952edo: Difference between revisions

Line 1:

== Theory ==

In the 2.3.~~13.17.19 subgroup~~, ~~952edo tempers out 793152/793117~~.

952edo is in[[consistent]] in the [[5-odd-limit]] despite having a decent approximation to [[3/1|harmonic 3]]. To start with, as an 11-limit temperament we may consider the 952ce [[val]] {{val| 952 1509 '''2211''' '''2673''' '''3294''' }} and the 952d val {{val| 952 1509 '''2210''' '''2672''' '''3293''' }}.

In the 19-limit ~~as a whole, 952edo tempers out 1445/1444, 1540/1539~~.

Despite having bad approximations, in light of having 28 as a divisor 952edo provides the optimal patent val for the [[oquatonic]] temperament in the 7-limit.

~~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.

=== Odd harmonics ===

~~Despite having bad approximations, in light of having 28 as a divisor 952edo provides the optimal patent val for the [[oquatonic]] temperament in the 7-limit.~~

=== Subsets and supersets ===

===~~Odd harmonics~~===

Since 952's factorization is 2<sup>3</sup> x 7 x 17, 952edo has subset EDOs {{EDOs| 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476}}.

===~~Divisors~~===

=== Miscellaneous properties ===

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}}~~.

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.

== Scales ==

* SouthSolstitial[169]

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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|952}}
 == Theory ==
-In the 2.3.13.17.19 subgroup, 952edo tempers out 793152/793117.
+edo is in[[consistent]] in the [[5-odd-limit]] despite having a decent approximation to [[3/1|harmonic 3]]. To start with, as an 11-limit temperament we may consider the 952ce [[val]] {{val| 952 1509 '''2211''' '''2673''' '''3294''' }} and the 952d val {{val| 952 1509 '''2210''' '''2672''' '''3293''' }}.
-In the 19-limit as a whole, 952edo tempers out 1445/1444, 1540/1539.
+Despite having bad approximations, in light of having 28 as a divisor 952edo provides the optimal patent val for the [[oquatonic]] temperament in the 7-limit.
-edo 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.
+=== Odd harmonics ===
+{{Harmonics in equal|952}}
-Despite having bad approximations, in light of having 28 as a divisor 952edo provides the optimal patent val for the [[oquatonic]] temperament in the 7-limit.
+=== Subsets and supersets ===
-===Odd harmonics===
+Since 952's factorization is 2<sup>3</sup> x 7 x 17, 952edo has subset EDOs {{EDOs| 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476}}.
-{{harmonics in equal|952}}
-===Divisors===
+=== Miscellaneous properties ===
-edo'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}}.
+edo 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.
 == Scales ==
 * SouthSolstitial[169]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->