80edo - Revision history

FloraC: /* Regular temperament properties */ leapfrog -> leapmonth

2026-04-29T18:16:08Z

Regular temperament properties: leapfrog -> leapmonth

← Older revision		Revision as of 18:16, 29 April 2026
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	\| 495		\| 495
	\| 4/3		\| 4/3
	\| [[~~Leapfrog~~]]		\| [[Leapmonth]]
	\|-		\|-
	\| 1		\| 1

Overthink: /* Intervals */ add 26/21

2026-03-26T03:25:06Z

Intervals: add 26/21

← Older revision		Revision as of 03:25, 26 March 2026
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	\| 24		\| 24
	\| 360		\| 360
	\| [[16/13]]		\| [[16/13]], ''[[26/21]]''
	\|-		\|-
	\| 25		\| 25

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:30:00Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:30, 13 March 2026
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	\| [[Degrees]]		\| [[Degrees]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Detemperaments ==		== Detemperaments ==

Godtone at 20:42, 20 February 2026

2026-02-20T20:42:59Z

← Older revision		Revision as of 20:42, 20 February 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	80edo is the first edo that represents the [[19-odd-limit]] [[tonality diamond]] [[consistent]]ly, though it barely manages to do so. Despite this, a large number of intervals in higher odd limits are consistent, and its [[patent val]] generally does well at approximating the [[29-limit\|29-prime-limited]] [[harmonic series]] segments, such as modes 16 through 30 but especially modes 8 through 15. It achieves this much consistency with all primes in the 29-limit except 13 being sharp of just; the inconsistencies usually arise through not cancelling the over-sharpness of compound harmonics [[21/1\|21]], [[27/1\|27]], [[35/1\|35]], [[45/1\|45]], [[49/1\|49]], and their octave-equivalents, which may be seen as an interesting limitation. This means it can be used as a general-purpose approximate 29-limit system with a relatively manageable number of tones, with some care taken around inconsistency. In fact, it is almost consistent to the no-21 no-27 [[29-odd-limit]], with the exception of [[25/13]] and its octave complement, meaning it makes a surprisingly reasonable 25-odd-limit system, with only [[26/21]], [[21/17]], [[21/16]] and their [[octave complement]]s as extra inconsistencies, which a theorist might find various justifications for. Possible additions to this include [[33/1\|33]], [[37/1\|37]], [[39/1\|39]], and [[41/1\|41]]. Thus, it can also model larger primes if one is willing to accept their sharpness, and for this purpose, it does well for its size at the no-31's [[41-limit]], or even the [[43-limit]] if you are fine with [[43/32]] being slightly flat causing more inconsistencies.		80edo is the first edo that represents the [[19-odd-limit]] [[tonality diamond]] [[consistent]]ly, though it barely manages to do so. Despite this, a large number of intervals in higher odd limits are consistent, and its [[patent val]] generally does well at approximating the [[29-limit\|29-prime-limited]] [[harmonic series]] segments, such as modes 16 through 30 but especially modes 8 through 15. It achieves this much consistency with all primes in the 29-limit except 13 being sharp of just; the inconsistencies usually arise through not cancelling the over-sharpness of compound harmonics [[21/1\|21]], [[27/1\|27]], [[35/1\|35]], [[45/1\|45]], [[49/1\|49]], and their octave-equivalents, which may be seen as an interesting limitation. This means it can be used as a general-purpose approximate 29-limit system with a relatively manageable number of tones, with some care taken around inconsistency. In fact, it is almost consistent to the no-21 no-27 [[29-odd-limit]], with the exception of [[25/13]] and its octave complement, meaning it makes a surprisingly reasonable [[25-odd-limit]] system, with only [[26/21]], [[21/17]], [[21/16]] and their [[octave complement]]s as extra inconsistencies, which a theorist might find various justifications for. Possible additions to this include [[33/1\|33]], [[37/1\|37]], [[39/1\|39]], and [[41/1\|41]]. Thus, it can also model larger primes if one is willing to accept their sharpness, and for this purpose, it does well for its size at the no-31's [[41-limit]], or even the [[43-limit]] if you are fine with [[43/32]] being slightly flat causing more inconsistencies.

	If one wants higher precision as one goes to higher primes to try to convey the subtle harmonic qualities of those primes, 80et arguably fails in general, although many specific cases may be convincing. A promising alternative is using 80et as a model in which to fit higher-limit JI by way of approximating as much of the harmonic series as possible, for which it can model the 125-odd-limit quite well (corresponding to the 113-prime-limit), leading to an excellent [[Ringer scale]] described in the [[#Ringer 80\|Ringer 80 section of this article]].		If one wants higher precision as one goes to higher primes to try to convey the subtle harmonic qualities of those primes, 80et arguably fails in general, although many specific cases may be convincing. A promising alternative is using 80et as a model in which to fit higher-limit JI by way of approximating as much of the harmonic series as possible, for which it can model the 125-odd-limit quite well (corresponding to the 113-prime-limit), leading to an excellent [[Ringer scale]] described in the [[#Ringer 80\|Ringer 80 section of this article]].

