988edo - 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"

2026-03-13T13:32:12Z

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 13:32, 13 March 2026
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	\| [[French deck]]		\| [[French deck]]
	\|}		\|}
	<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

	== Music ==		== Music ==

ArrowHead294 at 23:04, 20 February 2025

2025-02-20T23:04:52Z

← Older revision		Revision as of 23:04, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|988~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:07, 15 January 2025

2025-01-15T16:07:47Z

← Older revision		Revision as of 16:07, 15 January 2025
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	\| [[French deck]]		\| [[French deck]]
	\|}		\|}
	<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

	== Music ==		== Music ==

ArrowHead294: Partial undo

2024-11-16T12:44:17Z

Partial undo

← Older revision		Revision as of 12:44, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 17-limit temperaments supported by 494edo are not included.		Note: 17-limit temperaments supported by 494edo are not included.
	{{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
	\|-		\|-
	\| 4		\| 4
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	\| 134560000/107132311<br />(?)		\| 134560000/107132311<br />(?)
	\| [[French deck]]		\| [[French deck]]
	~~{{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

	== Music ==		== Music ==

ArrowHead294 at 04:02, 16 November 2024

2024-11-16T04:02:05Z

← Older revision		Revision as of 04:02, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 17-limit temperaments supported by 494edo are not included.		Note: 17-limit temperaments supported by 494edo are not included.
	{~~\| class="wikitable center~~-~~all left-5"~~		{{rank-2 begin}}
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 4		\| 4
	\| 261\988<br>(14\988)		\| 261\988<br />(14\988)
	\| 317.004<br>(17.004)		\| 317.004<br />(17.004)
	\| 6/5<br>(126/125)		\| 6/5<br />(126/125)
	\| [[Quadritikleismic]] (988ccd)		\| [[Quadritikleismic]] (988ccd)
	\|-		\|-
	\| 19		\| 19
	\| 141\988<br>(37\988)		\| 141\988<br />(37\988)
	\| 171.255<br>(44.939)		\| 171.255<br />(44.939)
	\| 6545/5928<br>(?)		\| 6545/5928<br />(?)
	\| [[Kalium]]		\| [[Kalium]]
	\|-		\|-
	\| 52		\| 52
	\| 325\988<br>(2\988)		\| 325\988<br />(2\988)
	\| 394.736<br>(2.429)		\| 394.736<br />(2.429)
	\| 134560000/107132311<br>(?)		\| 134560000/107132311<br />(?)
	\| [[French deck]]		\| [[French deck]]
	\|}		{{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}}

	== Music ==		== Music ==
	; [[birdshite stalactite]]		; [[birdshite stalactite]]
	* "clagworks" from ''clagworks / it's probably gout'' (2024) – [https://open.spotify.com/track/1Abk4KcVUHoRkKxYNSYm0F Spotify] \| [https://birdshitestalactite.bandcamp.com/track/clagworks Bandcamp] \| [https://www.youtube.com/watch?v=S0zS0rYtT2Y YouTube]		* "clagworks" from ''clagworks / it's probably gout'' (2024) – [https://open.spotify.com/track/1Abk4KcVUHoRkKxYNSYm0F Spotify] \| [https://birdshitestalactite.bandcamp.com/track/clagworks Bandcamp] \| [https://www.youtube.com/watch?v=S0zS0rYtT2Y YouTube]

	; [[Eliora]]		; [[Eliora]]

Francium: /* Music */ +music

2024-03-08T19:26:05Z

Music: +music

← Older revision		Revision as of 19:26, 8 March 2024
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	== Music ==		== Music ==
			; [[birdshite stalactite]]
			* "clagworks" from ''clagworks / it's probably gout'' (2024) – [https://open.spotify.com/track/1Abk4KcVUHoRkKxYNSYm0F Spotify] \| [https://birdshitestalactite.bandcamp.com/track/clagworks Bandcamp] \| [https://www.youtube.com/watch?v=S0zS0rYtT2Y YouTube]

	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023)		* [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023)

	[[Category:Listen]]		[[Category:Listen]]

Francium: +categories

2024-02-13T18:21:32Z

+categories

← Older revision		Revision as of 18:21, 13 February 2024
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	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023)		* [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023)

			[[Category:Listen]]

Eliora: /* Theory */ explain why notable

2023-11-30T17:04:21Z

Theory: explain why notable

← Older revision		Revision as of 17:04, 30 November 2023
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	== Theory ==		== Theory ==
	988edo is [[enfactoring\|enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a [[zeta edo]]. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. A [[comma basis]] for 988edo in the 19-limit is {[[1156/1155]], [[1275/1274]], [[1445/1444]], [[1716/1715]], [[2080/2079]], [[2431/2430]], [[4096/4095]]}. An alternate mapping for 17 would be the 988g val, where it tempers out [[2025/2023]], 13013/13005, 15625/15606, 31213/31212. In addition, in the 988ccd val it is a tuning for [[quadritikleismic]] temperament in the 7-limit.		988edo is [[enfactoring\|enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a [[zeta edo]]. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. A [[comma basis]] for 988edo in the 19-limit is {[[1156/1155]], [[1275/1274]], [[1445/1444]], [[1716/1715]], [[2080/2079]], [[2431/2430]], [[4096/4095]]}. An alternate mapping for 17 would be the 988g val, where it tempers out [[2025/2023]], 13013/13005, 15625/15606, 31213/31212.

