2118edo - Revision history

ArrowHead294 at 23:05, 20 February 2025

2025-02-20T23:05:57Z

← Older revision		Revision as of 23:05, 20 February 2025
Line 5:		Line 5:
	Primes approximated with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13's 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.		Primes approximated with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13's 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.

	2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.		2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a {{nowrap\|31 & 2118}} temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.

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

ArrowHead294 at 23:05, 20 February 2025

2025-02-20T23:05:29Z

← Older revision		Revision as of 23:05, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2118~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	== 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\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
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	\| {{monzo\| 38 -2 15 }}, {{monzo\| -11 130 -84 }}		\| {{monzo\| 38 -2 15 }}, {{monzo\| -11 130 -84 }}
	\| {{mapping\| 2118 3357 4918 }}		\| {{mapping\| 2118 3357 4918 }}
	\| -0.0186		\| −0.0186
	\| 0.0156		\| 0.0156
	\|		\|
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	\| 250047/250000, {{monzo\| -1 -18 -3 13 }}, {{monzo\| 38 -2 -15 }}		\| 250047/250000, {{monzo\| -1 -18 -3 13 }}, {{monzo\| 38 -2 -15 }}
	\| {{mapping\| 2118 3357 4918 5946 }}		\| {{mapping\| 2118 3357 4918 5946 }}
	\| -0.0150		\| −0.0150
	\| 0.0148		\| 0.0148
	\|		\|
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	\| 9801/9800, 250047/250000, {{monzo\| 25 1 -4 0 -5 }}, {{monzo\| 16 -7 -9 2 3 }}		\| 9801/9800, 250047/250000, {{monzo\| 25 1 -4 0 -5 }}, {{monzo\| 16 -7 -9 2 3 }}
	\| {{mapping\| 2118 3357 4918 5946 7927 }}		\| {{mapping\| 2118 3357 4918 5946 7927 }}
	\| -0.0096		\| −0.0096
	\| 0.0172		\| 0.0172
	\|		\|
	\|}		\|}

FloraC: Cleanup; -redundant categories

2023-10-15T13:26:06Z

Cleanup; -redundant categories

← Older revision		Revision as of 13:26, 15 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|2118}}~~		Primes approximated with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13's 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.
	Primes with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-~~13s~~ 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.

	2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.		2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.

	2118edo is 6 times the [[353edo]], meaning it can be used to play a compound of 6 chains of the [[Hemimean clan#Rectified ~~Hebrew~~\|~~Rectified Hebrew~~]] temperament.		=== Prime harmonics ===
			{{Harmonics in equal\|2118}}

			=== Subsets and supersets ===
			2118edo is 6 times the [[353edo]], meaning it can be used to play a compound of 6 chains of the [[Hemimean clan #Rectified hebrew\|rectified hebrew]] temperament.

	== 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		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	8ve ~~stretch~~ (¢)		! colspan="2" \| Tuning Error
	! colspan="2" \|Tuning ~~error~~
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|38 -2 15}}, {{monzo\| -11 130 -84}}		\| {{monzo\| 38 -2 15 }}, {{monzo\| -11 130 -84 }}
	\|[{{~~val~~\|2118 3357 4918}}]		\| {{mapping\| 2118 3357 4918 }}
	\| -0.0186		\| -0.0186
	\|0.0156		\| 0.0156
	\|		\|
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|250047/250000,{{monzo\|-1 -18 -3 13}}, {{monzo\|38 -2 -15 0}}		\| 250047/250000, {{monzo\| -1 -18 -3 13 }}, {{monzo\| 38 -2 -15 }}
	\|[{{~~val~~\|2118 3357 4918 5946}}]		\| {{mapping\| 2118 3357 4918 5946 }}
	\| -0.0150		\| -0.0150
	\|0.0148		\| 0.0148
	\|		\|
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|9801/9800, 250047/250000, {{monzo\|25 1 -4 0 -5}}, {{monzo\|16 -7 -9 2 3}}		\| 9801/9800, 250047/250000, {{monzo\| 25 1 -4 0 -5 }}, {{monzo\| 16 -7 -9 2 3 }}
	\|[{{~~val~~\|2118 3357 4918 5946 7927}}]		\| {{mapping\| 2118 3357 4918 5946 7927 }}
	\|~~<nowiki>~~-0.0096~~</nowiki>~~		\| -0.0096
	\|0.0172		\| 0.0172
	\|		\|
	\|}		\|}

