61edo - Revision history

FloraC: /* Theory */ subsectioning

2026-05-30T09:45:53Z

Theory: subsectioning

← Older revision		Revision as of 09:45, 30 May 2026
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	== Theory ==		== Theory ==
	61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.		61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.

	There are three reasonable vals in the [[13-limit]]: the patent val ({{val\| 61 97 142 171 211 226 }}), 61d ({{val\| 61 97 142 '''172''' 211 226 }}), and 61de ({{val\| 61 97 142 '''172''' '''212''' 226 }}). In any case, it is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. The 61d val supports 11-limit [[quasisupra]], and the 61de val supports 11- and 13-limit [[modus]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|61}}		{{Harmonics in equal\|61}}

			=== As a tuning of other temperaments ===
			There are three reasonable [[val]]s in the [[13-limit]]: the [[patent val]] ({{val\| 61 97 142 171 211 226 }}), 61d ({{val\| 61 97 142 '''172''' 211 226 }}), and 61de ({{val\| 61 97 142 '''172''' '''212''' 226 }}). In any case, it is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the patent val {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. The 61d val supports 11-limit [[quasisupra]], and the 61de val supports 11- and 13-limit [[modus]].

	=== Subsets and supersets ===		=== Subsets and supersets ===

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave"

2026-03-13T13:44:49Z

Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave"

← Older revision		Revision as of 13:44, 13 March 2026
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	\|[[Freivald]] (61)		\|[[Freivald]] (61)
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave

	== Instruments ==		== Instruments ==

Overthink: /* Theory */ fixed 61de

2025-11-25T21:40:32Z

Theory: fixed 61de

← Older revision		Revision as of 21:40, 25 November 2025
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	61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.		61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.

	There are three reasonable vals in the [[13-limit]]: the patent val ({{val\| 61 97 142 171 211 226 }}), 61d ({{val\| 61 97 142 '''172''' 211 226 }}), and 61de ({{val\| 61 97 142 '''172''' '''~~211~~''' 226 }}). In any case, it is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. The 61d val supports 11-limit [[quasisupra]], and the 61de val supports 11- and 13-limit [[modus]].		There are three reasonable vals in the [[13-limit]]: the patent val ({{val\| 61 97 142 171 211 226 }}), 61d ({{val\| 61 97 142 '''172''' 211 226 }}), and 61de ({{val\| 61 97 142 '''172''' '''212''' 226 }}). In any case, it is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. The 61d val supports 11-limit [[quasisupra]], and the 61de val supports 11- and 13-limit [[modus]].

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

FloraC: /* Theory */

2025-11-25T13:23:29Z

Theory

← Older revision		Revision as of 13:23, 25 November 2025
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	61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.		61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.

	There are three reasonable vals in the [[13-limit]]: the patent val ({{val\| 61 97 142 171 211 226}}), 61d ({{val\| 61 97 142 '''172''' 211 226}}), and 61de ({{val\| 61 97 142 '''172''' '''211''' 226}}). ~~As an equal temperament~~, ~~61et~~ is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. The 61d val supports 11-limit [[quasisupra]], and the 61de val supports 11- and 13-limit [[modus]].		There are three reasonable vals in the [[13-limit]]: the patent val ({{val\| 61 97 142 171 211 226 }}), 61d ({{val\| 61 97 142 '''172''' 211 226 }}), and 61de ({{val\| 61 97 142 '''172''' '''211''' 226 }}). In any case, it is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. The 61d val supports 11-limit [[quasisupra]], and the 61de val supports 11- and 13-limit [[modus]].

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

Overthink: /* Theory */ More info on temperaments

2025-11-22T05:16:54Z

Theory: More info on temperaments

← Older revision		Revision as of 05:16, 22 November 2025
Line 5:		Line 5:
	61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.		61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.

	As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]].		There are three reasonable vals in the [[13-limit]]: the patent val ({{val\| 61 97 142 171 211 226}}), 61d ({{val\| 61 97 142 '''172''' 211 226}}), and 61de ({{val\| 61 97 142 '''172''' '''211''' 226}}). As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. The 61d val supports 11-limit [[quasisupra]], and the 61de val supports 11- and 13-limit [[modus]].

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

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''61edo prelude'' (2025)

2025-09-15T01:03:18Z

Music: Add Bryan Deister's ''61edo prelude'' (2025)

← Older revision		Revision as of 01:03, 15 September 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/1Ai__APev5M ''microtonal improvisation in 61edo''] (2025)		* [https://www.youtube.com/shorts/1Ai__APev5M ''microtonal improvisation in 61edo''] (2025)
			* [https://www.youtube.com/shorts/S9bJnllI7CI ''61edo prelude''] (2025)

FloraC: +intro to the tuning profile, as a compensation for the removal of the poem

2025-04-11T11:36:45Z

+intro to the tuning profile, as a compensation for the removal of the poem

← Older revision		Revision as of 11:36, 11 April 2025
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	== Theory ==		== Theory ==
	As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\|15 &~~amp;~~ 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\|24 &~~amp;~~ 37}}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. {{Harmonics in equal\|61}}		61edo is only [[consistent]] to the [[5-odd-limit]]. Its [[3/1\|3rd]] and [[5/1\|5th]] [[harmonic]]s are sharp of just by more than 6 cents, and the [[7/1\|7th]] and [[11/1\|11th]], though they err by less, are on the flat side. This limits its harmonic inventory. However, it does possess reasonably good approximations of [[21/16]] and [[23/16]], only a bit more than one cent off in each case.

			As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\| 15 & 46 }}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\| 24 & 37 }}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]].

			=== Odd harmonics ===
			{{Harmonics in equal\|61}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

FloraC: No need to remind readers of what a regular temperament is everywhere

2025-04-11T11:14:26Z

No need to remind readers of what a regular temperament is everywhere

← Older revision		Revision as of 11:14, 11 April 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\|15 & 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\|24 & 37}}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~		As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\|15 & 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\|24 & 37}}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. {{Harmonics in equal\|61}}

	{{Harmonics in equal\|61}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

BudjarnLambeth: /* Theory */ (''See regular temperament for more about what all this means and how to use it.'')

2025-04-11T07:36:37Z

Theory: (''See regular temperament for more about what all this means and how to use it.'')

← Older revision		Revision as of 07:36, 11 April 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\|15 & 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\|24 & 37}}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. {{Harmonics in equal\|61}}		As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\|15 & 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\|24 & 37}}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. (''See [[regular temperament]] for more about what all this means and how to use it.'')

			{{Harmonics in equal\|61}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

Hkm: /* Theory */ removed out-of-place sentence introducing poem

2025-04-03T16:41:26Z

Theory: removed out-of-place sentence introducing poem

← Older revision		Revision as of 16:41, 3 April 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\|15 & 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\|24 & 37}}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. ~~[[Peter Kosmorsky]] has an interesting poem about its tuning profile, as follows.~~		As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val\| 61 97 142 '''171''' }} [[support]]s [[valentine]] ({{nowrap\|15 & 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap\|24 & 37}}) in the 7-, 11- and 13-limit. The 61d [[val]] {{val\| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. {{Harmonics in equal\|61}}

	~~=== Odd harmonics ===~~
	{{Harmonics in equal\|61}}

	=== Subsets and supersets ===		=== Subsets and supersets ===