9ed9/8 - Revision history

FloraC: /* Theory */ expand on its tuning characteristics

2025-04-18T14:24:30Z

Theory: expand on its tuning characteristics

← Older revision		Revision as of 14:24, 18 April 2025
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	== Theory ==		== Theory ==
	9ed9/8 corresponds to 52.9645…[[edo]], which is closely related to [[53edo]] but with the whole tone instead of the octave tuned pure. Like [[53edo]], 9ed9/8 is [[consistent]] to the [[integer limit\|10-integer-limit]].		9ed9/8 corresponds to 52.9645…[[edo]], which is closely related to [[53edo]] but with the whole tone instead of the octave tuned pure. Like [[53edo]], 9ed9/8 is [[consistent]] to the [[integer limit\|10-integer-limit]], but it has a sharp tendency, with all the [[harmonic]]s within 1 to 16 but [[11/1\|11]] tuned sharp.

	=== Harmonics ===		=== Harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	9ed9/8 is the first odd composite ed9/8, containing [[3ed9/8]] as a subset.		9ed9/8 is the first odd composite ed9/8, containing [[3ed9/8]] as a subset.

	== Intervals ==		== Intervals ==

FloraC: /* Intervals */ reduce cent values to one decimal place, per discussion on Discord

2025-03-24T10:57:19Z

Intervals: reduce cent values to one decimal place, per discussion on Discord

Show changes

FloraC: +subsets and supersets; +see also

2025-03-24T10:54:31Z

+subsets and supersets; +see also

← Older revision		Revision as of 10:54, 24 March 2025
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	{{Harmonics in equal\|9\|9\|8}}		{{Harmonics in equal\|9\|9\|8}}
	{{Harmonics in equal\|9\|9\|8\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 9ed9/8 (continued)}}		{{Harmonics in equal\|9\|9\|8\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 9ed9/8 (continued)}}

			=== Subsets and supersets ===
			9ed9/8 is the first odd composite ed9/8, containing [[3ed9/8]] as a subset.

	== Intervals ==		== Intervals ==
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	\| (9/8)<sup>6</sup> = 531441/262144		\| (9/8)<sup>6</sup> = 531441/262144
	\|}		\|}

			== See also ==
			* [[31edf]] – relative edf
			* [[53edo]] – relative edo
			* [[84edt]] – relative edt
			* [[137ed6]] – relative ed6

FloraC: Cleanup; -virtually duplicate stuff from 53edo that fails to undo octave reduction

2025-03-24T10:53:03Z

Cleanup; -virtually duplicate stuff from 53edo that fails to undo octave reduction

Show changes

BudjarnLambeth: Harmonics

2024-10-03T21:00:35Z

Harmonics

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{ED intro}} It corresponds to 52.9645 [[edo]], which is closely related to [[53edo]] but with the whole tone instead of the octave tuned pure.
 == Intervals ==

FloraC: Adopt template: ED intro. -reference to Turkish music (this interpretation instead of plain 53edo is absurd). Misc. cleanup

2024-05-24T09:06:30Z

Adopt template: ED intro. -reference to Turkish music (this interpretation instead of plain 53edo is absurd). Misc. cleanup

← Older revision		Revision as of 09:06, 24 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''9ED9/8''' is the [[Equal-step tuning\|equal division]] of the [[9/8\|Pythagorean whole tone]] into nine parts of 22~~.~~6567~~ [[~~cent\|cents~~]] ~~each~~, ~~corresponding~~ to ~~52.9645~~ [[~~edo~~]]~~. This tuning is used in Ottoman classical music theory, in which ninth root of~~ the ~~9/8~~ whole tone ~~is treated as~~ the ~~minimum interval~~.		{{ED intro}} It corresponds to 52.9645 [[edo]], which is closely related to [[53edo]] but with the whole tone instead of the octave tuned pure.

