173edo - Revision history

ArrowHead294 at 16:37, 20 February 2025

2025-02-20T16:37:27Z

← Older revision		Revision as of 16:37, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|173~~}}		{{ED intro}}

	173edo is in[[consistent]] to the [[5-odd-limit]]. Two mappings are to be considered for the 5-limit: {{val\| 173 274 402 }} ([[patent val]]) and {{val\| 173 274 '''401''' }} (173c).		173edo is in[[consistent]] to the [[5-odd-limit]]. Two mappings are to be considered for the 5-limit: {{val\| 173 274 402 }} ([[patent val]]) and {{val\| 173 274 '''401''' }} (173c).

FloraC: Cleanup

2024-04-26T07:30:25Z

Cleanup

← Older revision		Revision as of 07:30, 26 April 2024
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	{{EDO intro\|173}}		{{EDO intro\|173}}

	173edo is ~~only~~ consistent in the 3-limit. ~~Nonetheless, two~~ mappings are to be considered for the 5-limit: {{val\|173 274 402}} (patent val) and {{val\|173 274 '''401'''}} (173c).		173edo is in[[consistent]] to the [[5-odd-limit]]. Two mappings are to be considered for the 5-limit: {{val\| 173 274 402 }} ([[patent val]]) and {{val\| 173 274 '''401''' }} (173c).

	Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[~~Escapade family\|~~escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit [[~~Hemimean clan\|~~semisept ~~temperament~~]]; 676/675, 847/845, 1188/1183, and 1287/1280 in the 13-limit.		Using the patent val, it [[tempering out\|tempers out]] the [[unicorn comma]], 1594323/1562500 and the [[escapade comma]], 4294967296/4271484375 in the 5-limit; [[1728/1715]], [[3136/3125]], and 413343/409600 in the 7-limit; [[176/175]], [[540/539]], 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit [[semisept]] temperament; [[676/675]], [[847/845]], [[1188/1183]], and [[1287/1280]] in the 13-limit.

	Using the ~~173c~~ val, it tempers out the [[~~Amity~~ family\|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit, supporting the 7-limit [[~~Amity family\|~~hamity ~~temperament~~]]. Using the alternative 173cd val, {{val\|173 271 '''401 485'''}} it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit [[~~Marvel temperaments\|~~septimin ~~temperament~~]]; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; 325/324, 729/728, 847/845, and 1875/1859 in the 13-limit.		Using the 173e val, {{val\| 173 271 402 486 '''599''' }}, it tempers out [[441/440]], 1944/1925, [[4000/3993]], and [[5632/5625]] in the 11-limit; [[364/363]], 676/675, [[1001/1000]], and 3159/3125 in the 13-limit. Using the 173ef val, {{val\| 173 271 402 486 '''599 641''' }}, [[144/143]], 351/350, [[640/637]], and 847/845 are tempered out in the 13-limit.

			Using the 173d val, {{val\| 173 271 402 '''485''' }}, it tempers out [[126/125]], [[10976/10935]], and 28824005/28311552 in the 7-limit; [[385/384]], 1617/1600, 12005/11979, and [[14641/14580]] in the 11-limit; [[196/195]], [[351/350]], 676/675, 1287/1280, and [[10648/10647]] in the 13-limit, supporting the [[Unicorn family #Camahueto\|camahueto]] temperament.

			Using the 173c val, it tempers out the [[amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; [[2430/2401]], [[4000/3969]], and 234375/229376 in the 7-limit, supporting the 7-limit [[hamity]] temperament. Using the alternative 173cd val, {{val\| 173 271 '''401 485''' }} it tempers out [[225/224]], 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit [[septimin]] temperament; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; [[325/324]], [[729/728]], 847/845, and 1875/1859 in the 13-limit.

	Using the 173d val, {{val\|173 271 402 '''485'''}}, it tempers out 126/125, 10976/10935, and 28824005/28311552 in the 7-limit; 385/384, 1617/1600, 12005/11979, and 14641/14580 in the 11-limit; 196/195, 351/350, 676/675, 1287/1280, and 10648/10647 in the 13-limit, supporting the [[Starling temperaments\|camahueto temperament]]. Using the 173e val, {{val\|173 271 402 486 '''599'''}} it tempers out 441/440, 1944/1925, 4000/3993, and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, and 3159/3125 in the 13-limit. Using the 173ef val, {{val\|173 271 402 486 '''599 641'''}}, 144/143, 351/350, 640/637, and 847/845 are tempered out in the 13-limit.
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|173}}		{{Harmonics in equal\|173}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	173edo is the 40th [[prime ~~EDO~~]].		173edo is the 40th [[prime edo]].

