162edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro}} Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[4000/3969]], [[10976/10935]] and [[65625/65536]]. | |||
The | 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}} | {{Harmonics in equal|162}} | ||
Revision as of 11:10, 7 May 2024
| ← 161edo | 162edo | 163edo → |
Template:EDO intro Using the patent val, the equal temperament tempers out 4000/3969, 10976/10935 and 65625/65536.
The non-patent val ⟨162 257 377] (162c) 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. In the 11-limit ⟨162 257 377 455 561] (162ce) tempers out 126/125, 176/175 and 896/891, and so supports 11-limit diaschismic, and in fact has a fifth only 0.01 cents flatter than the POTE tuning. The 13-limit is even closer: ⟨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
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.75 | -1.13 | +1.54 | -3.17 | -3.49 | -1.25 | -1.22 | +1.36 | +0.05 | +3.11 |
| Relative (%) | +0.0 | +23.6 | -15.2 | +20.9 | -42.8 | -47.1 | -16.9 | -16.4 | +18.3 | +0.7 | +42.0 | |
| Steps (reduced) |
162 (0) |
257 (95) |
376 (52) |
455 (131) |
560 (74) |
599 (113) |
662 (14) |
688 (40) |
733 (85) |
787 (139) |
803 (155) | |