373edo: Difference between revisions
+RTT table and rank-2 temperaments |
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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | == Theory == | ||
373edo is consistent to the [[15-odd-limit]], tempering out | 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 [[breedsmic temperaments #Hemitert|hemitert temperament]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|373}} | |||
=== 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 stretch (¢) | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 22: | Line 28: | ||
| 2.3 | | 2.3 | ||
| {{monzo| -591 373 }} | | {{monzo| -591 373 }} | ||
| | | {{mapping| 373 591 }} | ||
| +0.1939 | | +0.1939 | ||
| 0.1939 | | 0.1939 | ||
| Line 29: | Line 35: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }} | | {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }} | ||
| | | {{mapping| 373 591 866 }} | ||
| +0.1658 | | +0.1658 | ||
| 0.1632 | | 0.1632 | ||
| Line 36: | 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 43: | 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 50: | 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 58: | 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 | |- | ||
! Generator | ! Periods<br />per 8ve | ||
! Cents | ! Generator* | ||
! Associated<br>ratio | ! Cents* | ||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 101: | Line 108: | ||
| [[Untriton]] (5-limit) | | [[Untriton]] (5-limit) | ||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Music == | |||
; [[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] | |||
* "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: | [[Category:Listen]] | ||