User:Eliora/1ed33/32 - Revision history

Fredg999: Fredg999 moved page 1ed33/32 to User:Eliora/1ed33/32 without leaving a redirect: XW:NG (moved to preserve temperament properties in case that's useful to someone)

2026-06-28T07:55:43Z

Fredg999 moved page 1ed33/32 to User:Eliora/1ed33/32 without leaving a redirect: XW:NG (moved to preserve temperament properties in case that's useful to someone)

← Older revision	Revision as of 07:55, 28 June 2026
(No difference)

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:20:42Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:20, 1 August 2025
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	~~[[Category:Edonoi]]~~

Fredg999: Propose merge

2025-08-01T04:27:51Z

Propose merge

← Older revision		Revision as of 04:27, 1 August 2025
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			{{todo\|merge articles\|inline=1\|text=Merge into [[33/32]]?}}
	{{Infobox ET\|1ed33/32}}		{{Infobox ET\|1ed33/32}}
	'''1 equal division of 33/32''' ('''1ed33/32'''), also known as '''ambitonal sequence of 33/32''' ('''AS33/32''') or '''33/32 equal-step tuning''', is an equal multiplication of [[33/32]] (the Alpharabian quarter-tone), and results in a nonoctave tuning equivalent to 22.5255 EDO.		'''1 equal division of 33/32''' ('''1ed33/32'''), also known as '''ambitonal sequence of 33/32''' ('''AS33/32''') or '''33/32 equal-step tuning''', is an equal multiplication of [[33/32]] (the Alpharabian quarter-tone), and results in a nonoctave tuning equivalent to 22.5255 EDO.

Cmloegcmluin: update name in page

2023-11-07T20:01:53Z

update name in page

← Older revision		Revision as of 20:01, 7 November 2023
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	Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.		Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.

	In the 5-limit, 33/32 ~~equal step tuning~~ tempers out the syntonic comma 81/80, making it meantone.		In the 5-limit, 1ed33/32 tempers out the syntonic comma 81/80, making it meantone.

	In the 7-limit, as a consequence of representing 6/5 and 7/6 well, it's great at representing the 5:6:7 otonal tetrad. This means that 385/384 is tempered out.		In the 7-limit, as a consequence of representing 6/5 and 7/6 well, it's great at representing the 5:6:7 otonal tetrad. This means that 385/384 is tempered out.

Cmloegcmluin: Cmloegcmluin moved page 33/32 equal step tuning to 1ed33/32: make 1ed name primary per https://en.xen.wiki/w/Talk:CET

2023-11-07T20:00:30Z

Cmloegcmluin moved page 33/32 equal step tuning to 1ed33/32: make 1ed name primary per https://en.xen.wiki/w/Talk:CET

← Older revision	Revision as of 20:00, 7 November 2023
(No difference)

Cmloegcmluin: make 1ed name primary and add AS name, per https://en.xen.wiki/w/Talk:CET

2023-11-07T20:00:18Z

make 1ed name primary and add AS name, per https://en.xen.wiki/w/Talk:CET

← Older revision		Revision as of 20:00, 7 November 2023
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	{{Infobox ET\|1ed33/32}}		{{Infobox ET\|1ed33/32}}
	~~The~~ '''equal multiplication of [[33/32]]~~''',~~ the Alpharabian quarter-tone, results in ~~an interesting~~ nonoctave tuning, equivalent to 22.5255 EDO.		'''1 equal division of 33/32''' ('''1ed33/32'''), also known as '''ambitonal sequence of 33/32''' ('''AS33/32''') or '''33/32 equal-step tuning''', is an equal multiplication of [[33/32]] (the Alpharabian quarter-tone), and results in a nonoctave tuning equivalent to 22.5255 EDO.

	Lookalikes: 5ed7/6, 45ed4		Lookalikes: 5ed7/6, 45ed4

Eliora: infobox et

2022-10-07T15:39:55Z

infobox et

← Older revision		Revision as of 15:39, 7 October 2022
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			{{Infobox ET\|1ed33/32}}
	The '''equal multiplication of [[33/32]]''', the Alpharabian quarter-tone, results in an interesting nonoctave tuning, equivalent to 22.5255 EDO.		The '''equal multiplication of [[33/32]]''', the Alpharabian quarter-tone, results in an interesting nonoctave tuning, equivalent to 22.5255 EDO.

Eliora: /* Theory */

2022-07-27T19:07:11Z

Theory

← Older revision		Revision as of 19:07, 27 July 2022
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	Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.		Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.

	In the 5-limit, 33/32 equal step tuning tempers out the syntonic comma 81/80.		In the 5-limit, 33/32 equal step tuning tempers out the syntonic comma 81/80, making it meantone.

	In the 7-limit, as a consequence of representing 6/5 and 7/6 well, it's great at representing the 5:6:7 otonal tetrad.		In the 7-limit, as a consequence of representing 6/5 and 7/6 well, it's great at representing the 5:6:7 otonal tetrad. This means that 385/384 is tempered out.

	== Regular temperament properties ==		== Regular temperament properties ==

Eliora at 15:00, 12 July 2022

2022-07-12T15:00:52Z

← Older revision		Revision as of 15:00, 12 July 2022
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	\|1 5		\|1 5
	\|}		\|}

			[[Category:Edonoi]]

Eliora: /* Theory */

2022-07-04T21:19:08Z

Theory

← Older revision		Revision as of 21:19, 4 July 2022
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	== Theory ==		== Theory ==
	{{Harmonics in equal\|1\|33\|32\|columns=11\|intervals=prime}}		{{Harmonics in equal\|1\|33\|32\|columns=11\|intervals=prime}}
	In this tuning, 2 steps correspond to the parapotome [[1089/1024]],		In this tuning, 2 steps by definition correspond to the parapotome [[1089/1024]].

	Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.		Intervals with excellent approximation in this tuning are: 7/6 (5), 20/13 (14), 18/11 (16). Other intervals with good approximation are: 6/5, 7/5, 9/5, 13/7, 13/9, 11/10, 19/12, 17/16, 17/15, 16/15.
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	In the 5-limit, 33/32 equal step tuning tempers out the syntonic comma 81/80.		In the 5-limit, 33/32 equal step tuning tempers out the syntonic comma 81/80.

	== Regular temperament ~~comma lists~~ ==		In the 7-limit, as a consequence of representing 6/5 and 7/6 well, it's great at representing the 5:6:7 otonal tetrad.

			== Regular temperament properties ==
	"Normal" subgroups calculated using the 23edo val that matches 33/32 equal step tuning patent val.		"Normal" subgroups calculated using the 23edo val that matches 33/32 equal step tuning patent val.
	{\| class="wikitable"		{\| class="wikitable"