93edo - Revision history

FloraC: /* Music */ cleanup

2026-03-24T12:09:30Z

Music: cleanup

← Older revision		Revision as of 12:09, 24 March 2026
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	== Music ==		== Music ==
			; [[ALLY195]]
			* [https://www.bilibili.com/video/BV1EF411v7Y9/ ''A Simple Show of Different Harmonic Waves''] (2022)
			* [https://www.bilibili.com/video/BV1t3411E7GZ/ ''愛する心 adaptation''] (2022)
			* [https://www.bilibili.com/video/BV1X44y1j7Dt/ ''Small Stars without Original Notes''] (2022)
			* [https://www.bilibili.com/video/BV1M3411p7Ps/ ''Root Note and Subharmonic Series Descent''] (2022)

	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/eknKeDeRlQs ''microtonal improvisation in 93edo''] (2025)		* [https://www.youtube.com/shorts/eknKeDeRlQs ''microtonal improvisation in 93edo''] (2025)

			; [[Pixel artisan-Yanyi]] (像素工匠-岩毅)
	~~ALLY195~~		* [https://www.bilibili.com/video/BV1H84y177fQ/ ''2345312 in 93 Keys''] (2023)

	* [~~https://www.bilibili.com/video/BV1EF411v7Y9/?spm_id_from=333.337.search-card.all.click&vd_source=3e5765d9963bdf3370712d765d3ff3e1 A simple show of different harmonic waves] (2022)~~
	* [~~https://www.bilibili.com/video/BV1t3411E7GZ/?spm_id_from=333.337.search~~-~~card.all.click&vd_source=3e5765d9963bdf3370712d765d3ff3e1 愛する心 adaptation~~] ~~(2022)~~
	* [https://www.bilibili.com/video/BV1X44y1j7Dt/?spm_id_from=333.337.search-card.all.click&vd_source=3e5765d9963bdf3370712d765d3ff3e1 Small stars without original notes] (~~2022)~~
	* [https://www.bilibili.com/video/BV1M3411p7Ps/?spm_id_from=333.337.search-~~card.all.click&vd_source=3e5765d9963bdf3370712d765d3ff3e1 Root note and subharmonic series descent] (2022~~)


	~~Pixel artisan-Yanyi~~

	* [https://www.bilibili.com/video/BV1H84y177fQ/~~?spm_id_from=333.337.search-card.all.click&vd_source=3e5765d9963bdf3370712d765d3ff3e1~~ 2345312 in 93 ~~keys~~] (2023)

	== See also ==		== See also ==
	* [[93edo and stretched hemififths]]		* [[93edo and stretched hemififths]]

Haidilao: Added pieces on Bilibili

2026-03-24T07:16:53Z

Added pieces on Bilibili

@@ Line 29: / Line 29: @@
 ; [[Bryan Deister]]
 * [https://www.youtube.com/shorts/eknKeDeRlQs ''microtonal improvisation in 93edo''] (2025)
 == See also ==
 * [[93edo and stretched hemififths]]

Contribution at 14:56, 2 July 2025

2025-07-02T14:56:13Z

← Older revision		Revision as of 14:56, 2 July 2025
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|93}}		{{Harmonics in equal\|93}}

			=== No-3 approach ===
			If prime 3 is ignored, 93edo represents the no-3 35-odd-limit consistently. 93edo is distinctly consistent within the no-3 19-integer-limit.

	== Intervals ==		== Intervals ==

Lucius Chiaraviglio: /* Scales */ Insert Instruments section after this, now that a Lumatone mapping for 93edo is available.

2025-06-01T06:33:21Z

Scales: Insert Instruments section after this, now that a Lumatone mapping for 93edo is available.

