700edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
==== Odd harmonics | == Theory == | ||
700edo is [[consistent]] to the [[7-odd-limit]], but its [[harmonic]] [[3/1|3]] is about halfway between its steps. It is strong in the 2.9.15.7.31 [[subgroup]], [[tempering out]] [[3969/3968]], [[420175/419904]], 10255177611/10240000000 and 2202927104/2197265625. The equal temperament can also be used in the 2.9.5.7.13.17.23 subgroup, tempering out [[1225/1224]], 46000/45927, 8281/8280, 426496/426465, 31250/31213 and 262395/262144. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|700}} | {{Harmonics in equal|700}} | ||
=== Subsets and supersets === | |||
Since 700 factors into 2<sup>2</sup> × 5<sup>2</sup> × 7, 700edo has subset edos {{EDOs| 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, and 350 }}. [[1400edo]], which doubles it, gives a good correction to the harmonic 3. | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.9 | |||
| {{monzo|317 -100}} | |||
| {{mapping|700 2219}} | |||
| -0.0142 | |||
| 0.0142 | |||
| 0.83 | |||
|- | |||
| 2.9.5 | |||
| {{monzo|-65 0 28}}, {{monzo|63 -25 7}} | |||
| {{mapping|700 2219 1625}} | |||
| +0.0766 | |||
| 0.1289 | |||
| 7.52 | |||
|- | |||
| 2.9.5.7 | |||
| 2100875/2097152, 184528125/184473632, 3500000000/3486784401 | |||
| {{mapping|700 2219 1625 1965}} | |||
| +0.0801 | |||
| 0.1118 | |||
| 6.52 | |||
|} | |||
== Music == | |||
; [[Francium]] | |||
* "wiloliquy" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/58pl5te81ab2ODOCVbhHdq Spotify] | [https://francium223.bandcamp.com/track/wiloliquy Bandcamp] | [https://www.youtube.com/watch?v=RHyi7Da4SHs YouTube] | |||