83edo - Revision history

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''83edo waltz'' (2025)

2025-07-20T17:06:41Z

Music: Add Bryan Deister's ''83edo waltz'' (2025)

← Older revision		Revision as of 17:06, 20 July 2025
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	== Music ==		== Music ==
	* [https://youtube.com/shorts/vYhK-A74Kpg?si=n8bjn_AOYAPY69qx ''Microtonal improvisation in 83edo''] - [[Bryan Deister]] (Mar 2025)		* [https://youtube.com/shorts/vYhK-A74Kpg?si=n8bjn_AOYAPY69qx ''Microtonal improvisation in 83edo''] - [[Bryan Deister]] (Mar 2025)
			* [https://www.youtube.com/shorts/FFNFQ4H-2D4 ''83edo waltz''] (2025)

VectorGraphics: we don't need to document an unnamed temperament.

2025-06-12T03:41:01Z

we don't need to document an unnamed temperament.

← Older revision		Revision as of 03:41, 12 June 2025
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	== Theory ==		== Theory ==
	The [[3/1\|harmonic 3]] is 6.5{{c}} sharp and the [[5/1\|5]] is 4{{c}} sharp, with [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] more accurate but a little flat. Using the [[patent val]], it [[tempering out\|tempers out]] [[15625/15552]] in the 5-limit and [[686/675]], [[4000/3969]] and [[6144/6125]] in the 7-limit~~, and provides the [[optimal patent val]] for the 7-limit {{nowrap\|27 & 56}} temperament with wedgie {{multival\| 5 18 17 17 13 -11 }}~~. In the 11-limit it tempers out [[121/120]], [[176/175]] and [[385/384]], and in the 13-limit [[91/90]], [[169/168]] and [[196/195]], and it provides the optimal patent val for the 11-limit {{nowrap\|22 & 61}} temperament and the 13-limit 15 & 83 temperament.		The [[3/1\|harmonic 3]] is 6.5{{c}} sharp and the [[5/1\|5]] is 4{{c}} sharp, with [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] more accurate but a little flat. Using the [[patent val]], it [[tempering out\|tempers out]] [[15625/15552]] in the 5-limit and [[686/675]], [[4000/3969]] and [[6144/6125]] in the 7-limit. In the 11-limit it tempers out [[121/120]], [[176/175]] and [[385/384]], and in the 13-limit [[91/90]], [[169/168]] and [[196/195]], and it provides the optimal patent val for the 11-limit {{nowrap\|22 & 61}} temperament and the 13-limit 15 & 83 temperament.

	Every odd harmonic between the 7th and the 17th is tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of the 9:11:13 [[triad]].		Every odd harmonic between the 7th and the 17th is tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of the 9:11:13 [[triad]].

Lucius Chiaraviglio: Add instruments section with link to Lumatone mapping for 83edo

2025-03-27T06:36:02Z

Add instruments section with link to Lumatone mapping for 83edo

← Older revision		Revision as of 06:36, 27 March 2025
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== Instruments ==
			A [[Lumatone mapping for 83edo]] has now been demonstrated (see the Ripple and Miracle mapping for full gamut coverage).

	== Music ==		== Music ==
	* [https://youtube.com/shorts/vYhK-A74Kpg?si=n8bjn_AOYAPY69qx ''Microtonal improvisation in 83edo''] - [[Bryan Deister]] (Mar 2025)		* [https://youtube.com/shorts/vYhK-A74Kpg?si=n8bjn_AOYAPY69qx ''Microtonal improvisation in 83edo''] - [[Bryan Deister]] (Mar 2025)

BudjarnLambeth: Added music

2025-03-20T22:17:25Z

Added music

← Older revision		Revision as of 22:17, 20 March 2025
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== Music ==
			* [https://youtube.com/shorts/vYhK-A74Kpg?si=n8bjn_AOYAPY69qx ''Microtonal improvisation in 83edo''] - [[Bryan Deister]] (Mar 2025)

