97edo - Revision history

FloraC: 41 & 56 has a name now

2026-01-22T11:37:25Z

41 & 56 has a name now

← Older revision		Revision as of 11:37, 22 January 2026
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	== Theory ==		== Theory ==
	97edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out\|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[385/384]] and [[441/440]] in the 11-limit, and [[196/195]], [[352/351]] and [[676/675]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit {{nowrap\|41 &~~amp; 97~~}} temperament ~~tempering~~ out 100/99, 196/195, 245/242 and 385/384.		97edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out\|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[385/384]] and [[441/440]] in the 11-limit, and [[196/195]], [[352/351]] and [[676/675]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit [[superana]] ({{nowrap\| 41 & 56 }}) temperament, which tempers out 100/99, 196/195, 245/242 and 385/384.

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

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Washing Machine Heart - Mitski (microtonal cover in 97edo)'' (2025)

2025-11-11T20:12:35Z

Music: Add Bryan Deister's ''Washing Machine Heart - Mitski (microtonal cover in 97edo)'' (2025)

← Older revision		Revision as of 20:12, 11 November 2025
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	* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025)		* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025)
	* [https://www.youtube.com/shorts/6iXy1D9RZ-U ''Charlie's Inferno - That Handsome Devil (microtonal cover in 97edo)''] (2025)		* [https://www.youtube.com/shorts/6iXy1D9RZ-U ''Charlie's Inferno - That Handsome Devil (microtonal cover in 97edo)''] (2025)
			* [https://www.youtube.com/shorts/U1X3oo9CGHg ''Washing Machine Heart - Mitski (microtonal cover in 97edo)''] (2025)

	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]

Lucius Chiaraviglio: Move Instruments section above Music to match most other EDO pages

2025-11-10T18:55:44Z

Move Instruments section above Music to match most other EDO pages

← Older revision		Revision as of 18:55, 10 November 2025
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== Instruments ==
			A [[Lumatone mapping for 97edo]] has now been demonstrated (see the Unnamed high-limit temperament mapping for full gamut coverage).

	== Music ==		== Music ==
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	; [[Mercury Amalgam]]		; [[Mercury Amalgam]]
	* [https://www.youtube.com/watch?v=3JwH0gZmXHk ''Thanatonautical Tetrapharmacon''] (2023)		* [https://www.youtube.com/watch?v=3JwH0gZmXHk ''Thanatonautical Tetrapharmacon''] (2023)

	~~== Instruments ==~~
	~~A [[Lumatone mapping for 97edo]] has now been demonstrated (see the Unnamed high-limit temperament mapping for full gamut coverage).~~

	[[Category:Listen]]		[[Category:Listen]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Charlie's Inferno - That Handsome Devil (microtonal cover in 97edo)'' (2025)

2025-11-10T18:45:56Z

Music: Add Bryan Deister's ''Charlie's Inferno - That Handsome Devil (microtonal cover in 97edo)'' (2025)

← Older revision		Revision as of 18:45, 10 November 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025)		* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025)
			* [https://www.youtube.com/shorts/6iXy1D9RZ-U ''Charlie's Inferno - That Handsome Devil (microtonal cover in 97edo)''] (2025)

	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]

Fredg999: Remove link to deleted page

2025-08-06T02:05:05Z

Remove link to deleted page

← Older revision		Revision as of 02:05, 6 August 2025
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	== Approximation to JI ==		== Approximation to JI ==
	97edo has very poor direct approximation for [[superparticular]] intervals among edos up to 200, and the worst for intervals up to 9/8 among edos up to 100. It has errors of well above one standard deviation (about 15.87%) in superparticular intervals with denominators up to 14. The first good approximation is the 16/15 semitone using the 9th note, with an error of 3%~~, meaning 97edo can be used as a rough version of [[16/15 equal-step tuning]]~~.		97edo has very poor direct approximation for [[superparticular]] intervals among edos up to 200, and the worst for intervals up to 9/8 among edos up to 100. It has errors of well above one standard deviation (about 15.87%) in superparticular intervals with denominators up to 14. The first good approximation is the 16/15 semitone using the 9th note, with an error of 3%.

	Since 97edo is a prime edo, it lacks specific modulation circles, symmetrical chords or sub-edos that are present in composite edos. When notable equal divisions like {{EDOs\|19, 31, 41, or 53}} have strong JI-based harmony, 97edo does not have easily representable modulation because of its inability to represent superparticulars. However, this might result in interest in this tuning through JI-agnostic approaches.		Since 97edo is a prime edo, it lacks specific modulation circles, symmetrical chords or sub-edos that are present in composite edos. When notable equal divisions like {{EDOs\|19, 31, 41, or 53}} have strong JI-based harmony, 97edo does not have easily representable modulation because of its inability to represent superparticulars. However, this might result in interest in this tuning through JI-agnostic approaches.

