23-limit - Revision history

FloraC: Sorting and - the pretention that a Wikipedia page exists

2026-03-30T15:01:09Z

Sorting and - the pretention that a Wikipedia page exists

← Older revision		Revision as of 15:01, 30 March 2026
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	; [[Francium]]		; [[Francium]]
	* "GAY SAPIENS" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/5vILBQgWJduJf2ctGGbyUv Spotify] \| [https://francium223.bandcamp.com/track/gay-sapiens Bandcamp] \| [https://www.youtube.com/watch?v=DHiwdGuZRII YouTube]		* "GAY SAPIENS" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/5vILBQgWJduJf2ctGGbyUv Spotify] \| [https://francium223.bandcamp.com/track/gay-sapiens Bandcamp] \| [https://www.youtube.com/watch?v=DHiwdGuZRII YouTube]

			; [[Noah Dean Jordan]]
			* [https://open.spotify.com/album/2OGG4tT7INfj7iBeN09KDJ ''Gracias a Dios''] (2023) for solo jarana (series 23/22, 23/21, …, 23/12)

	; {{W\|Franz Liszt}}		; {{W\|Franz Liszt}}
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	* [https://www.youtube.com/watch?v=jpHylRu6XLM ''ser0tonin circuits in a neural network''] (2023)		* [https://www.youtube.com/watch?v=jpHylRu6XLM ''ser0tonin circuits in a neural network''] (2023)
	* [https://www.youtube.com/watch?v=con4DTO8uQs ''Eyes Do More Than See''] (2026)		* [https://www.youtube.com/watch?v=con4DTO8uQs ''Eyes Do More Than See''] (2026)


	~~; {{W\|Noah Dean DaSilva Jordan}}~~
	* [https://open.spotify.com/album/2OGG4tT7INfj7iBeN09KDJ Gracias a Dios] (2023) for solo jarana (series 23/22, 23/21....23/12)

	[[Category:23-limit\| ]] <!-- main article -->		[[Category:23-limit\| ]] <!-- main article -->

Lucius Chiaraviglio: /* Music */ Add Randy Wells' ''Eyes Do More Than See'' (2026)

2026-03-02T10:33:53Z

Music: Add Randy Wells' ''Eyes Do More Than See'' (2026)

← Older revision		Revision as of 10:33, 2 March 2026
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	* [https://www.youtube.com/watch?v=m9QaxFOlnYg ''A Hycean World''] (2023)		* [https://www.youtube.com/watch?v=m9QaxFOlnYg ''A Hycean World''] (2023)
	* [https://www.youtube.com/watch?v=jpHylRu6XLM ''ser0tonin circuits in a neural network''] (2023)		* [https://www.youtube.com/watch?v=jpHylRu6XLM ''ser0tonin circuits in a neural network''] (2023)
			* [https://www.youtube.com/watch?v=con4DTO8uQs ''Eyes Do More Than See''] (2026)


