112edo - Revision history

MisterShafXen at 15:30, 23 April 2025

2025-04-23T15:30:27Z

← Older revision		Revision as of 15:30, 23 April 2025
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	* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv ''Circulating 2.3.7.11.13 Floaty Piano Improv'']		* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv ''Circulating 2.3.7.11.13 Floaty Piano Improv'']

			== See also ==
			[[Skip fretting system 112 9 11]]
	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294 at 16:51, 18 February 2025

2025-02-18T16:51:23Z

← Older revision		Revision as of 16:51, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|112~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	112edo has two great [[3/2\|perfect fifth]]s, the lower of which approximates [[quarter-comma meantone]] (just a tad lower), and the upper of ~~which – the~~ [[patent fifth]] ~~– is~~ identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27]] while -8 fifths gives a near-just [[39/32]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17]].		112edo has two great [[3/2\|perfect fifth]]s, the lower of which approximates [[quarter-comma meantone]] (just a tad lower), and the upper of which—the [[patent fifth]]—is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27]] while −8 fifths gives a near-just [[39/32]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17]].

	One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.		One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.

FloraC: +subsets and supersets

2024-06-04T06:41:39Z

+subsets and supersets

← Older revision		Revision as of 06:41, 4 June 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|112\|intervals=odd}}		{{Harmonics in equal\|112\|intervals=odd}}

			=== Subsets and supersets ===
			Since 112 factors into {{factorization\|112}}, 112edo has subset edos {{EDOs\| 2, 4, 7, 8, 14, 16, 28, and 56 }}. [[224edo]], which doubles it, is a strong 13-limit system.

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2024-06-04T06:38:52Z

Cleanup

← Older revision		Revision as of 06:38, 4 June 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|112}}		{{EDO intro\|112}}

	== Theory ==		== Theory ==
	112edo has two great perfect ~~fifths~~, the lower of which approximates ~~1/4~~-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/~~27\|28:~~27]] while -8 fifths gives a near-just [[39/32~~\|32:39~~]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17~~\|17:21~~]].		112edo has two great [[3/2\|perfect fifth]]s, the lower of which approximates [[quarter-comma meantone]] (just a tad lower), and the upper of which – the [[patent fifth]] – is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27]] while -8 fifths gives a near-just [[39/32]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17]].

	One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.		One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.
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	== Music ==		== Music ==
			; [[Cam Taylor]]
			* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv ''Circulating 2.3.7.11.13 Floaty Piano Improv'']

	* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv Circulating 2.3.7.11.13 Floaty Piano Improv] by [[Cam Taylor]]

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Listen]]		[[Category:Listen]]

BudjarnLambeth: Added interval table

2024-01-21T07:13:54Z

Added interval table

← Older revision		Revision as of 07:13, 21 January 2024
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|112\|intervals=odd}}		{{Harmonics in equal\|112\|intervals=odd}}

			== Intervals ==
			{{Interval table}}

	== Music ==		== Music ==

Eliora at 21:16, 30 May 2023

2023-05-30T21:16:47Z

← Older revision		Revision as of 21:16, 30 May 2023
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	{{Infobox ET}}		{{Infobox ET}}
			{{EDO intro\|112}}
	== Theory ==		== Theory ==
	~~'''~~112edo~~'''~~ has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27\|28:27]] while -8 fifths gives a near-just [[39/32\|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17\|17:21]].		112edo has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27\|28:27]] while -8 fifths gives a near-just [[39/32\|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17\|17:21]].

	One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.		One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.

Eliora: /* Circulating temperaments */

2023-05-30T21:16:18Z

Circulating temperaments

Show changes

BudjarnLambeth: /* Circulating temperaments */

2023-05-02T11:08:20Z

Circulating temperaments

← Older revision		Revision as of 11:08, 2 May 2023
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	== Circulating temperaments ==		== Circulating temperaments ==

	Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as [[circulating ~~temperaments~~]].		Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as [[circulating temperament]]s.

	{\| class="wikitable"		{\| class="wikitable"

BudjarnLambeth: Added harmonics table, moved circulating temperaments table into its own subheading

2023-05-02T11:08:06Z

Added harmonics table, moved circulating temperaments table into its own subheading

← Older revision		Revision as of 11:08, 2 May 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''~~112EDO~~''' has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27\|28:27]] while -8 fifths gives a near-just [[39/32\|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17\|17:21]].		'''112edo''' has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27\|28:27]] while -8 fifths gives a near-just [[39/32\|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17\|17:21]].

	One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.		One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.

	Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as circulating temperaments.		== Odd harmonics ==
			{{Harmonics in equal\|112\|intervals=odd}}

			== Circulating temperaments ==

			Since 112edo has a step of 10.714 cents, it also allows one to use its MOS scales as [[circulating temperaments]].

	{\| class="wikitable"		{\| class="wikitable"

Aura at 18:51, 4 October 2022

2022-10-04T18:51:19Z

← Older revision		Revision as of 18:51, 4 October 2022
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			{{Infobox ET}}
	'''112EDO''' has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27\|28:27]] while -8 fifths gives a near-just [[39/32\|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17\|17:21]].		'''112EDO''' has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27\|28:27]] while -8 fifths gives a near-just [[39/32\|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17\|17:21]].