353edo: Difference between revisions
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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. 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[130] scale consists of a stack of naively 18 "major scales" finished with one 11-edo tetratonic. | 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. 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[130] scale consists of a stack of naively 18 "major scales" finished with one 11-edo tetratonic. | ||
Such a temperament | 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. | ||
== Table of intervals == | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ | |||
!Step | |||
!Name | |||
<small>(diatonic Hebrew[19] version</small>) | |||
!Associated ratio | |||
<small>(2.5.7.13 subgroup)</small> | |||
|- | |||
|0 | |||
|C | |||
|1/1 | |||
|- | |||
|19 | |||
|C# | |||
| | |||
|- | |||
|38 | |||
|Db | |||
|[[14/13]] | |||
|- | |||
|57 | |||
|D | |||
| | |||
|- | |||
|76 | |||
|D# | |||
| | |||
|- | |||
|95 | |||
|Eb | |||
| | |||
|- | |||
|114 | |||
|E | |||
|[[6/5]] | |||
|- | |||
|133 | |||
|E#/Fb | |||
|[[13/10]] minor (best approximation is 134) | |||
|- | |||
|152 | |||
|F | |||
| | |||
|- | |||
|171 | |||
|F# | |||
|[[7/5]] | |||
|- | |||
|190 | |||
|Gb | |||
| | |||
|- | |||
|209 | |||
|G | |||
|98/65 | |||
|- | |||
|228 | |||
|G# | |||
| | |||
|- | |||
|247 | |||
|Ab | |||
|[[13/8]] | |||
|- | |||
|266 | |||
|A | |||
| | |||
|- | |||
|285 | |||
|A# | |||
|[[7/4]] | |||
|- | |||
|304 | |||
|Bb | |||
| | |||
|- | |||
|323 | |||
|B | |||
| | |||
|- | |||
|342 | |||
|B#/Cb | |||
| | |||
|- | |||
|353 | |||
|C | |||
|2/1 | |||
|} | |||
== Scales == | == Scales == | ||