353edo
The 353 equal divisions of the octave (353edo) divides the octave into parts of 3.3994 cents each.
Theory
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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