362edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|362}} == Theory == 362et is only consistent to the 5-odd-limit, with three mappings possible for the 7-limit: * {{val|362 574 841 1016}} (p..." |
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* {{val|362 574 '''840''' 1016}} (362c), | * {{val|362 574 '''840''' 1016}} (362c), | ||
* {{val|362 574 841 '''1017'''}} (362d). | * {{val|362 574 841 '''1017'''}} (362d). | ||
Using the patent val, it tempers out [[393216/390625]] and {{monzo|25 -48 22}} in the 5-limit; [[4375/4374]], [[458752/455625]] and 11529602/11390625 in the 7-limit, [[support]]ing [[barbados]]. | Using the patent val, it tempers out [[393216/390625]] and {{monzo|25 -48 22}} in the 5-limit; [[4375/4374]], [[458752/455625]] and 11529602/11390625 in the 7-limit, [[support]]ing [[barbados]]. | ||
Using the 362c val, it tempers out [[2109375/2097152]] and {{monzo|14 -22 9}} in the 5-limit; [[2401/2400]], [[10976/10935]] and 390625/387072 in the 7-limit. | Using the 362c val, it tempers out [[2109375/2097152]] and {{monzo|14 -22 9}} in the 5-limit; [[2401/2400]], [[10976/10935]] and 390625/387072 in the 7-limit. | ||
Using the 362d val, it tempers out 393216/390625 and {{monzo|25 -48 22}} in the 5-limit; [[5120/5103]], 118098/117649 and 1959552/1953125 in the 7-limit. | Using the 362d val, it tempers out 393216/390625 and {{monzo|25 -48 22}} in the 5-limit; [[5120/5103]], 118098/117649 and 1959552/1953125 in the 7-limit. | ||
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|387.85 | |387.85 | ||
|5/4 | |5/4 | ||
|[[Würschmidt | |[[Würschmidt]] | ||
|} | |} | ||
Revision as of 18:17, 3 February 2024
| ← 361edo | 362edo | 363edo → |
Theory
362et is only consistent to the 5-odd-limit, with three mappings possible for the 7-limit:
- ⟨362 574 841 1016] (patent val),
- ⟨362 574 840 1016] (362c),
- ⟨362 574 841 1017] (362d).
Using the patent val, it tempers out 393216/390625 and [25 -48 22⟩ in the 5-limit; 4375/4374, 458752/455625 and 11529602/11390625 in the 7-limit, supporting barbados.
Using the 362c val, it tempers out 2109375/2097152 and [14 -22 9⟩ in the 5-limit; 2401/2400, 10976/10935 and 390625/387072 in the 7-limit.
Using the 362d val, it tempers out 393216/390625 and [25 -48 22⟩ in the 5-limit; 5120/5103, 118098/117649 and 1959552/1953125 in the 7-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.81 | +1.53 | -0.87 | +1.61 | -1.04 | +1.46 | -0.98 | +1.12 | +0.83 | -0.06 | +1.56 |
| Relative (%) | +24.4 | +46.2 | -26.2 | +48.7 | -31.4 | +44.1 | -29.4 | +33.8 | +25.0 | -1.9 | +47.1 | |
| Steps (reduced) |
574 (212) |
841 (117) |
1016 (292) |
1148 (62) |
1252 (166) |
1340 (254) |
1414 (328) |
1480 (32) |
1538 (90) |
1590 (142) |
1638 (190) | |
Subsets and supersets
362 factors into 2 × 181, with 2edo and 181edo as its subset edos. 1448edo, which quadruples it, gives a good correction to the harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [287 -181⟩ | [⟨362 574]] | -0.2547 | 0.2547 | 7.68 |
| 2.3.5 | 393216/390625, [25 -48 22⟩ | [⟨362 574 841]] | -0.3896 | 0.2822 | 8.51 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 117\362 | 387.85 | 5/4 | Würschmidt |