← Older revision		Revision as of 06:33, 1 June 2025
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	* Superpyth Shailaja: 21 34 4 17 17 ((21 55 59 76 93)\93)		* Superpyth Shailaja: 21 34 4 17 17 ((21 55 59 76 93)\93)
	* Superpyth Subminor Hexatonic: 17 4 17 17 21 17 ((17 21 38 55 76 93)\93)		* Superpyth Subminor Hexatonic: 17 4 17 17 21 17 ((17 21 38 55 76 93)\93)

			== Instruments ==

			A [[Lumatone mapping for 93edo]] is available.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Scales */ Add Music section after this, starting with Bryan Deister's ''microtonal improvisation in 93edo'' (2025)

2025-05-31T20:40:25Z

Scales: Add Music section after this, starting with Bryan Deister's ''microtonal improvisation in 93edo'' (2025)

← Older revision		Revision as of 20:40, 31 May 2025
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	* Superpyth Shailaja: 21 34 4 17 17 ((21 55 59 76 93)\93)		* Superpyth Shailaja: 21 34 4 17 17 ((21 55 59 76 93)\93)
	* Superpyth Subminor Hexatonic: 17 4 17 17 21 17 ((17 21 38 55 76 93)\93)		* Superpyth Subminor Hexatonic: 17 4 17 17 21 17 ((17 21 38 55 76 93)\93)

			== Music ==
			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/eknKeDeRlQs ''microtonal improvisation in 93edo''] (2025)

	== See also ==		== See also ==
	* [[93edo and stretched hemififths]]		* [[93edo and stretched hemififths]]

ArrowHead294 at 14:50, 16 May 2025

2025-05-16T14:50:19Z

← Older revision		Revision as of 14:50, 16 May 2025
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	== Theory ==		== Theory ==
	Since {{nowrap\|93 {{=}} 3 × 31}}, 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out\|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[31st-octave_temperaments#Prajapati\|prajapati]] and 13-limit [[31st-octave_temperaments#Kumhar\|kumhar]] temperaments, and the 11- and 13-limit [[~~Meantone_family~~#Trimean\|trimean]] ({{nowrap\|43 & 50}}) temperament~~. It~~ is the 13th no-3s [[zeta peak edo]]. The 93bd val is close to the 9-odd limit minimax tuning for [[superpyth]] and approximates {{frac\|2\|7}}-[[64/63\|septimal~~ ~~comma]] superpyth very well.		Since {{nowrap\|93 {{=}} 3 × 31}}, 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out\|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]], and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[31st-octave_temperaments#Prajapati\|prajapati]] and 13-limit [[31st-octave_temperaments#Kumhar\|kumhar]] temperaments and the 11- and 13-limit [[Meantone family#Trimean\|trimean]] ({{nowrap\|43 & 50}}) temperament, and is the 13th no-3s [[zeta peak edo]]. The 93bd val is close to the 9-odd limit minimax tuning for [[superpyth]] and approximates {{nowrap\|{{frac\|2\|7}}-[[64/63\|septimal comma]]}} superpyth very well.

	Since 93edo has good approximations of [[13/1\|13th]], [[17/1\|17th]] and [[19/1\|19th]] [[harmonic]]s unlike 31edo (as 838.710{{c}}, 103.226{{c}}, and 296.774{{c}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.		Since 93edo has good approximations of [[13/1\|13th]], [[17/1\|17th]] and [[19/1\|19th]] [[harmonic]]s unlike 31edo (as 838.710{{c}}, 103.226{{c}}, and 296.774{{c}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.

ArrowHead294 at 16:24, 20 February 2025

2025-02-20T16:24:59Z

← Older revision		Revision as of 16:24, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|93~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	93 = 3 × 31, ~~and~~ 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out\|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[31st-octave_temperaments#Prajapati\|prajapati]] and 13-limit [[31st-octave_temperaments#Kumhar\|kumhar]] temperaments, and the 11- and 13-limit [[Meantone_family#Trimean\|trimean]] (43 & 50) temperament. It is the 13th no-3s [[zeta peak edo]]. The bd val is close to the 9-odd limit minimax tuning for [[superpyth]].		Since {{nowrap\|93 {{=}} 3 × 31}}, 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out\|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[31st-octave_temperaments#Prajapati\|prajapati]] and 13-limit [[31st-octave_temperaments#Kumhar\|kumhar]] temperaments, and the 11- and 13-limit [[Meantone_family#Trimean\|trimean]] ({{nowrap\|43 & 50}}) temperament. It is the 13th no-3s [[zeta peak edo]]. The 93bd val is close to the 9-odd limit minimax tuning for [[superpyth]] and approximates {{frac\|2\|7}}-[[64/63\|septimal comma]] superpyth very well.

