952edo: Difference between revisions
m Infobox ET added |
for now mos sequence, to say temperament i need to pick out a subgroup first and give it a name, also cleanup. |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|952}} | |||
== Theory == | == Theory == | ||
In the 2.3.13.17.19 subgroup, 952edo tempers out 793152/793117. | In the 2.3.13.17.19 subgroup, 952edo tempers out 793152/793117. | ||
In the 19-limit as a whole, 952edo tempers out 1445/1444, 1540/1539. | In the 19-limit as a whole, 952edo tempers out 1445/1444, 1540/1539. | ||
952edo is notable for having a [[concoctic]] scale which represents a natural phenomenon - 169\952 is useful both as a cycle length for a leap week calendar and its generator. The resulting calendar has a year length of 365 days 5h 49m 24.7s. 169/952 of a week, 1d 5h 49m 24.7s is roughly the fraction by which Earth's year length exceeds 52 weeks. The leap day cycle of 33\136 shares the exact same property of concoction, thus 952edo can be viewed as a compound of 7 such MOSes. | 952edo is notable for having a [[concoctic]] scale which represents a natural phenomenon - 169\952 is useful both as a cycle length for a leap week calendar and its generator, thus being associated with a 169 & 952 mos sequence. The resulting calendar has a year length of 365 days 5h 49m 24.7s. 169/952 of a week, 1d 5h 49m 24.7s is roughly the fraction by which Earth's year length exceeds 52 weeks. The leap day cycle of 33\136 shares the exact same property of concoction, thus 952edo can be viewed as a compound of 7 such MOSes. | ||
In light of having 28 as a divisor, 952edo provides the optimal patent val for the [[oquatonic]] temperament. | |||
===Harmonics in equal=== | |||
{{{harmonics in equal|952}} | |||
===Divisors=== | |||
952edo's factorization is 2<sup>3</sup> x 7 x 17, and it has subset EDOs {{EDOs|1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476}}. | |||
== Scales == | == Scales == | ||
Revision as of 21:20, 4 February 2023
| ← 951edo | 952edo | 953edo → |
Theory
In the 2.3.13.17.19 subgroup, 952edo tempers out 793152/793117.
In the 19-limit as a whole, 952edo tempers out 1445/1444, 1540/1539.
952edo is notable for having a concoctic scale which represents a natural phenomenon - 169\952 is useful both as a cycle length for a leap week calendar and its generator, thus being associated with a 169 & 952 mos sequence. The resulting calendar has a year length of 365 days 5h 49m 24.7s. 169/952 of a week, 1d 5h 49m 24.7s is roughly the fraction by which Earth's year length exceeds 52 weeks. The leap day cycle of 33\136 shares the exact same property of concoction, thus 952edo can be viewed as a compound of 7 such MOSes.
In light of having 28 as a divisor, 952edo provides the optimal patent val for the oquatonic temperament.
Harmonics in equal
{
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.146 | -0.599 | +0.502 | +0.292 | -0.478 | +0.229 | -0.454 | -0.334 | -0.034 | -0.613 | -0.543 |
| Relative (%) | +11.6 | -47.6 | +39.8 | +23.1 | -37.9 | +18.1 | -36.0 | -26.5 | -2.7 | -48.6 | -43.1 | |
| Steps (reduced) |
1509 (557) |
2210 (306) |
2673 (769) |
3018 (162) |
3293 (437) |
3523 (667) |
3719 (863) |
3891 (83) |
4044 (236) |
4181 (373) |
4306 (498) | |
Divisors
952edo's factorization is 23 x 7 x 17, and it has subset EDOs 1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476.
Scales
- SouthSolstitial[169]