162edo: Difference between revisions

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~~162edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.~~

~~The~~ [[~~Patent_val|non-~~patent val]] ~~<162 257 377| and its extensions are of considerable interest~~, ~~as this tempers~~ out ~~2048/2025. In the 7-limit, <162 257 377 455~~| tempers out ~~126/125 and 2048/2025 both, giving a tuning for 7-limit~~ [[~~Diaschismic_family|diaschismic~~]]~~. In the 11-limit <162 257 377 455 561| 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|POTE tuning~~]]. The 13-limit is even closer: the 13-limit val <162 257 377 455 561 600| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave 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]].

[[~~Category:Equal divisions~~ of the ~~octave~~|~~###~~]]

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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-edo divides the octave into 162 parts of 7.407 cents each. In the 7-limit it tempers out 4000/3969, 10976/10935 and 65625/65536.
+{{Infobox ET}}
+{{ED intro}}
-The [[Patent_val|non-patent val]] &lt;162 257 377| and its extensions are of considerable interest, as this tempers out 2048/2025. In the 7-limit, &lt;162 257 377 455| tempers out 126/125 and 2048/2025 both, giving a tuning for 7-limit [[Diaschismic_family|diaschismic]]. In the 11-limit &lt;162 257 377 455 561| 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|POTE tuning]]. The 13-limit is even closer: the 13-limit val &lt;162 257 377 455 561 600| tempers out 126/125, 196/195, 364/363, 2048/2025 giving 13-limit diaschismic, and the 162 fifth of 95/162 octave 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]].
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+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 }}.