718edo - 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"

2026-03-13T13:31:51Z

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 13:31, 13 March 2026
Line 104:		Line 104:
	\| [[Abigail]]		\| [[Abigail]]
	\|}		\|}
	<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

Lériendil: /* Theory */

2025-10-13T15:57:16Z

Theory

← Older revision		Revision as of 15:57, 13 October 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	718edo is [[consistency\|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit, with [[28/25]] and its octave complement [[25/14]] being the only inconsistencies in the [[31-odd-limit]]. It is closely related to [[359edo]], but the mapping differs for [[5/1\|5]], [[13/1\|13]], [[17/1\|17]] and [[31/1\|31]].		718edo is [[consistency\|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit, with [[28/25]] and its octave complement [[25/14]] being the only inconsistencies in the [[35-odd-limit]]. It is closely related to [[359edo]], but the mapping differs for [[5/1\|5]], [[13/1\|13]], [[17/1\|17]] and [[31/1\|31]].

	As does 359et, 718et [[Tempering out\|tempers out]] the 359-comma in the 3-limit, rendering a very accurate [[harmonic]] [[3/1\|3]]. In the 5-limit it [[tempering out\|tempers out]] the gammic comma, {{monzo\| -29 -11 20 }}, and the [[monzisma]], {{monzo\| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It [[support]]s [[gammic]], [[monzismic]] and [[abigail]].		As does 359et, 718et [[Tempering out\|tempers out]] the 359-comma in the 3-limit, rendering a very accurate [[harmonic]] [[3/1\|3]]. In the 5-limit it [[tempering out\|tempers out]] the gammic comma, {{monzo\| -29 -11 20 }}, and the [[monzisma]], {{monzo\| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It [[support]]s [[gammic]], [[monzismic]] and [[abigail]].

Overthink at 23:35, 5 October 2025

2025-10-05T23:35:37Z

← Older revision		Revision as of 23:35, 5 October 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	718edo is [[consistency\|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1\|5]], [[13/1\|13]], [[17/1\|17]] and [[31/1\|31]].		718edo is [[consistency\|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit, with [[28/25]] and its octave complement [[25/14]] being the only inconsistencies in the [[31-odd-limit]]. It is closely related to [[359edo]], but the mapping differs for [[5/1\|5]], [[13/1\|13]], [[17/1\|17]] and [[31/1\|31]].

	As does 359et, 718et [[Tempering out\|tempers out]] the 359-comma in the 3-limit, rendering a very accurate [[harmonic]] [[3/1\|3]]. In the 5-limit it [[tempering out\|tempers out]] the gammic comma, {{monzo\| -29 -11 20 }}, and the [[monzisma]], {{monzo\| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It [[support]]s [[gammic]], [[monzismic]] and [[abigail]].		As does 359et, 718et [[Tempering out\|tempers out]] the 359-comma in the 3-limit, rendering a very accurate [[harmonic]] [[3/1\|3]]. In the 5-limit it [[tempering out\|tempers out]] the gammic comma, {{monzo\| -29 -11 20 }}, and the [[monzisma]], {{monzo\| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It [[support]]s [[gammic]], [[monzismic]] and [[abigail]].

Francium: changed EDO intro to ED intro

2025-02-21T06:32:04Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:32, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|718~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:50, 15 January 2025

