703edo: Difference between revisions

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~~703 = 19 × 37, and~~ the ~~equal temperament~~ [[tempering out|tempers out]] the [[enneadeca]], {{monzo| -14 -19 19 }}. In the 7-limit the [[patent val]] tempers out [[16875/16807]] and [[~~65635~~/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].

703edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. It [[tempering out|tempers out]] the [[enneadeca]], {{monzo| -14 -19 19 }} in the 5-limit.

In the 7-limit, the [[patent val]] {{val| 703 1114 1632 '''1974''' }} and the 703d [[val]] {{val| 703 1114 1632 '''1973''' }} may be worth considering.

Using the patent val, it tempers out [[16875/16807]] and [[65625/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].

The alternative 703d [[val]] tempers out [[4375/4374]] and [[703125/702464]], supporting 7-limit [[enneadecal]].

=== Odd harmonics ===

=== Subsets and supersets ===

Since 703 factors into {{factorization|703}}, 703edo contains [[19edo]] and [[37edo]] as subsets.

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 {{Infobox ET}}
-{{EDO intro|703}}
+{{ED intro}}
-= 19 × 37, and the equal temperament [[tempering out|tempers out]] the [[enneadeca]], {{monzo| -14 -19 19 }}. In the 7-limit the [[patent val]] tempers out [[16875/16807]] and [[65635/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].
+edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. It [[tempering out|tempers out]] the [[enneadeca]], {{monzo| -14 -19 19 }} in the 5-limit.
+In the 7-limit, the [[patent val]] {{val| 703 1114 1632 '''1974''' }} and the 703d [[val]] {{val| 703 1114 1632 '''1973''' }} may be worth considering.
+Using the patent val, it tempers out [[16875/16807]] and [[65625/65536]] and in the 11-limit 1375/1372, [[540/539]] and [[3025/3024]], so that it [[support]]s and gives the [[optimal patent val]] for [[indra]] and [[eris]]. In the 13-limit, it tempers out [[729/728]], [[2080/2079]] and [[6656/6655]], and provides the optimal patent val for [[shibi]].
+The alternative 703d [[val]] tempers out [[4375/4374]] and [[703125/702464]], supporting 7-limit [[enneadecal]].
 === Odd harmonics ===
 {{Harmonics in equal|703}}
+=== Subsets and supersets ===
+Since 703 factors into {{factorization|703}}, 703edo contains [[19edo]] and [[37edo]] as subsets.