162edo: Difference between revisions

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{{EDO intro}} ~~Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].~~

The non-patent val {{val| 162 257 '''377''' }} (162c) and its [[extension]]s are of considerable interest, as this tempers out [[2048/2025]]. In the 7-limit, {{val| 162 257 377 455 }} tempers out [[126/125]] and 2048/2025 both, giving a tuning for 7-limit [[diaschismic]]. In the 11-limit {{val| 162 257 377 455 561 }} (162ce) tempers out 126/125, [[176/175]] and [[896/891]], and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: {{val| 162 257 377 455 561 600 }} (162cef) tempers out 126/125, 176/175, [[196/195]], [[364/363]] giving 13-limit diaschismic, and the fifth of 95\162 is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.

Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].

The non-patent val {{val| 162 257 '''377''' }} (162c) and its [[extension]]s are of considerable interest, as this tempers out [[2048/2025]]. In the 7-limit, {{val| 162 257 '''377''' 455 }} tempers out [[126/125]] and 2048/2025 both, giving a tuning for 7-limit [[diaschismic]]. In the 11-limit {{val| 162 257 '''377''' 455 '''561''' }} (162ce) tempers out 126/125, [[176/175]] and [[896/891]], and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: {{val| 162 257 '''377''' 455 '''561''' '''600''' }} (162cef) tempers out 126/125, 176/175, [[196/195]], [[364/363]] giving 13-limit diaschismic, and the fifth of 95\162 is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 162 factors into {{factorization|162}}, 162edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 27, 54, and 81 }}.

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 {{Infobox ET}}
-{{EDO intro}} Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].
+{{EDO intro}}
-The non-patent val {{val| 162 257 '''377''' }} (162c) and its [[extension]]s are of considerable interest, as this tempers out [[2048/2025]]. In the 7-limit, {{val| 162 257 377 455 }} tempers out [[126/125]] and 2048/2025 both, giving a tuning for 7-limit [[diaschismic]]. In the 11-limit {{val| 162 257 377 455 561 }} (162ce) tempers out 126/125, [[176/175]] and [[896/891]], and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: {{val| 162 257 377 455 561 600 }} (162cef) tempers out 126/125, 176/175, [[196/195]], [[364/363]] giving 13-limit diaschismic, and the fifth of 95\162 is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.
+Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]].
+The non-patent val {{val| 162 257 '''377''' }} (162c) and its [[extension]]s are of considerable interest, as this tempers out [[2048/2025]]. In the 7-limit, {{val| 162 257 '''377''' 455 }} tempers out [[126/125]] and 2048/2025 both, giving a tuning for 7-limit [[diaschismic]]. In the 11-limit {{val| 162 257 '''377''' 455 '''561''' }} (162ce) tempers out 126/125, [[176/175]] and [[896/891]], and so [[support]]s 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the [[POTE tuning]]. The 13-limit is even closer: {{val| 162 257 '''377''' 455 '''561''' '''600''' }} (162cef) tempers out 126/125, 176/175, [[196/195]], [[364/363]] giving 13-limit diaschismic, and the fifth of 95\162 is a mere 0.0000383 cents sharp of the 13-limit POTE tuning.
 === Prime harmonics ===
 {{Harmonics in equal|162}}
+=== Subsets and supersets ===
+Since 162 factors into {{factorization|162}}, 162edo has subset edos {{EDOs| 2, 3, 6, 9, 18, 27, 54, and 81 }}.