703edo: Difference between revisions
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[[ | 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 === | |||
{{Harmonics in equal|703}} | |||
=== Subsets and supersets === | |||
Since 703 factors into {{factorization|703}}, 703edo contains [[19edo]] and [[37edo]] as subsets. | |||
Latest revision as of 15:59, 20 February 2025
| ← 702edo | 703edo | 704edo → |
703 equal divisions of the octave (abbreviated 703edo or 703ed2), also called 703-tone equal temperament (703tet) or 703 equal temperament (703et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 703 equal parts of about 1.71 ¢ each. Each step represents a frequency ratio of 21/703, or the 703rd root of 2.
703edo is only consistent to the 5-odd-limit since harmonic 7 is about halfway between its steps. It tempers out the enneadeca, [-14 -19 19⟩ in the 5-limit.
In the 7-limit, the patent val ⟨703 1114 1632 1974] and the 703d 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 supports 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
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.390 | -0.538 | +0.733 | -0.781 | +0.033 | -0.698 | +0.778 | -0.830 | -0.500 | +0.343 | -0.109 |
| Relative (%) | -22.9 | -31.5 | +42.9 | -45.7 | +2.0 | -40.9 | +45.6 | -48.6 | -29.3 | +20.1 | -6.4 | |
| Steps (reduced) |
1114 (411) |
1632 (226) |
1974 (568) |
2228 (119) |
2432 (323) |
2601 (492) |
2747 (638) |
2873 (61) |
2986 (174) |
3088 (276) |
3180 (368) | |
Subsets and supersets
Since 703 factors into 19 × 37, 703edo contains 19edo and 37edo as subsets.