373edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
373edo is [[consistency|distinctly consistent]] to the [[15-odd-limit]]. It has a flat tendency, with [[harmonic]]s 3 through 13 all tuned flat. | 373edo is [[consistency|distinctly consistent]] to the [[15-odd-limit]]. It has a flat tendency, with [[harmonic]]s 3 through 13 all tuned flat. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| -51 19 9 }} (untriton comma) in the [[5-limit]]; 2401/2400 ([[breedsma]]), 65625/65536 ([[horwell comma]]), and 43046721/42875000 in the [[7-limit]]; [[3025/3024]], [[8019/8000]], 24057/24010, and 496125/495616 in the [[11-limit]]; [[729/728]], [[1001/1000]], [[1716/1715]], [[4225/4224]], and [[10648/10647]] in the [[13-limit]], enabling [[squbemic chords]] and [[sinbadmic chords]]. It also [[support]]s the [[hemitert]] temperament. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 10: | Line 10: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
373edo is the 74th [[prime edo]]. | 373edo is the 74th [[prime edo]]. | ||
== Intervals == | |||
{{Main|Table of 373edo intervals}} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
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|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| -591 373 }} | ||
| {{ | | {{Mapping| 373 591 }} | ||
| +0.1939 | | +0.1939 | ||
| 0.1939 | | 0.1939 | ||
| Line 30: | Line 34: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 8 14 -13 }}, {{monzo| -51 19 9 }} | ||
| {{ | | {{Mapping| 373 591 866 }} | ||
| +0.1658 | | +0.1658 | ||
| 0.1632 | | 0.1632 | ||
| Line 38: | Line 42: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 65625/65536, 43046721/42875000 | | 2401/2400, 65625/65536, 43046721/42875000 | ||
| {{ | | {{Mapping| 373 591 866 1047 }} | ||
| +0.1654 | | +0.1654 | ||
| 0.1413 | | 0.1413 | ||
| Line 45: | Line 49: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3025/3024, 8019/8000, 65625/65536 | | 2401/2400, 3025/3024, 8019/8000, 65625/65536 | ||
| {{ | | {{Mapping| 373 591 866 1047 1290 }} | ||
| +0.2008 | | +0.2008 | ||
| 0.1449 | | 0.1449 | ||
| Line 52: | Line 56: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224 | | 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224 | ||
| {{ | | {{Mapping| 373 591 866 1047 1290 1380 }} | ||
| +0.2056 | | +0.2056 | ||
| 0.1327 | | 0.1327 | ||
| Line 60: | Line 64: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 83: | Line 88: | ||
| 315.28 | | 315.28 | ||
| 6/5 | | 6/5 | ||
| [[ | | [[Counterpara]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 103: | Line 108: | ||
| [[Untriton]] (5-limit) | | [[Untriton]] (5-limit) | ||
|} | |} | ||
<nowiki>* | <nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Hi-Vis Dog In An Outfit" from ''You Are A...'' (2024) – [https://open.spotify.com/track/3h2LS9jR54sxEh1cpy0olI Spotify] | [https://francium223.bandcamp.com/track/hi-vis-dog-in-an-outfit Bandcamp] | [https://www.youtube.com/watch?v=z4I6CeiHC1M YouTube] | * "Hi-Vis Dog In An Outfit" from ''You Are A...'' (2024) – [https://open.spotify.com/track/3h2LS9jR54sxEh1cpy0olI Spotify] | [https://francium223.bandcamp.com/track/hi-vis-dog-in-an-outfit Bandcamp] | [https://www.youtube.com/watch?v=z4I6CeiHC1M YouTube] | ||
* "ambatukum" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/74FOCnuxR4G6rfoq5uIE6y Spotify] | [https://francium223.bandcamp.com/track/ambatukum Bandcamp] | [https://www.youtube.com/watch?v=utDi9XY25K0 YouTube] | |||
* "Onion?" from ''Questions, Vol. 2'' (2025) – [https://open.spotify.com/track/0HNcOEhQBPqFZeZ9kvhI1N Spotify] | [https://francium223.bandcamp.com/track/onion Bandcamp] | [https://www.youtube.com/watch?v=zvRUCarYJLI YouTube] | |||
[[Category:Listen]] | |||