118edo\|118et]] are not included.		Note: 5-limit temperaments supported by [[118edo\|118et]] are not included.

	{{rank-2 ~~begin}}~~		{\| 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
	\|-		\|-
	\| 2		\| 2
Line 88:		Line 104:
	\| 165/119<br />(?)		\| 165/119<br />(?)
	\| [[Oganesson]]		\| [[Oganesson]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Stearnscape]]		[[Category:Stearnscape]]

ArrowHead294 at 04:40, 16 November 2024

2024-11-16T04:40:40Z

← Older revision		Revision as of 04:40, 16 November 2024
Line 16:		Line 16:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| 32805/32768, 118098/117649, 250047/250000		\| 32805/32768, 118098/117649, 250047/250000
	\| {{mapping\| 354 561 822 994 }}		\| {{mapping\| 354 561 822 994 }}
	\| -0.0319		\| −0.0319
	\| 0.1432		\| 0.1432
	\| 4.23		\| 4.23
Line 36:		Line 28:
	\| 540/539, 4000/3993, 32805/32768, 137781/137500		\| 540/539, 4000/3993, 32805/32768, 137781/137500
	\| {{mapping\| 354 561 822 994 1225 }}		\| {{mapping\| 354 561 822 994 1225 }}
	\| -0.0963		\| −0.0963
	\| 0.1817		\| 0.1817
	\| 5.36		\| 5.36
Line 43:		Line 35:
	\| 540/539, 729/728, 1575/1573, 4096/4095, 31250/31213		\| 540/539, 729/728, 1575/1573, 4096/4095, 31250/31213
	\| {{mapping\| 354 561 822 994 1225 1310 }}		\| {{mapping\| 354 561 822 994 1225 1310 }}
	\| -0.0871		\| −0.0871
	\| 0.1671		\| 0.1671
	\| 4.93		\| 4.93
Line 50:		Line 42:
	\| 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 4096/4095		\| 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 4096/4095
	\| {{mapping\| 354 561 822 994 1225 1310 1447 }}		\| {{mapping\| 354 561 822 994 1225 1310 1447 }}
	\| -0.0791		\| −0.0791
	\| 0.1559		\| 0.1559
	\| 4.60		\| 4.60
Line 57:		Line 49:
	\| 540/539, 729/728, 936/935, 969/968, 1156/1155, 1445/1444, 1521/1520		\| 540/539, 729/728, 936/935, 969/968, 1156/1155, 1445/1444, 1521/1520
	\| {{mapping\| 354 561 822 994 1225 1310 1447 1504 }}		\| {{mapping\| 354 561 822 994 1225 1310 1447 1504 }}
	\| -0.0926		\| −0.0926
	\| 0.1509		\| 0.1509
	\| 4.43		\| 4.43
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 5-limit temperaments supported by [[118edo\|118et]] are not included.		Note: 5-limit temperaments supported by [[118edo\|118et]] are not included.

	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 2		\| 2
	\| 128\354<br>(49\354)		\| 128\354<br />(49\354)
	\| 433.90<br>(166.10)		\| 433.90<br />(166.10)
	\| 9/7<br>(11/10)		\| 9/7<br />(11/10)
	\| [[Pogo]]		\| [[Pogo]]
	\|-		\|-
	\| 3		\| 3
	\| 147\354<br>(29\354)		\| 147\354<br />(29\354)
	\| 498.31<br>(98.31)		\| 498.31<br />(98.31)
	\| 4/3<br>(18/17)		\| 4/3<br />(18/17)
	\| [[Term (temperament)\|Term]] / terminator		\| [[Term (temperament)\|Term]] / terminator
	\|-		\|-
	\| 6		\| 6
	\| 64\354<br>(5\354)		\| 64\354<br />(5\354)
	\| 216.95<br>(16.95)		\| 216.95<br />(16.95)
	\| 17/15<br>(245/243)		\| 17/15<br />(245/243)
	\| [[Stearnscape]]		\| [[Stearnscape]]
	\|-		\|-
	\| 6		\| 6
	\| 147\354<br>(29\354)		\| 147\354<br />(29\354)
	\| 498.31<br>(98.31)		\| 498.31<br />(98.31)
	\| 4/3<br>(18/17)		\| 4/3<br />(18/17)
	\| [[Semiterm]]		\| [[Semiterm]]
	\|-		\|-
	\| 118		\| 118
	\| 167\354<br>(2\354)		\| 167\354<br />(2\354)
	\| 566.101<br>(6.78)		\| 566.101<br />(6.78)
	\| 165/119<br>(?)		\| 165/119<br />(?)
	\| [[Oganesson]]		\| [[Oganesson]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	[[Category:Stearnscape]]		[[Category:Stearnscape]]

