131edt - Revision history

Lériendil at 04:23, 22 January 2026

2026-01-22T04:23:14Z

← Older revision		Revision as of 04:23, 22 January 2026
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	'''131edt''' is the [[EDT\|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent]]s each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 27-[[odd limit#Nonoctave equaves\|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.		'''131edt''' is the [[EDT\|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent]]s each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 27-[[odd limit#Nonoctave equaves\|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.

	131edt is the 16th [[the Riemann zeta function and tuning#Removing primes\|no-twos zeta peak EDT]], and is the smallest EDT to be [[purely consistent]]{{idio}} in the 27-odd-limit (i.e. maintains no greater than 25% relative error on all odd ~~harmonocs~~ up to and including 27).		131edt is the 16th [[the Riemann zeta function and tuning#Removing primes\|no-twos zeta peak EDT]], and is the smallest EDT to be [[purely consistent]]{{idio}} in the 27-odd-limit (i.e. maintains no greater than 25% relative error on all odd harmonics up to and including 27).

	== Theory ==		== Theory ==

Francium: /* Music */ typo

2025-04-13T14:13:48Z

Music: typo

← Older revision		Revision as of 14:13, 13 April 2025
Line 17:		Line 17:
	; [[Francium]]		; [[Francium]]
	* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobaltomenite, 131edt tuning		* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobaltomenite, 131edt tuning
	* "Boing Going Up?" from ''Questions, Vol. 2'' (2025) — [https://open.spotify.com/track/3kbXkD9GRC1qeENsMZtFmO Spotify] \| [https://francium223.bandcamp.com/track/boing-going-up Bandcamp] \| [https://www.youtube.com/watch?v=rsW7_utEdbc YouTube] − in Gordaite, 131edt tuning		* "Boing Going Up?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/3kbXkD9GRC1qeENsMZtFmO Spotify] \| [https://francium223.bandcamp.com/track/boing-going-up Bandcamp] \| [https://www.youtube.com/watch?v=rsW7_utEdbc YouTube] – in Gordaite, 131edt tuning

Francium: /* Music */ +music

2025-04-13T14:13:17Z

Music: +music

← Older revision		Revision as of 14:13, 13 April 2025
Line 17:		Line 17:
	; [[Francium]]		; [[Francium]]
	* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobaltomenite, 131edt tuning		* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobaltomenite, 131edt tuning
			* "Boing Going Up?" from ''Questions, Vol. 2'' (2025) — [https://open.spotify.com/track/3kbXkD9GRC1qeENsMZtFmO Spotify] \| [https://francium223.bandcamp.com/track/boing-going-up Bandcamp] \| [https://www.youtube.com/watch?v=rsW7_utEdbc YouTube] − in Gordaite, 131edt tuning

ArrowHead294 at 13:19, 10 April 2025

2025-04-10T13:19:53Z

← Older revision		Revision as of 13:19, 10 April 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''131edt''' is the [[EDT\|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent~~\|cents~~]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 27-[[odd limit#Nonoctave equaves\|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.		'''131edt''' is the [[EDT\|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent]]s each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 27-[[odd limit#Nonoctave equaves\|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.

	131edt is the 16th [[~~The_Riemann_Zeta_Function_and_Tuning~~#Removing primes\|no-twos zeta peak EDT]], and is the smallest EDT to be [[purely consistent]]{{idio}} in the 27-odd-limit (i.e. maintains no greater than 25% relative error on all odd harmonocs up to and including 27).		131edt is the 16th [[the Riemann zeta function and tuning#Removing primes\|no-twos zeta peak EDT]], and is the smallest EDT to be [[purely consistent]]{{idio}} in the 27-odd-limit (i.e. maintains no greater than 25% relative error on all odd harmonocs up to and including 27).

