202edo - Revision history

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"

2026-03-13T13:30:03Z

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
Line 95:		Line 95:
	\| [[Harry]]		\| [[Harry]]
	\|}		\|}
	<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

	== Scales ==		== Scales ==

Overthink: /* Theory */ linking

2026-01-31T05:46:56Z

Theory: linking

← Older revision		Revision as of 05:46, 31 January 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]].		202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]]. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% [[relative interval error\|relative error]]. Despite this, it is most notable in the [[11-limit]], providing the [[optimal patent val]] for many temperaments tempering out [[243/242]].

	Using the patent val, 202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the [[11-limit]]. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.		Using the patent val, 202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.

	It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 21-odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.		It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 21-odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.

Overthink: /* Theory */ fix typo

2025-12-24T00:51:43Z

Theory: fix typo

← Older revision		Revision as of 00:51, 24 December 2025
Line 7:		Line 7:
	Using the patent val, 202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the [[11-limit]]. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.		Using the patent val, 202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the [[11-limit]]. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.

	It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.		It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 21-odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.

	=== Prime harmonics ===		=== Prime harmonics ===

Overthink: /* Theory */ note patent val

2025-12-24T00:49:37Z

Theory: note patent val

← Older revision		Revision as of 00:49, 24 December 2025
Line 5:		Line 5:
	202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]].		202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]].

	202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the [[11-limit]]. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.		Using the patent val, 202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the [[11-limit]]. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.

	It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.		It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.

FloraC: /* Regular temperament properties */ style

2025-11-30T11:32:38Z

Regular temperament properties: style

← Older revision		Revision as of 11:32, 30 November 2025
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	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| -13 17 -6 }}, {{monzo\| 23 6 -14 }}		\| {{Monzo\| -13 17 -6 }}, {{monzo\| 23 6 -14 }}
	\| {{~~mapping~~\| 202 320 469 }}		\| {{Mapping\| 202 320 469 }}
	\| +0.2280		\| +0.2280
	\| 0.2710		\| 0.2710
Line 36:		Line 36:
	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 19683/19600, 65625/65536		\| 2401/2400, 19683/19600, 65625/65536
	\| {{~~mapping~~\| 202 320 469 567 }}		\| {{Mapping\| 202 320 469 567 }}
	\| +0.2164		\| +0.2164
	\| 0.2356		\| 0.2356
Line 43:		Line 43:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 243/242, 441/440, 4000/3993, 65625/65536		\| 243/242, 441/440, 4000/3993, 65625/65536
	\| {{~~mapping~~\| 202 320 469 567 699 }}		\| {{Mapping\| 202 320 469 567 699 }}
	\| +0.1061		\| +0.1061
	\| 0.3049		\| 0.3049
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	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 90:		Line 90:
	\|-		\|-
	\| 2		\| 2
	\| 87\202<br />(14\202)		\| 87\202<br>(14\202)
	\| 516.83<br />(83.17)		\| 516.83<br>(83.17)
	\| 27/20<br />(21/20)		\| 27/20<br>(21/20)
	\| [[Harry]]		\| [[Harry]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

FloraC: /* Theory */ sanity check

2025-11-30T11:31:53Z

Theory: sanity check

← Older revision		Revision as of 11:31, 30 November 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]] ~~(which explains why 11/9 is inconsistently sharp)~~.		202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]].

	202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]], equating a stack of 5 [[33/32]] ~~quarter tones~~ with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, ~~wich~~ also tempers out [[540/539]], and the rank-4 rastmic temperament ~~tempering~~ out 243/242.		202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the [[11-limit]]. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.

	It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out 351/350, 364/363, 676/675, 729/728, and 2080/2079, supporting [[~~Breed~~ family#Jovial\|jovial]] and [[~~Breed~~ family#Jovis\|jovis]], as well as 13-limit [[harry]]. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19 subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.		It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 202 factors into {{~~factorization~~\|~~202~~}}, 202edo contains [[2edo]] and [[101edo]] as ~~its subsets~~.		Since 202 factors into {{nowrap\| 2 × 101 }}, 202edo contains [[2edo]] and [[101edo]] as subset edos.

	== Regular temperament properties ==		== Regular temperament properties ==

Overthink: /* Theory */ expanded last paragraph

2025-11-30T03:37:21Z

Theory: expanded last paragraph

← Older revision		Revision as of 03:37, 30 November 2025
Line 7:		Line 7:
	202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]], equating a stack of 5 [[33/32]] quarter tones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, wich also tempers out [[540/539]], and the rank-4 rastmic temperament tempering out 243/242.		202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]], equating a stack of 5 [[33/32]] quarter tones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, wich also tempers out [[540/539]], and the rank-4 rastmic temperament tempering out 243/242.

