131edo - Revision history

Lériendil at 00:18, 8 July 2025

2025-07-08T00:18:31Z

← Older revision		Revision as of 00:18, 8 July 2025
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	131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].		131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].

	131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and logarithmic divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9[[EDN\|edn]] = 42\131), [[15/13]] (1\7edn = 27\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.		131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and logarithmic divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[4/3]] (2\7[[EDN\|edn]] = 54\131), [[5/4]] (2\9edn = 42\131), [[15/13]] (1\7edn = 27\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.

	=== Odd harmonics ===		=== Odd harmonics ===

Lériendil: removed armodue category since armodue theory isn't otherwise mentioned at all here and there's no obvious relation between 131edo and armodue scales

2025-04-23T06:04:47Z

removed armodue category since armodue theory isn't otherwise mentioned at all here and there's no obvious relation between 131edo and armodue scales

← Older revision		Revision as of 06:04, 23 April 2025
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	\|}		\|}

	~~[[Category:Armodue]]~~
	[[Category:Bohpier]]		[[Category:Bohpier]]
	[[Category:Immunity]]		[[Category:Immunity]]
	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Golden meantone]]		[[Category:Golden meantone]]

ArrowHead294 at 17:01, 18 February 2025

2025-02-18T17:01:32Z

← Older revision		Revision as of 17:01, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|131~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Lériendil: (why the hell was oneirotonic named after Father anyway)

2025-02-02T15:06:12Z

(why the hell was oneirotonic named after Father anyway)

← Older revision		Revision as of 15:06, 2 February 2025
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	\|-		\|-
	\| 19 12 19 19 12 19 19 12		\| 19 12 19 19 12 19 19 12
	\| [[5L_3s\|~~Father Tuning~~]] (comparable with [[55edo]])		\| [[5L_3s\|Oneirotonic tuning]] (comparable with [[55edo]])
	\|-		\|-
	\| 18 18 18 18 18 18 18 5		\| 18 18 18 18 18 18 18 5
	\| [[7L_1s\|Porcupine ~~Tuning~~]] (comparable with [[29edo]] and [[80edo]])		\| [[7L_1s\|Porcupine tuning]] (comparable with [[29edo]] and [[80edo]])
	\|-		\|-
	\| 17 17 17 6 17 17 17 17 6		\| 17 17 17 6 17 17 17 17 6

Lériendil at 05:11, 15 November 2024

2024-11-15T05:11:33Z

← Older revision		Revision as of 05:11, 15 November 2024
Line 5:		Line 5:
	131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].		131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].

	131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9[[EDN\|edn]] = 42\131), [[15/13]] (1\7edn = 27\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.		131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and logarithmic divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9[[EDN\|edn]] = 42\131), [[15/13]] (1\7edn = 27\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.

	=== Odd harmonics ===		=== Odd harmonics ===

Lériendil at 05:07, 15 November 2024

2024-11-15T05:07:27Z

← Older revision		Revision as of 05:07, 15 November 2024
Line 5:		Line 5:
	131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].		131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].

	131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9[[EDN\|edn]] = 42\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.		131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9[[EDN\|edn]] = 42\131), [[15/13]] (1\7edn = 27\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.

	=== Odd harmonics ===		=== Odd harmonics ===

Lériendil at 05:06, 15 November 2024

2024-11-15T05:06:19Z

← Older revision		Revision as of 05:06, 15 November 2024
Line 5:		Line 5:
	131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].		131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].

	131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9[[edn]] = 42\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.		131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9[[EDN\|edn]] = 42\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.

	=== Odd harmonics ===		=== Odd harmonics ===

Lériendil at 05:06, 15 November 2024

2024-11-15T05:06:08Z

← Older revision		Revision as of 05:06, 15 November 2024
Line 5:		Line 5:
	131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].		131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].

	131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\~~9edn~~ = 42\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.		131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9[[edn]] = 42\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.

	=== Odd harmonics ===		=== Odd harmonics ===

Lériendil: added discussion of natave properties

2024-11-15T05:05:30Z

added discussion of natave properties

← Older revision		Revision as of 05:05, 15 November 2024
Line 4:		Line 4:
	== Theory ==		== Theory ==
	131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].		131edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. However, it is the next [[edo]] after [[81edo]] on the [[Golden meantone\|Golden Tone System]] (''[[Das Goldene Tonsystem]]'') of Thorvald Kornerup, using the 131b [[val]]. The [[patent val]] has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out [[81/80]] it tempers out the [[immunity comma]], 1638400/1594323. In the 7-limit it tempers out [[3125/3087]] and [[245/243]], so that it [[support]]s [[bohpier]].

			131edo is also notable for having a good approximation to [[natave\|acoustic ''e'']], at 189\131, which is a [[semiconvergent]]. This number of steps, 189, is particularly well-factorizable, and divisors of acoustic ''e'' form a sequence of rapidly converging approximations to small rationals. Among these are [[5/4]] (2\9edn = 42\131), [[19/17]] (1\9edn = 21\131), [[11/10]] (2\21edn = 18\131), [[14/13]] (2\27edn = 14\131), and [[32/31]] (2\63edn = 6\131), with accuracy increasing the smaller the fraction.

	=== Odd harmonics ===		=== Odd harmonics ===

Lériendil at 03:47, 13 November 2024

2024-11-13T03:47:50Z

← Older revision		Revision as of 03:47, 13 November 2024
Line 6:		Line 6:

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|131\|columns=14}}		{{Harmonics in equal\|131\|columns=15}}

	=== Subsets and supersets ===		=== Subsets and supersets ===