	== Theory ==		== Theory ==

Francium: /* Music */ typo

2025-03-08T12:22:56Z

Music: typo

← Older revision		Revision as of 12:22, 8 March 2025
Line 16:		Line 16:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in ~~Cobalomenite~~, 131edt tuning		* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobaltomenite, 131edt tuning

Francium: /* Music */ typo

2025-03-08T12:22:29Z

Music: typo

← Older revision		Revision as of 12:22, 8 March 2025
Line 16:		Line 16:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "cocoon" from ''wiloliquy'' (2025) – https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobalomenite, 131edt tuning		* "cocoon" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobalomenite, 131edt tuning

Francium: +music

2025-03-08T12:22:06Z

+music

← Older revision		Revision as of 12:22, 8 March 2025
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	{{Harmonics in equal\|131\|3\|1\|intervals = prime\|columns = 9}}		{{Harmonics in equal\|131\|3\|1\|intervals = prime\|columns = 9}}
	{{Harmonics in equal\|131\|3\|1\|start = 12\|collapsed = 1\|intervals = odd\|columns = 15}}		{{Harmonics in equal\|131\|3\|1\|start = 12\|collapsed = 1\|intervals = odd\|columns = 15}}

			== Music ==
			; [[Francium]]
			* "cocoon" from ''wiloliquy'' (2025) – https://open.spotify.com/track/1XnR14gAGjVIe6SKf7bWfv Spotify] \| [https://francium223.bandcamp.com/track/cocoon Bandcamp] \| [https://www.youtube.com/watch?v=rVn0fcY0RBI YouTube] – in Cobalomenite, 131edt tuning

ArrowHead294 at 15:53, 2 March 2025

2025-03-02T15:53:43Z

← Older revision		Revision as of 15:53, 2 March 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''131edt''' is the [[EDT\|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent\|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 25-[[odd limit#Nonoctave equaves\|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.		'''131edt''' is the [[EDT\|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent\|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 27-[[odd limit#Nonoctave equaves\|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.

	131edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak EDT]].		131edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak EDT]], and is the smallest EDT to be [[purely consistent]]{{idio}} in the 27-odd-limit (i.e. maintains no greater than 25% relative error on all odd harmonocs up to and including 27).

	== Theory ==		== Theory ==

Francium: added tempered out commas and supported temperaments

2025-01-19T14:46:50Z

added tempered out commas and supported temperaments

← Older revision		Revision as of 14:46, 19 January 2025
Line 4:		Line 4:
	131edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak EDT]].		131edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak EDT]].

	== Intervals ==		== Theory ==
			131edt is strong in the 3.5.7.11.13.17.19.23 [[subgroup]], [[tempering out]] 1377/1375, [[1575/1573]], 3591/3575, [[4459/4455]], 1617/1615 and 6561/6545. Additionally, 131edt tempers out [[3213/3211]] in the 3.7.13.17.19 subgroup and [[2205/2197]] in the 3.5.7.13 subgroup. It [[support]]s [[procyon]], [[erigone]], [[hemigone]] and [[mebsuta]].

			=== Intervals ===
	{{Interval table}}		{{Interval table}}

	== Harmonics ==		=== Harmonics ===
	{{Harmonics in equal\|131\|3\|1\|intervals = prime\|columns = 9}}		{{Harmonics in equal\|131\|3\|1\|intervals = prime\|columns = 9}}
	{{Harmonics in equal\|131\|3\|1\|start = 12\|collapsed = 1\|intervals = odd\|columns = 15}}		{{Harmonics in equal\|131\|3\|1\|start = 12\|collapsed = 1\|intervals = odd\|columns = 15}}

Lériendil at 12:03, 5 October 2024

2024-10-05T12:03:11Z

← Older revision		Revision as of 12:03, 5 October 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''~~131EDT~~''' is the [[EDT\|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent\|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 25-[[odd limit#Nonoctave equaves\|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.		'''131edt''' is the [[EDT\|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent\|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 25-[[odd limit#Nonoctave equaves\|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.

	~~131EDT~~ is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak EDT]].		131edt is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes\|no-twos zeta peak EDT]].

	== Intervals ==		== Intervals ==