160edo - Revision history

Neutraldown at 02:14, 28 November 2025

2025-11-28T02:14:26Z

← Older revision		Revision as of 02:14, 28 November 2025
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	Using the 160bce val {{val\| 160 '''253''' '''371''' 449 '''553''' 592 }}, it tempers out [[78732/78125]] and 145282683375/137438953472 in the 5-limit; [[1029/1024]], [[2430/2401]], and 390625/387072 in the 7-limit; [[385/384]], 441/440, 2187/2156, and 9375/9317 in the 11-limit; [[351/350]], [[847/845]], 1287/1280, 1573/1568, and 1875/1859 in the 13-limit.		Using the 160bce val {{val\| 160 '''253''' '''371''' 449 '''553''' 592 }}, it tempers out [[78732/78125]] and 145282683375/137438953472 in the 5-limit; [[1029/1024]], [[2430/2401]], and 390625/387072 in the 7-limit; [[385/384]], 441/440, 2187/2156, and 9375/9317 in the 11-limit; [[351/350]], [[847/845]], 1287/1280, 1573/1568, and 1875/1859 in the 13-limit.

	Using the 160ce val {{val\| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.		Using the 160ce val {{val\| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, [[4125/4096]], and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.

	As every other step of [[320edo]], a comprehensive full 19-limit system, 160edo might make more sense as a 2.9.7.13.17 subgroup temperament, where it tempers out [[729/728]], [[833/832]] and [[5832/5831]].		As every other step of [[320edo]], a comprehensive full 19-limit system, 160edo might make more sense as a 2.9.7.13.17 subgroup temperament, where it tempers out [[729/728]], [[833/832]] and [[5832/5831]].

Francium: changed EDO intro to ED intro

2025-02-19T18:02:11Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:02, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|160~~}}		{{ED intro}}

	160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, [[tempering out]] [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).		160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, [[tempering out]] [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).

Fredg999: Internal links

2024-07-06T16:58:00Z

Internal links

← Older revision		Revision as of 16:58, 6 July 2024
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	160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, [[tempering out]] [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).		160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, [[tempering out]] [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).

	Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.		Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; [[196/195]], [[325/324]], [[352/351]], [[832/825]], and 3146/3125 in the 13-limit.

	Using the 160bce val {{val\| 160 '''253''' '''371''' 449 '''553''' 592 }}, it tempers out [[78732/78125]] and 145282683375/137438953472 in the 5-limit; [[1029/1024]], [[2430/2401]], and 390625/387072 in the 7-limit; [[385/384]], 441/440, 2187/2156, and 9375/9317 in the 11-limit; [[351/350]], [[847/845]], 1287/1280, 1573/1568, and 1875/1859 in the 13-limit.		Using the 160bce val {{val\| 160 '''253''' '''371''' 449 '''553''' 592 }}, it tempers out [[78732/78125]] and 145282683375/137438953472 in the 5-limit; [[1029/1024]], [[2430/2401]], and 390625/387072 in the 7-limit; [[385/384]], 441/440, 2187/2156, and 9375/9317 in the 11-limit; [[351/350]], [[847/845]], 1287/1280, 1573/1568, and 1875/1859 in the 13-limit.

FloraC: Section titles

2024-05-07T11:19:33Z

Section titles

← Older revision		Revision as of 11:19, 7 May 2024
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	{{EDO intro\|160}}		{{EDO intro\|160}}

	160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, tempering out [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).		160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, [[tempering out]] [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).

	Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.		Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.
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	As every other step of [[320edo]], a comprehensive full 19-limit system, 160edo might make more sense as a 2.9.7.13.17 subgroup temperament, where it tempers out [[729/728]], [[833/832]] and [[5832/5831]].		As every other step of [[320edo]], a comprehensive full 19-limit system, 160edo might make more sense as a 2.9.7.13.17 subgroup temperament, where it tempers out [[729/728]], [[833/832]] and [[5832/5831]].

	=== ~~Prime~~ harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|160\|columns=12}}		{{Harmonics in equal\|160\|columns=12}}

	=== ~~Divisors~~ ===		=== Subsets and supersets ===
	Since 160 factors into 2<sup>5</sup> × 5, 160edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, and 80 }}.		Since 160 factors into 2<sup>5</sup> × 5, 160edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, and 80 }}.