			In addition, in the 988ccd val provides a tuning that is extremely close to the [[POTE tuning]] for [[quadritikleismic]] temperament in the 7-limit.

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

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T11:16:45Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 11:16, 2 November 2023
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	== Theory ==		== Theory ==
	988edo is [[enfactoring\|enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a zeta edo. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. ~~The~~ comma basis for 988edo in the 19-limit is {[[1156/1155]], [[1275/1274]], [[1445/1444]], [[1716/1715]], [[2080/2079]], [[2431/2430]], [[4096/4095]]}. An alternate mapping for 17 would be the 988g val, where it tempers out [[2025/2023]], 13013/13005, 15625/15606, 31213/31212. In addition, in the 988ccd val it is a tuning for [[quadritikleismic]] temperament in the 7-limit.		988edo is [[enfactoring\|enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a [[zeta edo]]. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. A [[comma basis]] for 988edo in the 19-limit is {[[1156/1155]], [[1275/1274]], [[1445/1444]], [[1716/1715]], [[2080/2079]], [[2431/2430]], [[4096/4095]]}. An alternate mapping for 17 would be the 988g val, where it tempers out [[2025/2023]], 13013/13005, 15625/15606, 31213/31212. In addition, in the 988ccd val it is a tuning for [[quadritikleismic]] temperament in the 7-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	988edo has subset edos {{EDOs\| 2, 4, 13, 19, 26, 38, 52, 76, 247, and 494 }}.		Since 988 factors into {{factorization\|988}}, 988edo has subset edos {{EDOs\| 2, 4, 13, 19, 26, 38, 52, 76, 247, and 494 }}.

	One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb.		One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb.
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-

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

2023-10-19T15:50:08Z

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

← Older revision		Revision as of 15:50, 19 October 2023
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	== Theory ==		== Theory ==
	988edo ~~provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, 59th harmonics and a reasonable tuning for 23, 29, 31, 41st harmonics, making a strong higher-limit system. In lower limits, it~~ is [[enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a zeta edo. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. The comma basis for 988edo in the 19-limit is {1156/1155, 1275/1274, 1445/1444, 1716/1715, 2080/2079, 2431/2430, 4096/4095}.		988edo is [[enfactoring\|enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a zeta edo. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. The comma basis for 988edo in the 19-limit is {[[1156/1155]], [[1275/1274]], [[1445/1444]], [[1716/1715]], [[2080/2079]], [[2431/2430]], [[4096/4095]]}. An alternate mapping for 17 would be the 988g val, where it tempers out [[2025/2023]], 13013/13005, 15625/15606, 31213/31212. In addition, in the 988ccd val it is a tuning for [[quadritikleismic]] temperament in the 7-limit.

			=== Prime harmonics ===
			{{Harmonics in equal\|988\|columns=11}}

	An alternate mapping for 17 would be the 988g val, where it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212. In addition, in the 988ccd val it is a tuning for [[quadritikleismic]] temperament in the 7-limit.
	=== Higher limits ===		=== Higher limits ===
			988edo provides excellent approximations for harmonics 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, and 59, and reasonable approximations for harmonics 23, 29, 31, and 41, making it a strong higher-limit system.

	In the 2.5.11.13.19.29.31 it supports period-52 temperament called [[french deck]], with the tempering out of [[6656/6655]] inherited from 494edo.		In the 2.5.11.13.19.29.31 it supports period-52 temperament called [[french deck]], with the tempering out of [[6656/6655]] inherited from 494edo.

	988edo is similar to [[2016edo]] in the fact that both tune well the 2.5.11.13.19.41.47 subgroup. The result is the 988 & 2016 temperament, which reaches [[13/8]] in four generators and has a comma basis {7943/7942, 322465/322373, 16777475/16777216, 22151168/22150865, 12998046875/12994428928}.		988edo is similar to [[2016edo]] in the fact that both tune well the 2.5.11.13.19.41.47 subgroup. The result is the 988 & 2016 temperament, which reaches [[13/8]] in four generators and has a comma basis {7943/7942, 322465/322373, 16777475/16777216, 22151168/22150865, 12998046875/12994428928}.

	=== Subsets and supersets ===		=== Subsets and supersets ===
	988edo has subset edos {{EDOs\|1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494}}.		988edo has subset edos {{EDOs\| 2, 4, 13, 19, 26, 38, 52, 76, 247, and 494 }}.

	One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb.		One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb.

	~~=== Prime harmonics ===~~
	~~{{Harmonics in equal\|988\|columns=11}}~~

	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: temperaments ~~represented~~ by 494edo are not included.		Note: 17-limit temperaments supported by 494edo are not included.
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	!Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperaments		! Temperaments
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	\| 394.736<br>(2.429)		\| 394.736<br>(2.429)
	\| 134560000/107132311<br>(?)		\| 134560000/107132311<br>(?)
	\|[[French deck]]		\| [[French deck]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==
	* [https://www.youtube.com/watch?v=c7BW2xnQBb4 Alien ethnic motive in 13edo and 12rdo] ~~by [[Eliora]]~~		; [[Eliora]]
			* [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023)
	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~