	; {{W\|Noah Dean DaSilva Jordan}}		; {{W\|Noah Dean DaSilva Jordan}}

Overthink: /* Edo approximation */ caps

2026-01-12T07:36:42Z

Edo approximation: caps

← Older revision		Revision as of 07:36, 12 January 2026
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	Here is a list of edos which provides relatively good tunings for 23-limit intervals ([[TE relative error]] < 5%): {{EDOs\| 94, 190g, 193, 217, 243e, 270, 282, 311, 328h, 373g, 388, 422, 436, 460, 525, 540, 566g, 581, 624, 639h, 643i, 653, 692i, 718, 742i, 764(h), 814, 860, 882, 908, 935, 954h, 997, 1012, 1046dgh, 1075, 1106, 1125, 1178, 1205g, 1224, 1236(h), 1258, 1282, 1308, 1323, 1357efhi, 1385, 1395, 1419, 1448(g), 1506hi, 1578, 1600, 1646, 1672h, 1677e, 1696, 1718, 1730(g), 1759, 1768gi, 1817hi, 1821ef, 1889, 1920, 1966, 2000, 2038, 2041, 2072, 2087h, 2103, 2113, 2132eh, 2159, 2217, 2231, 2243e, 2270i, 2311, 2320, 2414, 2460 }} and so on.		Here is a list of edos which provides relatively good tunings for 23-limit intervals ([[TE relative error]] < 5%): {{EDOs\| 94, 190g, 193, 217, 243e, 270, 282, 311, 328h, 373g, 388, 422, 436, 460, 525, 540, 566g, 581, 624, 639h, 643i, 653, 692i, 718, 742i, 764(h), 814, 860, 882, 908, 935, 954h, 997, 1012, 1046dgh, 1075, 1106, 1125, 1178, 1205g, 1224, 1236(h), 1258, 1282, 1308, 1323, 1357efhi, 1385, 1395, 1419, 1448(g), 1506hi, 1578, 1600, 1646, 1672h, 1677e, 1696, 1718, 1730(g), 1759, 1768gi, 1817hi, 1821ef, 1889, 1920, 1966, 2000, 2038, 2041, 2072, 2087h, 2103, 2113, 2132eh, 2159, 2217, 2231, 2243e, 2270i, 2311, 2320, 2414, 2460 }} and so on.

	{{Note\| [[~~wart~~ notation]] is used to specify the [[val]] chosen for the edo. In the above list, "58hi" means taking the second closest approximations of harmonics 19 and 23. }}		{{Note\| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "58hi" means taking the second closest approximations of harmonics 19 and 23. }}

	[[94edo]] is the first [[edo]] to be consistent in the [[23-odd-limit]]. The smallest edo where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent.		[[94edo]] is the first [[edo]] to be consistent in the [[23-odd-limit]]. The smallest edo where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent.

FloraC: /* Edo approximation */ adopt template

2025-12-27T17:45:13Z

Edo approximation: adopt template

← Older revision		Revision as of 17:45, 27 December 2025
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	Here is a list of edos which provides relatively good tunings for 23-limit intervals ([[TE relative error]] < 5%): {{EDOs\| 94, 190g, 193, 217, 243e, 270, 282, 311, 328h, 373g, 388, 422, 436, 460, 525, 540, 566g, 581, 624, 639h, 643i, 653, 692i, 718, 742i, 764(h), 814, 860, 882, 908, 935, 954h, 997, 1012, 1046dgh, 1075, 1106, 1125, 1178, 1205g, 1224, 1236(h), 1258, 1282, 1308, 1323, 1357efhi, 1385, 1395, 1419, 1448(g), 1506hi, 1578, 1600, 1646, 1672h, 1677e, 1696, 1718, 1730(g), 1759, 1768gi, 1817hi, 1821ef, 1889, 1920, 1966, 2000, 2038, 2041, 2072, 2087h, 2103, 2113, 2132eh, 2159, 2217, 2231, 2243e, 2270i, 2311, 2320, 2414, 2460 }} and so on.		Here is a list of edos which provides relatively good tunings for 23-limit intervals ([[TE relative error]] < 5%): {{EDOs\| 94, 190g, 193, 217, 243e, 270, 282, 311, 328h, 373g, 388, 422, 436, 460, 525, 540, 566g, 581, 624, 639h, 643i, 653, 692i, 718, 742i, 764(h), 814, 860, 882, 908, 935, 954h, 997, 1012, 1046dgh, 1075, 1106, 1125, 1178, 1205g, 1224, 1236(h), 1258, 1282, 1308, 1323, 1357efhi, 1385, 1395, 1419, 1448(g), 1506hi, 1578, 1600, 1646, 1672h, 1677e, 1696, 1718, 1730(g), 1759, 1768gi, 1817hi, 1821ef, 1889, 1920, 1966, 2000, 2038, 2041, 2072, 2087h, 2103, 2113, 2132eh, 2159, 2217, 2231, 2243e, 2270i, 2311, 2320, 2414, 2460 }} and so on.

	~~: '''~~Note~~''':~~ [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "58hi" means taking the second closest approximations of harmonics 19 and 23.		{{Note\| [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "58hi" means taking the second closest approximations of harmonics 19 and 23. }}

	[[94edo]] is the first [[edo]] to be consistent in the [[23-odd-limit]]. The smallest edo where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent.		[[94edo]] is the first [[edo]] to be consistent in the [[23-odd-limit]]. The smallest edo where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent.

