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373edo: Difference between revisions

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{{Infobox ET
{{Infobox ET}}
| Prime factorization = 373 (prime)
{{ED intro}}
| Step size = 3.21716¢
| Fifth = 218\373 (701.34¢)
| Semitones = 34:29 (109.38¢ : 93.30¢)
| Consistency = 15
}}
The '''373 equal divisions of the octave''' ('''373edo'''), or the '''373(-tone) equal temperament''' ('''373tet''', '''373et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 373 parts of about 3.22 [[cent]]s each.


== Theory ==
== Theory ==
373edo is [[consistent]] to the [[15-odd-limit]], with harmonics 3 through 13 all tuned flat. It tempers out {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| -51 19 9 }} (untriton comma) in the 5-limit; 2401/2400 ([[breedsma]]), 65625/65536 (horwell), 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 supports the [[Breedsmic temperaments #Hemitert|hemitert temperament]].
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]].


=== Prime harmonics ===
== Intervals ==
{{Primes in edo|373}}
{{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
|-
|-
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| 2.3
| 2.3
| {{monzo| -591 373 }}
| {{monzo| -591 373 }}
| [{{val| 373 591 }}]
| {{mapping| 373 591 }}
| +0.1939
| +0.1939
| 0.1939
| 0.1939
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| 2.3.5
| 2.3.5
| {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }}
| {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }}
| [{{val| 373 591 866 }}]
| {{mapping| 373 591 866 }}
| +0.1658
| +0.1658
| 0.1632
| 0.1632
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| 2.3.5.7
| 2.3.5.7
| 2401/2400, 65625/65536, 43046721/42875000
| 2401/2400, 65625/65536, 43046721/42875000
| [{{val| 373 591 866 1047 }}]
| {{mapping| 373 591 866 1047 }}
| +0.1654
| +0.1654
| 0.1413
| 0.1413
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| 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
| [{{val| 373 591 866 1047 1290 }}]
| {{mapping| 373 591 866 1047 1290 }}
| +0.2008
| +0.2008
| 0.1449
| 0.1449
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| 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
| [{{val| 373 591 866 1047 1290 1380 }}]
| {{mapping| 373 591 866 1047 1290 1380 }}
| +0.2056
| +0.2056
| 0.1327
| 0.1327
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=== 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 octave
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| [[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:Equal divisions of the octave]]
[[Category:Listen]]
[[Category:Prime EDO]]
Retrieved from "https://en.xen.wiki/w/373edo"