FloraC: +as a subset of 320edo

2023-01-06T07:55:17Z

+as a subset of 320edo

← Older revision		Revision as of 07:55, 6 January 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''160edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 160 ~~parts of exact 7.5 cents each.~~		{{EDO intro\|160}}

	It is closely related to [[80edo]], but the patent ~~vals~~ differ on the mapping for 7. It is [[contorted]] in the 5-limit, tempering out [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).		160edo is closely related to [[80edo]], but the [[patent val]]s differ on the mapping for 7. It is [[contorted]] in the 5-limit, tempering out [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).

	Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.		Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.
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	Using the 160ce val {{val\| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.		Using the 160ce val {{val\| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.

			As every other step of [[320edo]], a comprehensive full 19-limit system, 160edo might make more sense as a 2.9.7.13.17 subgroup temperament, where it tempers out [[729/728]], [[833/832]] and [[5832/5831]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|160\|columns=12}}		{{Harmonics in equal\|160\|columns=12}}

	~~[[Category:Equal divisions of the octave\|###]]~~ <~~!-- 3-digit number --~~>		=== Divisors ===
			Since 160 factors into 2<sup>5</sup> × 5, 160edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, and 80 }}.

Aura at 03:57, 6 January 2023

2023-01-06T03:57:11Z

← Older revision		Revision as of 03:57, 6 January 2023
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	Using the 160ce val {{val\| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.		Using the 160ce val {{val\| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.

			=== Prime harmonics ===
			{{Harmonics in equal\|160\|columns=12}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Aura at 19:09, 4 October 2022

2022-10-04T19:09:34Z

← Older revision		Revision as of 19:09, 4 October 2022
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			{{Infobox ET}}
	'''160edo''' is the [[EDO\|equal division of the octave]] into 160 parts of exact 7.5 cents each.		'''160edo''' is the [[EDO\|equal division of the octave]] into 160 parts of exact 7.5 cents each.

Fredg999 category edits: Sort key

2022-07-02T21:10:40Z

Sort key

← Older revision		Revision as of 21:10, 2 July 2022
Line 9:		Line 9:
	Using the 160ce val {{val\| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.		Using the 160ce val {{val\| 160 254 '''371''' 449 '''553''' 592 }}, it tempers out [[1638400/1594323]] and 2197265625/2147483648 in the 5-limit; [[875/864]], [[2401/2400]], and 2097152/2066715 in the 7-limit; [[896/891]], 3388/3375, 4125/4096, and 12005/11979 in the 11-limit; 275/273, 572/567, 847/845, 1573/1568, and 3185/3168 in the 13-limit.

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Cmloegcmluin: remove temporary link to defactoring

2021-11-12T23:07:25Z

remove temporary link to defactoring

← Older revision		Revision as of 23:07, 12 November 2021
Line 1:		Line 1:
	'''160edo''' is the [[EDO\|equal division of the octave]] into 160 parts of exact 7.5 cents each.		'''160edo''' is the [[EDO\|equal division of the octave]] into 160 parts of exact 7.5 cents each.

	It is closely related to [[80edo]], but the patent vals differ on the mapping for 7. It is [[contorted]] ~~(or [[enfactored]])~~ in the 5-limit, tempering out [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).		It is closely related to [[80edo]], but the patent vals differ on the mapping for 7. It is [[contorted]] in the 5-limit, tempering out [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).

	Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.		Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.

Cmloegcmluin: add link for defactoring

2021-09-29T19:47:59Z

add link for defactoring

← Older revision		Revision as of 19:47, 29 September 2021
Line 1:		Line 1:
	'''160edo''' is the [[EDO\|equal division of the octave]] into 160 parts of exact 7.5 cents each.		'''160edo''' is the [[EDO\|equal division of the octave]] into 160 parts of exact 7.5 cents each.

	It is closely related to [[80edo]], but the patent vals differ on the mapping for 7. It is contorted in the 5-limit, tempering out [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).		It is closely related to [[80edo]], but the patent vals differ on the mapping for 7. It is [[contorted]] (or [[enfactored]]) in the 5-limit, tempering out [[2048/2025]] (diaschisma) and 390625000/387420489 (quartonic comma).

	Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.		Using the [[patent val]] {{val\| 160 254 372 449 554 592 }}, it tempers out [[245/243]], [[6144/6125]], and 3176523/3125000 in the 7-limit; [[441/440]], [[2200/2187]], [[4000/3993]], and 6912/6875 in the 11-limit; 196/195, 325/324, 352/351, 832/825, and 3146/3125 in the 13-limit.