703edo: Difference between revisions

(4 intermediate revisions by 2 users not shown)

Line 1:

The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, |-14 -19 19>. In the 7-limit it 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|optimal patent val]] in [[Mirkwai_family|indra temperament]] and [[Mirkwai_clan#Eris|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi|shibi temperament]].

[[~~Category:Equal divisions of~~ the ~~octave~~|~~###~~]]

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.

@@ Line 1: / Line 1: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-The '''703 equal division''' divides the octave into 703 equal parts of 1.707 cents each. 703 = 19 * 37, and 703 tempers out the enneadeca, the 19-comma, |-14 -19 19&gt;. In the 7-limit it 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|optimal patent val]] in [[Mirkwai_family|indra temperament]] and [[Mirkwai_clan#Eris|eris temperament]]. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for [[Mirkwai_family#Indra-Shibi|shibi temperament]].
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+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.