FloraC: /* Edo approximation */ calibrate the list according to my research results

2025-08-20T16:20:42Z

Edo approximation: calibrate the list according to my research results

← Older revision		Revision as of 16:20, 20 August 2025
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	== Edo approximation ==		== Edo approximation ==
	Here is a list of [[edo]]s with progressively better tunings for 23-limit intervals (decreasing [[TE error]]): {{EDOs\| 80, 87, 94, 111, 121i, 130, 140, 152fg, 159, 183, 190g, 193, 217, 243e, 270, 282, 311, 373g, 422, 525, 566g, 581, 718, 742i, 814, 935, 954h, 1106, 1178, 1308, 1323, 1395, 1506hi, 1578, 1889, 2000, 2460 }} and so on.		Here is a list of [[edo]]s with progressively better tunings for 23-limit intervals ([[monotonicity limit]] ≥ 23 and decreasing [[TE error]]): {{EDOs\| 58hi, 62, 68e, 72, 94, 111, 121i, 130, 140, 152fg, 159, 183, 190g, 193, 217, 243e, 270, 282, 311, 373g, 422, 525, 566g, 581, 718, 742i, 814, 935, 954h, 1106, 1178, 1308, 1323, 1395, 1506hi, 1578, 1889, 2000, 2460 }} and so on. For a more comprehensive list, see [[Sequence of equal temperaments by error]].

	Here is a list of edos which provides relatively good tunings for 23-limit intervals ([[TE relative error]] < 5%): {{EDOs\| 94, 190g, 193, 217, 243e, 270, 282, 311, 328h, 373g, 388, 422, 436, 460, 525, 540, 566g, 581, 624, 639h, 643i, 653, 692i, 718, 742i, 764(h), 814, 860, 882, 908, 935, 954h, 997, 1012, 1046dgh, 1075, 1106, 1125, 1178, 1205g, 1224, 1236(h), 1258, 1282, 1308, 1323, 1357efhi, 1385, 1395, 1419, 1448(g), 1506hi, 1578, 1600, 1646, 1672h, 1677e, 1696, 1718, 1730(g), 1759, 1768gi, 1817hi, 1821ef, 1889, 1920, 1966, 2000, 2038, 2041, 2072, 2087h, 2103, 2113, 2132eh, 2159, 2217, 2231, 2243e, 2270i, 2311, 2320, 2414, 2460 }} and so on.		Here is a list of edos which provides relatively good tunings for 23-limit intervals ([[TE relative error]] < 5%): {{EDOs\| 94, 190g, 193, 217, 243e, 270, 282, 311, 328h, 373g, 388, 422, 436, 460, 525, 540, 566g, 581, 624, 639h, 643i, 653, 692i, 718, 742i, 764(h), 814, 860, 882, 908, 935, 954h, 997, 1012, 1046dgh, 1075, 1106, 1125, 1178, 1205g, 1224, 1236(h), 1258, 1282, 1308, 1323, 1357efhi, 1385, 1395, 1419, 1448(g), 1506hi, 1578, 1600, 1646, 1672h, 1677e, 1696, 1718, 1730(g), 1759, 1768gi, 1817hi, 1821ef, 1889, 1920, 1966, 2000, 2038, 2041, 2072, 2087h, 2103, 2113, 2132eh, 2159, 2217, 2231, 2243e, 2270i, 2311, 2320, 2414, 2460 }} and so on.

	: '''Note''': [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "~~121i~~" means taking the second closest ~~approximation~~ of harmonics 23.		: '''Note''': [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "58hi" means taking the second closest approximations of harmonics 19 and 23.

	[[94edo]] is the first [[edo]] to be consistent in the [[23-odd-limit]]. The smallest edo where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent.		[[94edo]] is the first [[edo]] to be consistent in the [[23-odd-limit]]. The smallest edo where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent.

