353edo: Difference between revisions

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=== 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 simply the diatonic major scale. Following this logic, a temperament can be constructed for the Rectified Hebrew calendar, containing 130 notes of the ~~353-edo~~ scale. Hebrew[130] scale can be described as 18 19-edo scales completed by a single 4 out of 11 scale of [[11edo]]~~. The generator of this temperament is the ''lunar logarithmic interval''~~ - ~~0.36826 of an octave~~. ~~Although~~ it ~~lacks an acoustic application, in real life it is the fraction of~~ a ~~month by which 12 lunar months fall short of a solar year~~.

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.

== Temperaments ==

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* [[Maximal evenness]]

== Links ==

[[wikipedia:Octaeteris]]

[https://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]

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 === 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 simply the diatonic major scale. Following this logic, a temperament can be constructed for the Rectified Hebrew calendar, containing 130 notes of the 353-edo scale. Hebrew[130] scale can be described as 18 19-edo scales completed by a single 4 out of 11 scale of [[11edo]]. The generator of this temperament is the ''lunar logarithmic interval'' - 0.36826 of an octave. Although it lacks an acoustic application, in real life it is the fraction of a month by which 12 lunar months fall short of a solar year.
+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.
 == Temperaments ==
@@ Line 15: / Line 17: @@
 * [[Maximal evenness]]
 == Links ==
+[[wikipedia:Octaeteris]]
 [https://individual.utoronto.ca/kalendis/hebrew/rect.htm Rectified Hebrew Calendar]