2025-01-15T19:50:50Z

← Older revision		Revision as of 19:50, 15 January 2025
Line 35:		Line 35:
	\| 4375/4374, 40500000/40353607, {{monzo\| 31 -6 -2 -6 }}		\| 4375/4374, 40500000/40353607, {{monzo\| 31 -6 -2 -6 }}
	\| {{mapping\| 718 1138 1667 2016 }}		\| {{mapping\| 718 1138 1667 2016 }}
	\| ~~−0~~.0207		\| −0.0207
	\| 0.1063		\| 0.1063
	\| 6.36		\| 6.36
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	\| 3025/3024, 4375/4374, 131072/130977, 40500000/40353607		\| 3025/3024, 4375/4374, 131072/130977, 40500000/40353607
	\| {{mapping\| 718 1138 1667 2016 2484 }}		\| {{mapping\| 718 1138 1667 2016 2484 }}
	\| ~~−0~~.0290		\| −0.0290
	\| 0.0965		\| 0.0965
	\| 5.77		\| 5.77
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	\| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 7031250/7014007		\| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 7031250/7014007
	\| {{mapping\| 718 1138 1667 2016 2484 2657 }}		\| {{mapping\| 718 1138 1667 2016 2484 2657 }}
	\| ~~−0~~.0305		\| −0.0305
	\| 0.0881		\| 0.0881
	\| 5.27		\| 5.27
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	\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 3025/3024, 4096/4095		\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 3025/3024, 4096/4095
	\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 }}		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 }}
	\| ~~−0~~.0379		\| −0.0379
	\| 0.0836		\| 0.0836
	\| 5.00		\| 5.00
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	\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 2432/2431, 3025/3024, 3250/3249		\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 2432/2431, 3025/3024, 3250/3249
	\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 }}		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 }}
	\| ~~−0~~.0326		\| −0.0326
	\| 0.0795		\| 0.0795
	\| 4.76		\| 4.76
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	\| 1275/1274, 1716/1715, 2024/2023, 2025/2023, 2080/2079, 2185/2184, 2432/2431, 3025/3024		\| 1275/1274, 1716/1715, 2024/2023, 2025/2023, 2080/2079, 2185/2184, 2432/2431, 3025/3024
	\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 3248 }}		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 3248 }}
	\| ~~−0~~.0323		\| −0.0323
	\| 0.0749		\| 0.0749
	\| 4.48		\| 4.48
Line 104:		Line 104:
	\| [[Abigail]]		\| [[Abigail]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T12:21:22Z

Partial undo

← Older revision		Revision as of 12:21, 16 November 2024
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	== 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		\| 2.3.5
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	\| 0.0749		\| 0.0749
	\| 4.48		\| 4.48
	~~{{comma basis end}~~}		\|}
	* 718et has a lower [[Tenney-Euclidean temperament measures #TE error\|absolute error]] in the 23-limit than any previous equal temperaments, past [[581edo\|581]] and followed by [[742edo\|742i]].		* 718et has a lower [[Tenney-Euclidean temperament measures #TE error\|absolute error]] in the 23-limit than any previous equal temperaments, past [[581edo\|581]] and followed by [[742edo\|742i]].

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{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
	\|-		\|-
	\| 1		\| 1
Line 87:		Line 103:
	\| 44/39		\| 44/39
	\| [[Abigail]]		\| [[Abigail]]
	~~{{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

ArrowHead294 at 04:57, 16 November 2024

2024-11-16T04:57:24Z

← Older revision		Revision as of 04:57, 16 November 2024
Line 14:		Line 14:

	== 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		\| 2.3.5
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	\| 4375/4374, 40500000/40353607, {{monzo\| 31 -6 -2 -6 }}		\| 4375/4374, 40500000/40353607, {{monzo\| 31 -6 -2 -6 }}
	\| {{mapping\| 718 1138 1667 2016 }}		\| {{mapping\| 718 1138 1667 2016 }}
	\| -0.0207		\| −0.0207
	\| 0.1063		\| 0.1063
	\| 6.36		\| 6.36
Line 41:		Line 33:
	\| 3025/3024, 4375/4374, 131072/130977, 40500000/40353607		\| 3025/3024, 4375/4374, 131072/130977, 40500000/40353607
	\| {{mapping\| 718 1138 1667 2016 2484 }}		\| {{mapping\| 718 1138 1667 2016 2484 }}
	\| -0.0290		\| −0.0290
	\| 0.0965		\| 0.0965
	\| 5.77		\| 5.77
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	\| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 7031250/7014007		\| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 7031250/7014007
	\| {{mapping\| 718 1138 1667 2016 2484 2657 }}		\| {{mapping\| 718 1138 1667 2016 2484 2657 }}
	\| -0.0305		\| −0.0305
	\| 0.0881		\| 0.0881
	\| 5.27		\| 5.27
Line 55:		Line 47:
	\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 3025/3024, 4096/4095		\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 3025/3024, 4096/4095
	\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 }}		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 }}
	\| -0.0379		\| −0.0379
	\| 0.0836		\| 0.0836
	\| 5.00		\| 5.00
Line 62:		Line 54:
	\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 2432/2431, 3025/3024, 3250/3249		\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 2432/2431, 3025/3024, 3250/3249
	\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 }}		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 }}
	\| -0.0326		\| −0.0326
	\| 0.0795		\| 0.0795
	\| 4.76		\| 4.76
Line 69:		Line 61:
	\| 1275/1274, 1716/1715, 2024/2023, 2025/2023, 2080/2079, 2185/2184, 2432/2431, 3025/3024		\| 1275/1274, 1716/1715, 2024/2023, 2025/2023, 2080/2079, 2185/2184, 2432/2431, 3025/3024
	\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 3248 }}		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 3248 }}
	\| -0.0323		\| −0.0323
	\| 0.0749		\| 0.0749
	\| 4.48		\| 4.48
	\|}		{{comma basis end}}
	* 718et has a lower [[Tenney-Euclidean temperament measures #TE error\|absolute error]] in the 23-limit than any previous equal temperaments, past [[581edo\|581]] and followed by [[742edo\|742i]].		* 718et has a lower [[Tenney-Euclidean temperament measures #TE error\|absolute error]] in the 23-limit than any previous equal temperaments, past [[581edo\|581]] and followed by [[742edo\|742i]].

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| 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~~
	\|-		\|-
	\| 1		\| 1
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	\| 44/39		\| 44/39
	\| [[Abigail]]		\| [[Abigail]]
	\|}		{{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}}

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T12:27:16Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 12:27, 2 November 2023
Line 5:		Line 5:
	718edo is [[consistency\|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1\|5]], [[13/1\|13]], [[17/1\|17]] and [[31/1\|31]].		718edo is [[consistency\|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1\|5]], [[13/1\|13]], [[17/1\|17]] and [[31/1\|31]].

	As does 359et, 718et [[Tempering out\|tempers out]] the 359-comma in the 3-limit, rendering a very accurate ~~perfect fifth~~. In the 5-limit it tempers out the gammic comma, {{monzo\| -29 -11 20 }}, and the [[monzisma]], {{monzo\| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It ~~supports~~ [[gammic]], [[monzismic]] and [[abigail]].		As does 359et, 718et [[Tempering out\|tempers out]] the 359-comma in the 3-limit, rendering a very accurate [[harmonic]] [[3/1\|3]]. In the 5-limit it [[tempering out\|tempers out]] the gammic comma, {{monzo\| -29 -11 20 }}, and the [[monzisma]], {{monzo\| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It [[support]]s [[gammic]], [[monzismic]] and [[abigail]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 718 factors into ~~2 × 359~~, 718edo contains [[2edo]] and [[359edo]] as subsets.		Since 718 factors into {{factorization\|718}}, 718edo contains [[2edo]] and [[359edo]] as subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 81:		Line 81:
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-

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

2023-10-22T08:12:57Z

Cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 08:12, 22 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	718edo is ~~distinctly~~ [[consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1\|5]], [[13/1\|13]], [[17/1\|17]] and [[31/1\|31]].		718edo is [[consistency\|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1\|5]], [[13/1\|13]], [[17/1\|17]] and [[31/1\|31]].