Eliora: Cleanup

2023-10-22T15:15:19Z

Cleanup

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''173edo''' is the [[EDO|equal division of the octave]] into 173 parts of 6.9364 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: &lt;173 274 402| (patent val) and &lt;173 274 401| (173c). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Escapade family|escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit [[Hemimean clan|semisept temperament]]; 676/675, 847/845, 1188/1183, and 1287/1280 in the 13-limit. Using the 173c val, it tempers out the [[Amity family|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit, supporting the 7-limit [[Amity family|hamity temperament]]. Using the alternative 173cd val, it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit [[Marvel temperaments|septimin temperament]]; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; 325/324, 729/728, 847/845, and 1875/1859 in the 13-limit. Using the 173d val, it tempers out 126/125, 10976/10935, and 28824005/28311552 in the 7-limit; 385/384, 1617/1600, 12005/11979, and 14641/14580 in the 11-limit; 196/195, 351/350, 676/675, 1287/1280, and 10648/10647 in the 13-limit, supporting the [[Starling temperaments|camahueto temperament]]. Using the 173e val, it tempers out 441/440, 1944/1925, 4000/3993, and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, and 3159/3125 in the 13-limit. Using the 173ef val, 144/143, 351/350, 640/637, and 847/845 are tempered out in the 13-limit.
+{{EDO intro|173}}
 edo is the 40th [[prime EDO]].

Plumtree: Infobox ET added

2022-10-04T21:11:50Z

Infobox ET added

← Older revision		Revision as of 21:11, 4 October 2022
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			{{Infobox ET}}
	'''173edo''' is the [[EDO\|equal division of the octave]] into 173 parts of 6.9364 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <173 274 402\| (patent val) and <173 274 401\| (173c). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Escapade family\|escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit [[Hemimean clan\|semisept temperament]]; 676/675, 847/845, 1188/1183, and 1287/1280 in the 13-limit. Using the 173c val, it tempers out the [[Amity family\|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit, supporting the 7-limit [[Amity family\|hamity temperament]]. Using the alternative 173cd val, it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit [[Marvel temperaments\|septimin temperament]]; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; 325/324, 729/728, 847/845, and 1875/1859 in the 13-limit. Using the 173d val, it tempers out 126/125, 10976/10935, and 28824005/28311552 in the 7-limit; 385/384, 1617/1600, 12005/11979, and 14641/14580 in the 11-limit; 196/195, 351/350, 676/675, 1287/1280, and 10648/10647 in the 13-limit, supporting the [[Starling temperaments\|camahueto temperament]]. Using the 173e val, it tempers out 441/440, 1944/1925, 4000/3993, and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, and 3159/3125 in the 13-limit. Using the 173ef val, 144/143, 351/350, 640/637, and 847/845 are tempered out in the 13-limit.		'''173edo''' is the [[EDO\|equal division of the octave]] into 173 parts of 6.9364 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <173 274 402\| (patent val) and <173 274 401\| (173c). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Escapade family\|escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit [[Hemimean clan\|semisept temperament]]; 676/675, 847/845, 1188/1183, and 1287/1280 in the 13-limit. Using the 173c val, it tempers out the [[Amity family\|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit, supporting the 7-limit [[Amity family\|hamity temperament]]. Using the alternative 173cd val, it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit [[Marvel temperaments\|septimin temperament]]; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; 325/324, 729/728, 847/845, and 1875/1859 in the 13-limit. Using the 173d val, it tempers out 126/125, 10976/10935, and 28824005/28311552 in the 7-limit; 385/384, 1617/1600, 12005/11979, and 14641/14580 in the 11-limit; 196/195, 351/350, 676/675, 1287/1280, and 10648/10647 in the 13-limit, supporting the [[Starling temperaments\|camahueto temperament]]. Using the 173e val, it tempers out 441/440, 1944/1925, 4000/3993, and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, and 3159/3125 in the 13-limit. Using the 173ef val, 144/143, 351/350, 640/637, and 847/845 are tempered out in the 13-limit.

Fredg999 category edits: Sort key

2022-07-02T21:19:54Z

Sort key

← Older revision		Revision as of 21:19, 2 July 2022
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	173edo is the 40th [[prime EDO]].		173edo is the 40th [[prime EDO]].