Eliora: /* Theory */ expand, a bit of paragraph sectioning

2024-08-27T16:28:40Z

Theory: expand, a bit of paragraph sectioning

← Older revision		Revision as of 16:28, 27 August 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	354edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by [[tempering out]] the [[schisma]] and the [[parakleisma]], but the approximation to higher [[harmonic]]s are much improved. In the 7-limit, the equal temperament tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. It provides the [[optimal patent val]] for [[stearnscape]], the 72 & 282 temperament, and 13- and 17-limit [[terminator]], the 171 & 183 temperament.		354edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by [[tempering out]] the [[schisma]] and the [[parakleisma]], but the approximation to higher [[harmonic]]s are much improved.

			In the 7-limit, the equal temperament tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. In the 13-limit, particularly 2.3.5.13 subgroup, one should consider [[peithoian]], as it preserves 5-limit tuning of 118edo while also improving the first harmonic 118edo tunes inconsistently.

			354edo provides the [[optimal patent val]] for [[stearnscape]], the 72 & 282 temperament, and 13- and 17-limit [[terminator]], the 171 & 183 temperament.

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

FloraC: /* Regular temperament properties */ generator

2023-11-10T10:15:24Z

Regular temperament properties: generator

← Older revision		Revision as of 10:15, 10 November 2023
Line 84:		Line 84:
	\| 64\354<br>(5\354)		\| 64\354<br>(5\354)
	\| 216.95<br>(16.95)		\| 216.95<br>(16.95)
	\| ~~567~~/~~500~~<br>(245/243)		\| 17/15<br>(245/243)
	\| [[Stearnscape]]		\| [[Stearnscape]]
	\|-		\|-

FloraC: Rework; cleanup; clarify the title row of the rank-2 temp table

2023-11-10T10:14:28Z

Rework; cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 10:14, 10 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	354edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]], but the approximation to higher ~~harmonics~~ are much improved. In the 7-limit, the equal temperament tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma~~\|landscape~~]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. It provides the [[optimal patent val]] for [[stearnscape]].		354edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by [[tempering out]] the [[schisma]] and the [[parakleisma]], but the approximation to higher [[harmonic]]s are much improved. In the 7-limit, the equal temperament tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. It provides the [[optimal patent val]] for [[stearnscape]], the 72 & 282 temperament, and 13- and 17-limit [[terminator]], the 171 & 183 temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 354 factors into ~~2 × 3 × 59~~, 354edo has subset edos {{EDOs\| 2, 3, 6, 59, 118, and 177 }}.		Since 354 factors into {{factorization\|354}}, 354edo has subset edos {{EDOs\| 2, 3, 6, 59, 118, and 177 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 24:		Line 24:
	\| 2.3.5.7		\| 2.3.5.7
	\| 32805/32768, 118098/117649, 250047/250000		\| 32805/32768, 118098/117649, 250047/250000
	\| [{{~~val~~\| 354 561 822 994 }}]		\| {{mapping\| 354 561 822 994 }}
	\| -0.0319		\| -0.0319
	\| 0.1432		\| 0.1432
Line 31:		Line 31:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 540/539, 4000/3993, 32805/32768, 137781/137500		\| 540/539, 4000/3993, 32805/32768, 137781/137500
	\| [{{~~val~~\| 354 561 822 994 1225 }}]		\| {{mapping\| 354 561 822 994 1225 }}
	\| -0.0963		\| -0.0963
	\| 0.1817		\| 0.1817
Line 38:		Line 38:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 540/539, 729/728, 1575/1573, 4096/4095, 31250/31213		\| 540/539, 729/728, 1575/1573, 4096/4095, 31250/31213
	\| [{{~~val~~\| 354 561 822 994 1225 1310 }}]		\| {{mapping\| 354 561 822 994 1225 1310 }}
	\| -0.0871		\| -0.0871
	\| 0.1671		\| 0.1671
Line 45:		Line 45:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 4096/4095		\| 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 4096/4095
	\| [{{~~val~~\| 354 561 822 994 1225 1310 1447 }}]		\| {{mapping\| 354 561 822 994 1225 1310 1447 }}
	\| -0.0791		\| -0.0791
	\| 0.1559		\| 0.1559
Line 52:		Line 52:
	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 540/539, 729/728, 936/935, 969/968, 1156/1155, 1445/1444, 1521/1520		\| 540/539, 729/728, 936/935, 969/968, 1156/1155, 1445/1444, 1521/1520
	\| [{{~~val~~\| 354 561 822 994 1225 1310 1447 1504 }}]		\| {{mapping\| 354 561 822 994 1225 1310 1447 1504 }}
	\| -0.0926		\| -0.0926
	\| 0.1509		\| 0.1509
Line 64:		Line 64:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 79:		Line 79:
	\| 498.31<br>(98.31)		\| 498.31<br>(98.31)
	\| 4/3<br>(18/17)		\| 4/3<br>(18/17)
	\| [[Term]] / terminator		\| [[Term (temperament)\|Term]] / terminator
	\|-		\|-
	\| 6		\| 6
Line 99:		Line 99:
	\| [[Oganesson]]		\| [[Oganesson]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			[[Category:Stearnscape]]