	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~

BudjarnLambeth at 07:01, 9 July 2023

2023-07-09T07:01:02Z

← Older revision		Revision as of 07:01, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2118}}		{{EDO intro\|2118}}

BudjarnLambeth at 04:38, 9 July 2023

2023-07-09T04:38:45Z

← Older revision		Revision as of 04:38, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|2118}}		{{EDO intro\|2118}}

Plumtree: Infobox ET now computes most parameters automatically

2022-10-04T19:26:16Z

Infobox ET now computes most parameters automatically

← Older revision		Revision as of 19:26, 4 October 2022
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	{{Infobox ET		{{Infobox ET}}
	~~\|Prime factorization = 2 × 3 × 353~~
	~~\|Fifth = 1239\2118 (→[[706edo\|413/706]])~~
	~~\|Major 2nd = 360\2118~~
	~~\|Semitones = 201:159~~
	~~\|Consistency=11~~}}
	{{EDO intro\|2118}}		{{EDO intro\|2118}}

Eliora: /* Theory */ comma basis

2022-09-04T22:17:36Z

Theory: comma basis

← Older revision		Revision as of 22:17, 4 September 2022
Line 11:		Line 11:
	Primes with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13s 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.		Primes with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13s 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.

	2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth.		2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.

	2118edo is 6 times the [[353edo]], meaning it can be used to play a compound of 6 chains of the [[Hemimean clan#Rectified Hebrew\|Rectified Hebrew]] temperament.		2118edo is 6 times the [[353edo]], meaning it can be used to play a compound of 6 chains of the [[Hemimean clan#Rectified Hebrew\|Rectified Hebrew]] temperament.

Fredg999 category edits: Categories

2022-07-04T01:25:34Z

Eliora at 09:06, 2 June 2022

2022-06-02T09:06:54Z

← Older revision		Revision as of 09:06, 2 June 2022
Line 11:		Line 11:
	Primes with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13s 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.		Primes with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13s 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.

	2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps). In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth.		2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth.

	2118edo is 6 times the [[353edo]], meaning it can be used to play a compound of 6 chains of the [[Hemimean clan#Rectified Hebrew\|Rectified Hebrew]] temperament.		2118edo is 6 times the [[353edo]], meaning it can be used to play a compound of 6 chains of the [[Hemimean clan#Rectified Hebrew\|Rectified Hebrew]] temperament.

Eliora at 22:14, 14 May 2022

2022-05-14T22:14:45Z

← Older revision		Revision as of 22:14, 14 May 2022
Line 4:		Line 4:
	\|Major 2nd = 360\2118		\|Major 2nd = 360\2118
	\|Semitones = 201:159		\|Semitones = 201:159
	}}		\|Consistency=11}}
	{{EDO intro\|2118}}		{{EDO intro\|2118}}

← Older revision		Revision as of 19:26, 4 October 2022
Line 1:		Line 1:
	{{Infobox ET		{{Infobox ET}}
	~~\|Prime factorization = 2 × 3 × 353~~
	~~\|Fifth = 1239\2118 (→[[706edo\|413/706]])~~
	~~\|Major 2nd = 360\2118~~
	~~\|Semitones = 201:159~~
	~~\|Consistency=11~~}}
	{{EDO intro\|2118}}		{{EDO intro\|2118}}

← Older revision		Revision as of 01:25, 4 July 2022
Line 48:		Line 48:
	\|		\|
	\|}		\|}

			[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->