	As does 359et, 718et tempers out the 359-comma in the 3-limit, rendering a very accurate perfect fifth. In the 5-limit it tempers out the gammic comma, {{monzo\| -29 -11 20 }}, and the [[monzisma]], {{monzo\| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It supports [[gammic]], [[monzismic]] and [[abigail]].		As does 359et, 718et [[Tempering out\|tempers out]] the 359-comma in the 3-limit, rendering a very accurate perfect fifth. In the 5-limit it tempers out the gammic comma, {{monzo\| -29 -11 20 }}, and the [[monzisma]], {{monzo\| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It supports [[gammic]], [[monzismic]] and [[abigail]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	718 contains [[2edo]] and [[359edo]] as subsets.		Since 718 factors into 2 × 359, 718edo contains [[2edo]] and [[359edo]] as subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 26:		Line 26:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -29 -11 20 }}, {{monzo\| 54 -37 2 }}		\| {{monzo\| -29 -11 20 }}, {{monzo\| 54 -37 2 }}
	\| [{{~~val~~\| 718 1138 1667 }}]		\| {{mapping\| 718 1138 1667 }}
	\| +0.0357		\| +0.0357
	\| 0.0482		\| 0.0482
Line 33:		Line 33:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 40500000/40353607, {{monzo\| 31 -6 -2 -6 }}		\| 4375/4374, 40500000/40353607, {{monzo\| 31 -6 -2 -6 }}
	\| [{{~~val~~\| 718 1138 1667 2016 }}]		\| {{mapping\| 718 1138 1667 2016 }}
	\| -0.0207		\| -0.0207
	\| 0.1063		\| 0.1063
Line 40:		Line 40:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 4375/4374, 131072/130977, 40500000/40353607		\| 3025/3024, 4375/4374, 131072/130977, 40500000/40353607
	\| [{{~~val~~\| 718 1138 1667 2016 2484 }}]		\| {{mapping\| 718 1138 1667 2016 2484 }}
	\| -0.0290		\| -0.0290
	\| 0.0965		\| 0.0965
Line 47:		Line 47:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 7031250/7014007		\| 1716/1715, 2080/2079, 3025/3024, 4096/4095, 7031250/7014007
	\| [{{~~val~~\| 718 1138 1667 2016 2484 2657 }}]		\| {{mapping\| 718 1138 1667 2016 2484 2657 }}
	\| -0.0305		\| -0.0305
	\| 0.0881		\| 0.0881
Line 54:		Line 54:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 3025/3024, 4096/4095		\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 3025/3024, 4096/4095
	\| [{{~~val~~\| 718 1138 1667 2016 2484 2657 2935 }}]		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 }}
	\| -0.0379		\| -0.0379
	\| 0.0836		\| 0.0836
Line 61:		Line 61:
	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 2432/2431, 3025/3024, 3250/3249		\| 1275/1274, 1716/1715, 2025/2023, 2080/2079, 2432/2431, 3025/3024, 3250/3249
	\| [{{~~val~~\| 718 1138 1667 2016 2484 2657 2935 3050 }}]		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 }}
	\| -0.0326		\| -0.0326
	\| 0.0795		\| 0.0795
Line 68:		Line 68:
	\| 2.3.5.7.11.13.17.19.23		\| 2.3.5.7.11.13.17.19.23
	\| 1275/1274, 1716/1715, 2024/2023, 2025/2023, 2080/2079, 2185/2184, 2432/2431, 3025/3024		\| 1275/1274, 1716/1715, 2024/2023, 2025/2023, 2080/2079, 2185/2184, 2432/2431, 3025/3024
	\| [{{~~val~~\| 718 1138 1667 2016 2484 2657 2935 3050 3248 }}]		\| {{mapping\| 718 1138 1667 2016 2484 2657 2935 3050 3248 }}
	\| -0.0323		\| -0.0323
	\| 0.0749		\| 0.0749
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	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per ~~Octave~~		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperaments		! Temperaments
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	\| [[Abigail]]		\| [[Abigail]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

FloraC: /* Regular temperament properties */ correction

2023-08-13T14:42:53Z

Regular temperament properties: correction

← Older revision		Revision as of 14:42, 13 August 2023
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	\| 4.48		\| 4.48
	\|}		\|}
	* 718et has a lower [[Tenney-Euclidean temperament measures #TE ~~simple badness~~\|~~relative~~ error]] in the 23-limit than any previous equal temperaments, past [[581edo\|581]] and followed by [[742edo\|742i]].		* 718et has a lower [[Tenney-Euclidean temperament measures #TE error\|absolute error]] in the 23-limit than any previous equal temperaments, past [[581edo\|581]] and followed by [[742edo\|742i]].

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===