ArrowHead294 at 16:13, 20 February 2025

2025-02-20T16:13:19Z

← Older revision		Revision as of 16:13, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|83~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	The [[3/1\|harmonic 3]] is 6.5 ~~cents~~ sharp and the [[5/1\|5]] is 4 ~~cents~~ sharp, with [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] more accurate but a little flat. Using the [[patent val]], it [[tempering out\|tempers out]] [[15625/15552]] in the 5-limit and [[686/675]], [[4000/3969]] and [[6144/6125]] in the 7-limit, and provides the [[optimal patent val]] for the 7-limit 27 & 56 temperament with wedgie {{multival\| 5 18 17 17 13 -11 }}. In the 11-limit it tempers out [[121/120]], [[176/175]] and [[385/384]], and in the 13-limit [[91/90]], [[169/168]] and [[196/195]], and it provides the optimal patent val for the 11-limit 22 & 61 temperament and the 13-limit 15 & 83 temperament.		The [[3/1\|harmonic 3]] is 6.5{{c}} sharp and the [[5/1\|5]] is 4{{c}} sharp, with [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] more accurate but a little flat. Using the [[patent val]], it [[tempering out\|tempers out]] [[15625/15552]] in the 5-limit and [[686/675]], [[4000/3969]] and [[6144/6125]] in the 7-limit, and provides the [[optimal patent val]] for the 7-limit {{nowrap\|27 & 56}} temperament with wedgie {{multival\| 5 18 17 17 13 -11 }}. In the 11-limit it tempers out [[121/120]], [[176/175]] and [[385/384]], and in the 13-limit [[91/90]], [[169/168]] and [[196/195]], and it provides the optimal patent val for the 11-limit {{nowrap\|22 & 61}} temperament and the 13-limit 15 & 83 temperament.

	Every odd harmonic between the 7th and the 17th is tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of the 9:11:13 [[triad]].		Every odd harmonic between the 7th and the 17th is tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of the 9:11:13 [[triad]].

FloraC: /* Subsets and supersets */

2024-06-27T09:57:27Z

Subsets and supersets

← Older revision		Revision as of 09:57, 27 June 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	83edo is the 23rd [[prime edo]].		83edo is the 23rd [[prime edo]], following [[79edo]] and before [[89edo]].

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

FloraC: Cleanup

2024-06-21T09:28:26Z

Cleanup

← Older revision		Revision as of 09:28, 21 June 2024
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	== Theory ==		== Theory ==
			The [[3/1\|harmonic 3]] is 6.5 cents sharp and the [[5/1\|5]] is 4 cents sharp, with [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] more accurate but a little flat. Using the [[patent val]], it [[tempering out\|tempers out]] [[15625/15552]] in the 5-limit and [[686/675]], [[4000/3969]] and [[6144/6125]] in the 7-limit, and provides the [[optimal patent val]] for the 7-limit 27 & 56 temperament with wedgie {{multival\| 5 18 17 17 13 -11 }}. In the 11-limit it tempers out [[121/120]], [[176/175]] and [[385/384]], and in the 13-limit [[91/90]], [[169/168]] and [[196/195]], and it provides the optimal patent val for the 11-limit 22 & 61 temperament and the 13-limit 15 & 83 temperament.

			Every odd harmonic between the 7th and the 17th is tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of the 9:11:13 [[triad]].

			=== Odd harmonics ===
	{{Harmonics in equal\|83}}		{{Harmonics in equal\|83}}
	The 3/1 is 6.5 cents sharp and the 5/1 is 4 cents sharp, with 7, 11, and 13 more accurate but a little flat. It tempers out 15625/15552 in the 5-limit and 686/675, 4000/3969 and 6144/6125 in the 7-limit, and provides the optimal patent val for the 7-limit 27&56 temperament with wedgie {{multival\|5 18 17 17 13 -11}}. In the 11-limit it tempers out 121/120, 176/175 and 385/384, and in the 13-limit 91/90, 169/168 and 196/195, and it provides the optimal patent val for the 11-limit 22&61 temperament and the 13-limit 15&83 temperament. 83edo is the 23rd [[prime EDO]].

	~~Every odd harmonic between the 7th~~ and ~~the 17th~~ is ~~tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of~~ the ~~9:11:13~~ [[~~triad~~]].		=== Subsets and supersets ===
			83edo is the 23rd [[prime edo]].

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

	~~{{Todo\| expand }}~~

FloraC: -redundant categories

2023-11-27T14:44:13Z

-redundant categories

← Older revision		Revision as of 14:44, 27 November 2023
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	Every odd harmonic between the 7th and the 17th is tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of the 9:11:13 [[triad]].		Every odd harmonic between the 7th and the 17th is tuned flatly. As a consequence, this tuning provides a good approximation of the 7:9:11:13:15:17 [[hexad]], and especially of the 9:11:13 [[triad]].

	~~[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->~~
	~~[[Category:Prime EDO]]~~

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}
	{{~~todo~~\|expand}}
			{{Todo\| expand }}

CompactStar at 03:14, 5 July 2023

2023-07-05T03:14:00Z

← Older revision		Revision as of 03:14, 5 July 2023
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	[[Category:Prime EDO]]		[[Category:Prime EDO]]

			== Intervals ==
			{{Interval table}}
	{{todo\|expand}}		{{todo\|expand}}

Aura at 18:41, 4 October 2022

2022-10-04T18:41:04Z

← Older revision		Revision as of 18:41, 4 October 2022
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			{{Infobox ET}}
	{{EDO intro\|83}}		{{EDO intro\|83}}