	==Intervals==		== Intervals ==
	{\| class="wikitable right-2"		{\| class="wikitable right-2"
	\|-		\|-
	! ~~degree~~		! #
	! ~~cents value~~		! Cents Value
	! ~~ratio~~		! Ratio
	\|-		\|-
	\| 0		\| 0
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	\|}		\|}

	== ~~Just approximation~~ ==		== Approximation to JI ==
	=== 15-odd-limit mappings ===		=== 15-odd-limit mappings ===
	The following table shows how [[15-odd-limit intervals]] are represented in 9ed9/8 (ordered by absolute error).		The following table shows how [[15-odd-limit intervals]] are represented in 9ed9/8 (ordered by absolute error).
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	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|-		\|-
	\|+ Direct ~~mapping~~ (even if inconsistent)		\|+ Direct approximation (even if inconsistent)
	\|-		\|-
	! Interval(s)		! Interval(s)
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	\| 10.491		\| 10.491
	\|}		\|}

	~~==See also==~~
	* [http://en.wikipedia.org/wiki/Ottoman_classical_music Ottoman classical music - Wikipedia]
	* [http://en.wikipedia.org/wiki/Makam Makam - Wikipedia]

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Whole tone]]		[[Category:Whole tone]]

ArrowHead294 at 04:32, 24 May 2024

2024-05-24T04:32:39Z

← Older revision		Revision as of 04:32, 24 May 2024
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	==See also==		==See also==
	*[http://en.wikipedia.org/wiki/Ottoman_classical_music Ottoman classical music - Wikipedia]		* [http://en.wikipedia.org/wiki/Ottoman_classical_music Ottoman classical music - Wikipedia]
	*[http://en.wikipedia.org/wiki/Makam Makam - Wikipedia]		* [http://en.wikipedia.org/wiki/Makam Makam - Wikipedia]

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
	[[Category:Whole tone]]		[[Category:Whole tone]]

Plumtree: Infobox ET added

2022-10-05T20:11:27Z

Infobox ET added

← Older revision		Revision as of 20:11, 5 October 2022
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			{{Infobox ET}}
	'''9ED9/8''' is the [[Equal-step tuning\|equal division]] of the [[9/8\|Pythagorean whole tone]] into nine parts of 22.6567 [[cent\|cents]] each, corresponding to 52.9645 [[edo]]. This tuning is used in Ottoman classical music theory, in which ninth root of the 9/8 whole tone is treated as the minimum interval.		'''9ED9/8''' is the [[Equal-step tuning\|equal division]] of the [[9/8\|Pythagorean whole tone]] into nine parts of 22.6567 [[cent\|cents]] each, corresponding to 52.9645 [[edo]]. This tuning is used in Ottoman classical music theory, in which ninth root of the 9/8 whole tone is treated as the minimum interval.

Xenwolf: /* 15-odd-limit mappings */ linebreak in table title looks not that great (revert my idea)

2021-12-04T11:48:27Z

15-odd-limit mappings: linebreak in table title looks not that great (revert my idea)

← Older revision		Revision as of 11:48, 4 December 2021
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	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|-		\|-
	\|+ Direct mapping ~~<br>~~ (even if inconsistent)		\|+ Direct mapping (even if inconsistent)
	\|-		\|-
	! Interval(s)		! Interval(s)

Xenwolf: /* 15-odd-limit mappings */ minor adjustments on table to improve readability of wikitext (add space around meta chars)

2021-12-04T11:47:00Z

15-odd-limit mappings: minor adjustments on table to improve readability of wikitext (add space around meta chars)

← Older revision		Revision as of 11:47, 4 December 2021
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	=== 15-odd-limit mappings ===		=== 15-odd-limit mappings ===
	The following table shows how [[15-odd-limit intervals]] are represented in 9ed9/8 (ordered by absolute error).		The following table shows how [[15-odd-limit intervals]] are represented in 9ed9/8 (ordered by absolute error).

