353edo: Difference between revisions
Cleanup; expansion; +categories |
→Relation to a calendar reform: fixed information |
||
| Line 11: | Line 11: | ||
In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. | In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern are leap. When converted to [[19edo]], this results in [[5L 2s]] mode, and simply the diatonic major scale. | ||
Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale. Hebrew[130] scale | Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale. The generator and the EDO itself have a relationship that 334 was originally proposed for HC improvement, not 353 (see link below). | ||
Using such small of a generator helps explore the 353edo's "upside down" side. | |||
== Scales == | == Scales == | ||
* Hebrew[130] | * Hebrew[130] | ||
== See also == | == See also == | ||
| Line 22: | Line 23: | ||
== Links == | == Links == | ||
* [https://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar] | * [https://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar] | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Didacus]] | [[Category:Didacus]] | ||
Revision as of 18:07, 7 November 2021
The 353 equal divisions of the octave (353edo) divides the octave into parts of 3.3994 cents each.
Theory
Script error: No such module "primes_in_edo".
From the prime number standpoint, 353edo is suitable for use with 2.7.11.17.23.29.31.37 subgroup. This makes 353edo an "upside-down" EDO – poor approximation of the low harmonics, but an improvement over the high ones. Nonetheless, it provides the optimal patent val for didacus, the 2.5.7 subgroup temperament tempering out 3136/3125.
353edo is the 71st prime EDO.
Relation to a calendar reform
In the original Hebrew calendar, years number 3, 6, 8, 11, 14, 17, and 19 within a 19-year pattern are leap. When converted to 19edo, this results in 5L 2s mode, and simply the diatonic major scale.
Following this logic, a temperament can be constructed for the Rectified Hebrew calendar (see below), containing 130 notes of the 353edo scale. Hebrew[130] scale has 334\353 as its generator, which is a supermajor seventh, or alternately, 19\353, about a third-tone, since inverting the generator has no effect on the scale. The generator and the EDO itself have a relationship that 334 was originally proposed for HC improvement, not 353 (see link below).
Using such small of a generator helps explore the 353edo's "upside down" side.
Scales
- Hebrew[130]