	It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out 351/350, 364/363, 676/675, 729/728, and 2080/2079, supporting [[Breed family#Jovial\|jovial]] and [[Breed family#Jovis\|jovis]], as well as 13-limit [[harry]].		It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out 351/350, 364/363, 676/675, 729/728, and 2080/2079, supporting [[Breed family#Jovial\|jovial]] and [[Breed family#Jovis\|jovis]], as well as 13-limit [[harry]]. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19 subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.

	=== Prime harmonics ===		=== Prime harmonics ===

Overthink: /* Theory */ Expanded theory

2025-11-29T22:08:42Z

Theory: Expanded theory

← Older revision		Revision as of 22:08, 29 November 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, and the rank-4 rastmic temperament tempering out 243/242.		202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]] (which explains why 11/9 is inconsistently sharp).

			202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the 7-limit, and [[243/242]], [[441/440]], [[4000/3993]] in the 11-limit. It also notably tempers out the [[quartisma]], equating a stack of 5 [[33/32]] quarter tones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, wich also tempers out [[540/539]], and the rank-4 rastmic temperament tempering out 243/242.

			It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out 351/350, 364/363, 676/675, 729/728, and 2080/2079, supporting [[Breed family#Jovial\|jovial]] and [[Breed family#Jovis\|jovis]], as well as 13-limit [[harry]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 13:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 202 factors into {{factorization\|202}}, 202edo contains [[2edo]] and [[101edo]] as its subsets.		Since 202 factors into {{factorization\|202}}, 202edo contains [[2edo]] and [[101edo]] as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==

Overthink: /* Regular temperament properties */ deleted 2.3 as 202edo is contorted in that subgroup

2025-10-05T04:58:58Z

Regular temperament properties: deleted 2.3 as 202edo is contorted in that subgroup

← Older revision		Revision as of 04:58, 5 October 2025
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	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-
	~~\| 2.3~~
	~~\| {{monzo\| -160 101 }}~~
	~~\| {{mapping\| 202 320 }}~~
	~~\| +0.3044~~
	~~\| 0.3045~~
	~~\| 5.13~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5

ArrowHead294 at 14:13, 20 February 2025

2025-02-20T14:13:42Z

← Older revision		Revision as of 14:13, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

← Older revision		Revision as of 00:49, 24 December 2025
Line 5:		Line 5:
	202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]].		202edo is [[consistent]] to the [[9-odd-limit]] with a flat tendency in harmonics 3, 5, and 7. It also has a decent harmonic [[11/1\|11]], though it is sharp unlike the previous harmonics, with [[11/9]] barely exceeding 50% relative error. Despite this, it is most notable in the 11-limit, providing the optimal patent val for many temperaments tempering out [[243/242]].

	202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the [[11-limit]]. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.		Using the patent val, 202et [[tempering out\|tempers out]] [[2401/2400]], [[19683/19600]] and [[65625/65536]] in the [[7-limit]], and [[243/242]], [[441/440]], [[4000/3993]] in the [[11-limit]]. It also notably tempers out the [[quartisma]], equating a stack of five [[33/32]] quartertones with [[7/6]]. It is the [[optimal patent val]] for the 11-limit rank-2 temperaments [[harry]] and [[tertiaseptal]], the rank-3 temperament [[jove]] tempering out 243/242 and 441/440, which also tempers out [[540/539]], and the rank-4 [[rastmic]] temperament, which tempers out 243/242.

	It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.		It extends less well to the [[13-limit]], with harmonic [[13/1\|13]] being about halfway between its steps. Nonetheless, the patent val tempers out [[351/350]], [[364/363]], [[676/675]], [[729/728]], and [[2080/2079]], supporting [[breed family #Jovial\|jovial]] and [[breed family #Jovis\|jovis]], as well as 13-limit harry. Primes [[17/1\|17]] and [[23/1\|23]] are quite sharp, but prime [[19/1\|19]] is accurate. 202edo can thus be considered a 2.3.5.7.11.13.19-subgroup temperament with a mostly flat tendency, with the exception of prime 11. The intervals [[11/9]], [[13/11]], and their octave complements are the only inconsistencies in the no-17 [[21-odd-limit]], and the no-11 no-17 odd limit is completely consistent, though one may also want to exclude prime 13 given its inaccuracy, giving us the 2.3.5.7.19 subgroup.

← Older revision		Revision as of 04:58, 5 October 2025
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	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-
	~~\| 2.3~~
	~~\| {{monzo\| -160 101 }}~~
	~~\| {{mapping\| 202 320 }}~~
	~~\| +0.3044~~
	~~\| 0.3045~~
	~~\| 5.13~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5