173edo: Difference between revisions

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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 ===

=== Subsets and supersets ===

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

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

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 {{EDO intro|173}}
-edo 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).
+edo 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 ===
 {{Harmonics in equal|173}}
 === Subsets and supersets ===
-edo is the 40th [[prime EDO]].
+edo is the 40th [[prime edo]].