Lucius Chiaraviglio: Lumatone mapping for 97edo now available; harmonics table extended to include up to 29 to match the unnamed high-limit temperament corresponding to this mapping

2025-04-18T06:00:03Z

Lumatone mapping for 97edo now available; harmonics table extended to include up to 29 to match the unnamed high-limit temperament corresponding to this mapping

← Older revision		Revision as of 06:00, 18 April 2025
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|97}}		{{Harmonics in equal\|97\|columns=14}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
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	; [[Mercury Amalgam]]		; [[Mercury Amalgam]]
	* [https://www.youtube.com/watch?v=3JwH0gZmXHk ''Thanatonautical Tetrapharmacon''] (2023)		* [https://www.youtube.com/watch?v=3JwH0gZmXHk ''Thanatonautical Tetrapharmacon''] (2023)

			== Instruments ==
			A [[Lumatone mapping for 97edo]] has now been demonstrated (see the Unnamed high-limit temperament mapping for full gamut coverage).

	[[Category:Listen]]		[[Category:Listen]]

Francium: /* Music */ typo

2025-04-16T13:09:10Z

Music: typo

← Older revision		Revision as of 13:09, 16 April 2025
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	== Music ==		== Music ==
	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo'']] (2025)		* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025)

	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]

Lucius Chiaraviglio: /* Music */ Add microtonal improvisation in 97edo by Bryan Deister (retry — first attempt didn't take)

2025-04-08T09:34:16Z

Music: Add microtonal improvisation in 97edo by Bryan Deister (retry — first attempt didn't take)

← Older revision		Revision as of 09:34, 8 April 2025
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	== Music ==		== Music ==
			; [[Bryan Deister]]
			* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo'']] (2025)

	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* [https://www.youtube.com/watch?v=h7bT1oL8T0w ''Joyous Stellaris''] (2023) – [[semiquartal]] in 97edo tuning		* [https://www.youtube.com/watch?v=h7bT1oL8T0w ''Joyous Stellaris''] (2023) – [[semiquartal]] in 97edo tuning

ArrowHead294 at 16:22, 20 February 2025

2025-02-20T16:22:22Z

← Older revision		Revision as of 16:22, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|97~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	97edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out\|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[385/384]] and [[441/440]] in the 11-limit, and [[196/195]], [[352/351]] and [[676/675]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit 41 & 97 temperament tempering out 100/99, 196/195, 245/242 and 385/384.		97edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out\|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[385/384]] and [[441/440]] in the 11-limit, and [[196/195]], [[352/351]] and [[676/675]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit {{nowrap\|41 & 97}} temperament tempering out 100/99, 196/195, 245/242 and 385/384.

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

FloraC: /* Theory */ +one-liner overview

2024-06-11T12:04:43Z

Theory: +one-liner overview

← Older revision		Revision as of 12:04, 11 June 2024
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	== Theory ==		== Theory ==
	The [[patent val]] of 97edo [[tempering out\|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[385/384]] and [[441/440]] in the 11-limit, and [[196/195]], [[352/351]] and [[676/675]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit 41 & 97 temperament tempering out 100/99, 196/195, 245/242 and 385/384.		97edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out\|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[385/384]] and [[441/440]] in the 11-limit, and [[196/195]], [[352/351]] and [[676/675]] in the 13-limit. It provides the [[optimal patent val]] for the 13-limit 41 & 97 temperament tempering out 100/99, 196/195, 245/242 and 385/384.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	97edo is the 25th [[prime edo]].		97edo is the 25th [[prime edo]], following [[89edo]] and before [[101edo]].

	[[388edo]] and [[2619edo]], which contain 97edo as a subset, have very high consistency limits – 37 and 33 respectively. [[3395edo]], which divides the edostep in 35, is a [[The Riemann zeta function and tuning\|zeta edo]]. The [[berkelium]] temperament realizes some relationships between them through a regular temperament perspective.		[[388edo]] and [[2619edo]], which contain 97edo as a subset, have very high consistency limits – 37 and 33 respectively. [[3395edo]], which divides the edostep in 35, is a [[The Riemann zeta function and tuning\|zeta edo]]. The [[berkelium]] temperament realizes some relationships between them through a regular temperament perspective.