353edo: Difference between revisions
Cleanup; expansion; +categories |
|||
| Line 1: | Line 1: | ||
353edo divides the octave into parts of 3.3994 | The '''353 equal divisions of the octave''' ('''353edo''') divides the [[octave]] into parts of 3.3994 [[cent]]s each. | ||
== Theory == | == Theory == | ||
{{primes in edo|353|columns=12}} | {{primes in edo|353|columns=12}} | ||
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 | |||
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 === | === 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. | 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 can be described as 18 19-edo scales completed by a single 4 out of 11 scale of [[11edo]], or alternately, 19 [[11edo]] cycles merged with 18 octaeteris-type [[8edo]] cycles. This makes it a [[93L 37s]] MOS 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 can be described as 18 19-edo scales completed by a single 4 out of 11 scale of [[11edo]], or alternately, 19 [[11edo]] cycles merged with 18 octaeteris-type [[8edo]] cycles. This makes it a [[93L 37s]] MOS scale. | ||
== | == Scales == | ||
* Hebrew[130] | * Hebrew[130] | ||
* Hebrew[223] | * Hebrew[223] – the complement | ||
== See also == | == See also == | ||
* [[293edo]] | * [[293edo]] | ||
* [[Maximal evenness]] | * [[Maximal evenness]] | ||
== Links == | == Links == | ||
[[ | * [[Wikipedia: Octaeteris]] | ||
* [https://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar] | |||
[ | [[Category:Equal divisions of the octave]] | ||
[[Category:Didacus]] | |||
Revision as of 22:28, 3 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 can be described as 18 19-edo scales completed by a single 4 out of 11 scale of 11edo, or alternately, 19 11edo cycles merged with 18 octaeteris-type 8edo cycles. This makes it a 93L 37s MOS scale.
Scales
- Hebrew[130]
- Hebrew[223] – the complement