FloraC: The diagram is fine but doesn't warrant a section

2025-04-01T11:41:07Z

The diagram is fine but doesn't warrant a section

← Older revision		Revision as of 11:41, 1 April 2025
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	== 23-odd-limit intervals ==		== 23-odd-limit intervals ==
			[[File:Some 23-limit otonal chords.png\|thumb\|15 pentads and 1 hexad, with 23 as the highest odd harmonic, avoiding steps smaller than 23/21.]]

	Ratios of 23 in the 23-odd-limit are:		Ratios of 23 in the 23-odd-limit are:

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	\| vicesimotertial major seventh		\| vicesimotertial major seventh
	\|}		\|}

	~~== 23-Limit Harmony ==~~
	~~[[File:Some 23-limit otonal chords.png\|thumb\|15 pentads and 1 hexad, with 23 as the highest odd harmonic, avoiding steps smaller than 23/21.]]~~

	== Trivia ==		== Trivia ==

Xenji: /* 23-Limit Harmony */More clarification?

2025-03-31T17:46:27Z

23-Limit Harmony: More clarification?

← Older revision		Revision as of 17:46, 31 March 2025
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	== 23-Limit Harmony ==		== 23-Limit Harmony ==
			[[File:Some 23-limit otonal chords.png\|thumb\|15 pentads and 1 hexad, with 23 as the highest odd harmonic, avoiding steps smaller than 23/21.]]

	== Trivia ==		== Trivia ==
	* Unlike most other prime limits, the smallest [[superparticular ratio]] of [[Harmonic class\|HC23]] is larger than the smallest one of HC19. 23 is the first prime limit to show this phenomenon. The ratio is, in fact, larger than the second smallest one of HC19. See [[List of superparticular intervals]].		* Unlike most other prime limits, the smallest [[superparticular ratio]] of [[Harmonic class\|HC23]] is larger than the smallest one of HC19. 23 is the first prime limit to show this phenomenon. The ratio is, in fact, larger than the second smallest one of HC19. See [[List of superparticular intervals]].

Xenji: /* 23-odd-limit intervals */Moving content around.

2025-03-31T17:43:08Z

23-odd-limit intervals: Moving content around.

← Older revision		Revision as of 17:43, 31 March 2025
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	\| vicesimotertial major seventh		\| vicesimotertial major seventh
	\|}		\|}
	~~[[File:Some 23-limit otonal chords.png\|thumb\|Some 23-limit otonal chords.]]~~

	== 23-Limit Harmony ==		== 23-Limit Harmony ==

Xenji at 14:20, 31 March 2025

2025-03-31T14:20:28Z

← Older revision		Revision as of 14:20, 31 March 2025
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	== 23-Limit Harmony ==		== 23-Limit Harmony ==
	~~[[File:Some 23-limit otonal chords.png\|thumb]]~~

	== Trivia ==		== Trivia ==
	* Unlike most other prime limits, the smallest [[superparticular ratio]] of [[Harmonic class\|HC23]] is larger than the smallest one of HC19. 23 is the first prime limit to show this phenomenon. The ratio is, in fact, larger than the second smallest one of HC19. See [[List of superparticular intervals]].		* Unlike most other prime limits, the smallest [[superparticular ratio]] of [[Harmonic class\|HC23]] is larger than the smallest one of HC19. 23 is the first prime limit to show this phenomenon. The ratio is, in fact, larger than the second smallest one of HC19. See [[List of superparticular intervals]].

Xenji: I added an image showing some 23-limit otonal chords. Apologies, I haven't done much editing in recent years. Please feel free to clean this up, if the formatting seems weird, veteran editors. Thank you!

2025-03-31T14:19:41Z

I added an image showing some 23-limit otonal chords. Apologies, I haven't done much editing in recent years. Please feel free to clean this up, if the formatting seems weird, veteran editors. Thank you!

← Older revision		Revision as of 14:19, 31 March 2025
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	\| vicesimotertial major seventh		\| vicesimotertial major seventh
	\|}		\|}
			[[File:Some 23-limit otonal chords.png\|thumb\|Some 23-limit otonal chords.]]

			== 23-Limit Harmony ==
			[[File:Some 23-limit otonal chords.png\|thumb]]

	== Trivia ==		== Trivia ==