	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+ Direct mapping (even if inconsistent)		\|-
			\|+ Direct mapping <br> (even if inconsistent)
	\|-		\|-
	! Interval(s)		! Interval(s)
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	\|-		\|-
	\| [[9/8]]		\| [[9/8]]
	\|0.0		\| 0.000
	\|-		\|-
	\| [[3/2]], [[4/3]]		\| [[3/2]], [[4/3]]
	\|0.402		\| 0.402
	\|-		\|-
	\| [[26/15]]		\| [[26/15]]
	\|0.679		\| 0.679
	\|-		\|-
	\| [[15/8]], [[5/3]]		\| [[15/8]], [[5/3]]
	\|0.749		\| 0.749
	\|-		\|-
	\| [[16/9]]		\| [[16/9]]
	\|0.803		\| 0.803
	\|-		\|-
	\| [[13/10]]		\| [[13/10]]
	\|1.081		\| 1.081
	\|-		\|-
	\| [[5/4]], [[10/9]]		\| [[5/4]], [[10/9]]
	\|1.15		\| 1.150
	\|-		\|-
	\| [[15/13]]		\| [[15/13]]
	\|1.482		\| 1.482
	\|-		\|-
	\| [[6/5]], [[16/15]]		\| [[6/5]], [[16/15]]
	\|1.552		\| 1.552
	\|-		\|-
	\| [[20/13]]		\| [[20/13]]
	\|1.884		\| 1.884
	\|-		\|-
	\| [[9/5]], [[8/5]]		\| [[9/5]], [[8/5]]
	\|1.954		\| 1.954
	\|-		\|-
	\| [[13/8]], [[13/9]]		\| [[13/8]], [[13/9]]
	\|2.231		\| 2.231
	\|-		\|-
	\| [[13/12]]		\| [[13/12]]
	\|2.633		\| 2.633
	\|-		\|-
	\| [[16/13]], [[18/13]]		\| [[16/13]], [[18/13]]
	\|3.034		\| 3.034
	\|-		\|-
	\| [[24/13]]		\| [[24/13]]
	\|3.436		\| 3.436
	\|-		\|-
	\| [[12/7]]		\| [[12/7]]
	\|4.206		\| 4.206
	\|-		\|-
	\| [[22/13]]		\| [[22/13]]
	\|4.524		\| 4.524
	\|-		\|-
	\| [[9/7]], [[8/7]]		\| [[9/7]], [[8/7]]
	\|4.607		\| 4.607
	\|-		\|-
	\| [[7/6]]		\| [[7/6]]
	\|5.009		\| 5.009
	\|-		\|-
	\| [[13/11]]		\| [[13/11]]
	\|5.327		\| 5.327
	\|-		\|-
	\| [[7/4]], [[14/9]]		\| [[7/4]], [[14/9]]
	\|5.411		\| 5.411
	\|-		\|-
	\| [[10/7]]		\| [[10/7]]
	\|5.758		\| 5.758
	\|-		\|-
	\| [[22/15]]		\| [[22/15]]
	\|6.006		\| 6.006
	\|-		\|-
	\| [[15/14]]		\| [[15/14]]
	\|6.159		\| 6.159
	\|-		\|-
	\| [[11/10]]		\| [[11/10]]
	\|6.408		\| 6.408
	\|-		\|-
	\| [[7/5]]		\| [[7/5]]
	\|6.561		\| 6.561
	\|-		\|-
	\| [[15/11]]		\| [[15/11]]
	\|6.809		\| 6.809
	\|-		\|-
	\| [[13/7]]		\| [[13/7]]
	\|6.838		\| 6.838
	\|-		\|-
	\| [[28/15]]		\| [[28/15]]
	\|6.963		\| 6.963
	\|-		\|-
	\| [[11/6]]		\| [[11/6]]
	\|7.156		\| 7.156
	\|-		\|-
	\| [[20/11]]		\| [[20/11]]
	\|7.211		\| 7.211
	\|-		\|-
	\| [[11/9]], [[11/8]]		\| [[11/9]], [[11/8]]
	\|7.558		\| 7.558
	\|-		\|-
	\| [[14/13]]		\| [[14/13]]
	\|7.642		\| 7.642
	\|-		\|-
	\| [[12/11]]		\| [[12/11]]
	\|7.96		\| 7.960
	\|-		\|-
	\| [[18/11]], [[16/11]]		\| [[18/11]], [[16/11]]
	\|8.361		\| 8.361
	\|-		\|-
	\| [[14/11]]		\| [[14/11]]
	\|9.688		\| 9.688
	\|-		\|-
	\| [[11/7]]		\| [[11/7]]
	\|10.491		\| 10.491
	\|}		\|}