FloraC: /* Theory */ quality of higher harmonics

2023-07-31T10:58:23Z

Theory: quality of higher harmonics

← Older revision		Revision as of 10:58, 31 July 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	354edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma\|landscape]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. It provides the [[optimal patent val]] for [[stearnscape]].		354edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]], but the approximation to higher harmonics are much improved. In the 7-limit, the equal temperament tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma\|landscape]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. It provides the [[optimal patent val]] for [[stearnscape]].

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

FloraC: Template; style; -redundant category

2023-06-09T05:57:14Z

Template; style; -redundant category

← Older revision		Revision as of 05:57, 9 June 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~The '''354 equal divisions of the octave''' ('''354edo'''), or the '''354(-tone) equal temperament''' ('''354tet''', '''354et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO\|~~equal division of the octave]] into~~ 354 ~~parts of about 3.39 [[cent]]s each.~~		{{EDO intro\|354}}

	== Theory ==		== Theory ==
	354edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma\|landscape]]), and 703125/702464 ([[~~meter comma\|~~meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. It provides the [[optimal patent val]] for [[stearnscape]].		354edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out 118098/117649 (stearnsma), 250047/250000 ([[landscape comma\|landscape]]), and 703125/702464 ([[meter]]); in the 11-limit, [[540/539]], and [[4000/3993]]; in the 13-limit, [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]]. It provides the [[optimal patent val]] for [[stearnscape]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{~~Primes~~ in ~~edo~~\|354}}		{{Harmonics in equal\|354}}

			=== Subsets and supersets ===
			Since 354 factors into 2 × 3 × 59, 354edo has subset edos {{EDOs\| 2, 3, 6, 59, 118, and 177 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \| Subgroup		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~stretch~~ (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \| Tuning ~~error~~		! colspan="2" \| Tuning Error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
Line 61:		Line 64:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator<br>(~~reduced~~)		! Generator<br>(Reduced)
	! Cents<br>(~~reduced~~)		! Cents<br>(Reduced)
	! Associated<br>~~ratio~~		! Associated<br>Ratio
	! Temperaments		! Temperaments
	\|-		\|-
Line 75:		Line 78:
	\| 147\354<br>(29\354)		\| 147\354<br>(29\354)
	\| 498.31<br>(98.31)		\| 498.31<br>(98.31)
	\| 4/3<br>(~~200~~/~~189~~)		\| 4/3<br>(18/17)
	\| [[Term]] / terminator		\| [[Term]] / terminator
	\|-		\|-
Line 87:		Line 90:
	\| 147\354<br>(29\354)		\| 147\354<br>(29\354)
	\| 498.31<br>(98.31)		\| 498.31<br>(98.31)
	\| 4/3<br>(~~200~~/~~189~~)		\| 4/3<br>(18/17)
	\| [[Semiterm]]		\| [[Semiterm]]
	\|-		\|-
	\|118		\| 118
	\|167\354<br>(2\354)		\| 167\354<br>(2\354)
	\|566.101<br>(6.78)		\| 566.101<br>(6.78)
	\|165/119<br>(?)		\| 165/119<br>(?)
	\|[[Oganesson]]		\| [[Oganesson]]
	\|}		\|}

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