Godtone: note 25-odd-limit capability

2026-02-20T20:42:14Z

note 25-odd-limit capability

← Older revision		Revision as of 20:42, 20 February 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	80edo is the first edo that represents the [[19-odd-limit]] [[tonality diamond]] [[consistent]]ly, though it barely manages to do so. Despite this, a large number of intervals in higher odd limits are consistent, and its [[patent val]] generally does well at approximating the [[29-limit\|29-prime-limited]] [[harmonic series]] segments, such as modes 16 through 30 but especially modes 8 through 15. It achieves this much consistency with all primes in the 29-limit except 13 being sharp of just; the inconsistencies usually arise through not cancelling the over-sharpness of compound harmonics [[21/1\|21]], [[27/1\|27]], [[35/1\|35]], [[45/1\|45]], [[49/1\|49]], and their octave-equivalents, which may be seen as an interesting limitation. This means it can be used as a general-purpose approximate 29-limit system with a relatively manageable number of tones, with some care taken around inconsistency. In fact, it is almost consistent to the no-21 no-27 [[29-odd-limit]], with the exception of [[25/13]] and its octave complement. Possible additions to this include [[33/1\|33]], [[37/1\|37]], [[39/1\|39]], and [[41/1\|41]]. Thus, it can also model larger primes if one is willing to accept their sharpness, and for this purpose, it does well for its size at the no-31's [[41-limit]], or even the [[43-limit]] if you are fine with [[43/32]] being slightly flat causing more inconsistencies.		80edo is the first edo that represents the [[19-odd-limit]] [[tonality diamond]] [[consistent]]ly, though it barely manages to do so. Despite this, a large number of intervals in higher odd limits are consistent, and its [[patent val]] generally does well at approximating the [[29-limit\|29-prime-limited]] [[harmonic series]] segments, such as modes 16 through 30 but especially modes 8 through 15. It achieves this much consistency with all primes in the 29-limit except 13 being sharp of just; the inconsistencies usually arise through not cancelling the over-sharpness of compound harmonics [[21/1\|21]], [[27/1\|27]], [[35/1\|35]], [[45/1\|45]], [[49/1\|49]], and their octave-equivalents, which may be seen as an interesting limitation. This means it can be used as a general-purpose approximate 29-limit system with a relatively manageable number of tones, with some care taken around inconsistency. In fact, it is almost consistent to the no-21 no-27 [[29-odd-limit]], with the exception of [[25/13]] and its octave complement, meaning it makes a surprisingly reasonable 25-odd-limit system, with only [[26/21]], [[21/17]], [[21/16]] and their [[octave complement]]s as extra inconsistencies, which a theorist might find various justifications for. Possible additions to this include [[33/1\|33]], [[37/1\|37]], [[39/1\|39]], and [[41/1\|41]]. Thus, it can also model larger primes if one is willing to accept their sharpness, and for this purpose, it does well for its size at the no-31's [[41-limit]], or even the [[43-limit]] if you are fine with [[43/32]] being slightly flat causing more inconsistencies.

	If one wants higher precision as one goes to higher primes to try to convey the subtle harmonic qualities of those primes, 80et arguably fails in general, although many specific cases may be convincing. A promising alternative is using 80et as a model in which to fit higher-limit JI by way of approximating as much of the harmonic series as possible, for which it can model the 125-odd-limit quite well (corresponding to the 113-prime-limit), leading to an excellent [[Ringer scale]] described in the [[#Ringer 80\|Ringer 80 section of this article]].		If one wants higher precision as one goes to higher primes to try to convey the subtle harmonic qualities of those primes, 80et arguably fails in general, although many specific cases may be convincing. A promising alternative is using 80et as a model in which to fit higher-limit JI by way of approximating as much of the harmonic series as possible, for which it can model the 125-odd-limit quite well (corresponding to the 113-prime-limit), leading to an excellent [[Ringer scale]] described in the [[#Ringer 80\|Ringer 80 section of this article]].

Overthink: /* Intervals */ fixed prime limit

2025-11-07T07:11:29Z

Intervals: fixed prime limit

← Older revision		Revision as of 07:11, 7 November 2025
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	\| …		\| …
	\|}		\|}
	<nowiki>*</nowiki> {{sg\|no-31's [[37-limit]]}} Inconsistent interpretations in ''italic''.		<nowiki>*</nowiki> {{sg\|80edo\|limit=no-31's [[37-limit]]}} Inconsistent interpretations in ''italic''.

	== Notation ==		== Notation ==

FloraC: Link

2025-10-27T13:32:08Z

Link

← Older revision		Revision as of 13:32, 27 October 2025
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	\| 44.9%		\| 44.9%
	\| Normal		\| Normal
	\| [[Supermajor]]		\| [[Supermajor (temperament)\|Supermajor]]
	\| [[Echidna]], [[semisupermajor]]		\| [[Echidna]], [[semisupermajor]]
	\| ?		\| ?
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	\| 435		\| 435
	\| 9/7		\| 9/7
	\| [[Supermajor]]		\| [[Supermajor (temperament)\|Supermajor]]
	\|-		\|-
	\| 1		\| 1

FloraC: /* Approximation to JI */

2025-10-21T12:33:50Z

Approximation to JI

← Older revision		Revision as of 12:33, 21 October 2025
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	\| [[Srutal archagall]]		\| [[Srutal archagall]]
	\| [[Bidia]]		\| [[Bidia]]
	\| [[~~Pentorwell~~]]		\| [[Pentaorwell]]
	\| 80 & 104		\| 80 & 104
	\| [[Linus]] retraction		\| [[Linus]] retraction

FloraC: /* Regular temperament properties */

2025-10-21T12:32:14Z

Regular temperament properties

← Older revision		Revision as of 12:32, 21 October 2025
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	\| 225<br>(15)		\| 225<br>(15)
	\| 8/7<br>(64/63)		\| 8/7<br>(64/63)
	\| [[~~Pentorwell~~]]		\| [[Pentaorwell]]
	\|-		\|-
	\| 5		\| 5

BudjarnLambeth: /* Rank-2 temperaments */

2025-10-20T11:56:27Z

Rank-2 temperaments

← Older revision		Revision as of 11:56, 20 October 2025
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	\| 105		\| 105
	\| 17/16		\| 17/16
	\| [[~~Frost~~]]		\| [[Lucite]]
	\|-		\|-
	\| 1		\| 1