	Since 93edo has good approximations of [[13/1\|13th]], [[17/1\|17th]] and [[19/1\|19th]] [[harmonic]]s unlike 31edo (as 838.710{{~~cent~~}}, 103.226{{~~cent~~}}, and 296.774{{~~cent~~}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.		Since 93edo has good approximations of [[13/1\|13th]], [[17/1\|17th]] and [[19/1\|19th]] [[harmonic]]s unlike 31edo (as 838.710{{c}}, 103.226{{c}}, and 296.774{{c}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.

	=== Odd harmonics ===		=== Odd harmonics ===

Yourmusic Productions: Grammar.

2024-12-07T17:45:13Z

Grammar.

← Older revision		Revision as of 17:45, 7 December 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	93 = 3 × 31, and 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out\|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[31st-octave_temperaments#Prajapati\|prajapati]] and 13-limit [[31st-octave_temperaments#Kumhar\|kumhar]] temperaments, and the 11- and 13-limit [[Meantone_family#Trimean\|trimean]] (43 & 50) temperament. It is the 13th no-3s [[zeta peak edo]]. The bd val is close to the 9-limit minimax tuning for [[superpyth]].		93 = 3 × 31, and 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out\|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[31st-octave_temperaments#Prajapati\|prajapati]] and 13-limit [[31st-octave_temperaments#Kumhar\|kumhar]] temperaments, and the 11- and 13-limit [[Meantone_family#Trimean\|trimean]] (43 & 50) temperament. It is the 13th no-3s [[zeta peak edo]]. The bd val is close to the 9-odd limit minimax tuning for [[superpyth]].

	Since 93edo has good approximations of [[13/1\|13th]], [[17/1\|17th]] and [[19/1\|19th]] [[harmonic]]s unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.		Since 93edo has good approximations of [[13/1\|13th]], [[17/1\|17th]] and [[19/1\|19th]] [[harmonic]]s unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.

Yourmusic Productions: Fix wrong temperament reference, link blank ones.

2024-12-07T17:43:58Z

Fix wrong temperament reference, link blank ones.

← Older revision		Revision as of 17:43, 7 December 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	93 = 3 × 31, and 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out\|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[prajapati]] and 13-limit [[kumhar]] temperaments, and the 11- and 13-limit [[~~superpine~~]] (43 & 50) temperament. It is the 13th no-3s [[zeta peak edo]].		93 = 3 × 31, and 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out\|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[31st-octave_temperaments#Prajapati\|prajapati]] and 13-limit [[31st-octave_temperaments#Kumhar\|kumhar]] temperaments, and the 11- and 13-limit [[Meantone_family#Trimean\|trimean]] (43 & 50) temperament. It is the 13th no-3s [[zeta peak edo]]. The bd val is close to the 9-limit minimax tuning for [[superpyth]].

	Since 93edo has good approximations of [[13/1\|13th]], [[17/1\|17th]] and [[19/1\|19th]] [[harmonic]]s unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.		Since 93edo has good approximations of [[13/1\|13th]], [[17/1\|17th]] and [[19/1\|19th]] [[harmonic]]s unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.

FloraC: Cleanup (2/2)

2024-06-17T05:23:10Z

Cleanup (2/2)

@@ Line 14: / Line 14: @@
 == Scales ==
-Meantone Chromatic
+* Superpyth[5]: 21 17 17 21 17 ((21 38 55 76 93)\93)
+* Superpyth[12]: 4 13 4 13 4 13 4 4 13 4 13 4 ((4 17 21 34 38 51 55 59 72 76 89 93)\93)
-* 116.129
+* Superpyth Shailaja: 21 34 4 17 17 ((21 55 59 76 93)\93)
-* 193.548
+* Superpyth Subminor Hexatonic: 17 4 17 17 21 17 ((17 21 38 55 76 93)\93)
 == See also ==
 * [[93edo and stretched hemififths]]