|Steps (reduced)||353 (0)||559 (206)||820 (114)||991 (285)||1221 (162)||1306 (247)||1443 (31)||1500 (88)||1597 (185)||1715 (303)||1749 (337)||1839 (74)|
From the prime number standpoint, 353edo is suitable for use with 220.127.116.11.18.104.22.168 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 (makhzor, plural:makhzorim) 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 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. Using such small of a generator helps explore the 353edo's "upside down" side. In addition, every sub-pattern in a 19-note generator is actually a Hebrew makhzor, that is a mini-19edo on its own, until it is truncated to an 11-note pattern. Just as the original calendar reform consists of 18 makhzorim with 1 hendecaeteris, Hebrew scale consists of a stack of naively 18 "major scales" finished with one 11-edo tetratonic.
Specific chords and intervals
Such a temperament gives 19edo a unique stretch: 6\19 corresponds to 5/4, 13\19 corresponds to 13/8, and 15\19 corresponds to 7/4. When measured relative to the generator, the error is less than 1 in 5000. In the 13-limit, the it tempers out 3136/3125, 4394/4375, 10985/10976, and 1968512/1953125. This gives it a few more unique intervals.
If 209\353 is loosely assumed to equal 3/2, it offers a 710c stretched fifth, and the following resolution sequence: 7/4 D7 - 13/8 D2 - D53 - T53. This has a very pleasant sound, with 13/8 acting as a "doubled resolvant" or "resolution into resolution". Such an arrangement also "tempers out" 169/168.
Table of intervals
(diatonic Hebrew version)
|133||E#/Fb||13/10 minor (best approximation is 134)|
- RectifiedHebrew - 18L 1s
- 18-Glacial - same as above
- RectifiedHebrew - 93L 37s