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

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:13Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
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	173edo is the 40th [[prime EDO]].		173edo is the 40th [[prime EDO]].

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]
	[[Category:Prime EDO]]		[[Category:Prime EDO]]

Xenllium at 23:50, 17 December 2018

2018-12-17T23:50:32Z

← Older revision		Revision as of 23:50, 17 December 2018
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	'''173edo''' is the [[EDO\|equal division of the octave]] into 173 parts of 6.9364 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <173 274 402\| (~~optimal~~ patent val) and <173 274 401\| (173c). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Escapade family\|escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit. Using the 173c val, it tempers out the [[Amity family\|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit~~; 385/384, 1331/1323~~, ~~and 4000/3993 in~~ the 11-limit. Using the alternative 173cd val, it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit. Using the ~~alternative~~ 173e val, 441/440, 1944/1925, 4000/3993, and 5632/5625 are tempered out in the 11-limit.		'''173edo''' is the [[EDO\|equal division of the octave]] into 173 parts of 6.9364 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <173 274 402\| (patent val) and <173 274 401\| (173c). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Escapade family\|escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit [[Hemimean clan\|semisept temperament]]; 676/675, 847/845, 1188/1183, and 1287/1280 in the 13-limit. Using the 173c val, it tempers out the [[Amity family\|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit, supporting the 7-limit [[Amity family\|hamity temperament]]. Using the alternative 173cd val, it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit [[Marvel temperaments\|septimin temperament]]; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; 325/324, 729/728, 847/845, and 1875/1859 in the 13-limit. Using the 173d val, it tempers out 126/125, 10976/10935, and 28824005/28311552 in the 7-limit; 385/384, 1617/1600, 12005/11979, and 14641/14580 in the 11-limit; 196/195, 351/350, 676/675, 1287/1280, and 10648/10647 in the 13-limit, supporting the [[Starling temperaments\|camahueto temperament]]. Using the 173e val, it tempers out 441/440, 1944/1925, 4000/3993, and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, and 3159/3125 in the 13-limit. Using the 173ef val, 144/143, 351/350, 640/637, and 847/845 are tempered out in the 13-limit.

	173edo is the 40th [[prime EDO]].		173edo is the 40th [[prime EDO]].

Xenllium at 13:50, 13 December 2018

2018-12-13T13:50:16Z

← Older revision		Revision as of 13:50, 13 December 2018
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	'''173edo''' is the [[EDO\|equal division of the octave]] into 173 parts of 6.9364 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <173 274 402\| (optimal patent val) and <173 274 401\| (173c). Using the ~~optimal~~ patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Escapade family\|escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit. Using the 173c val, it tempers out the [[Amity family\|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit. Using the alternative 173cd val, 225/224, 84035/82944, and 1250000/1240029 are tempered out in the 7-limit.		'''173edo''' is the [[EDO\|equal division of the octave]] into 173 parts of 6.9364 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <173 274 402\| (optimal patent val) and <173 274 401\| (173c). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Escapade family\|escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit. Using the 173c val, it tempers out the [[Amity family\|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit; 385/384, 1331/1323, and 4000/3993 in the 11-limit. Using the alternative 173cd val, it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit. Using the alternative 173e val, 441/440, 1944/1925, 4000/3993, and 5632/5625 are tempered out in the 11-limit.

	173edo is the 40th [[prime EDO]].		173edo is the 40th [[prime EDO]].

Xenllium: Created page with "'''173edo''' is the equal division of the octave into 173 parts of 6.9364 cents each. It is inconsistent to the 5-limit and higher limit, with two mappings possibl..."

2018-12-02T12:41:44Z

Created page with "'''173edo''' is the equal division of the octave into 173 parts of 6.9364 cents each. It is inconsistent to the 5-limit and higher limit, with two mappings possibl..."

New page

'''173edo''' is the [[EDO|equal division of the octave]] into 173 parts of 6.9364 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <173 274 402| (optimal patent val) and <173 274 401| (173c). Using the optimal patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Escapade family|escapade comma]], 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit. Using the 173c val, it tempers out the [[Amity family|amity comma]], 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit. Using the alternative 173cd val, 225/224, 84035/82944, and 1250000/1240029 are tempered out in the 7-limit.

173edo is the 40th [[prime EDO]].

[[Category:Edo]]
[[Category:Prime EDO]]