373edo: Difference between revisions

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-'''373edo''' is the [[EDO|equal division of the octave]] into 373 parts of 3.21716 [[cent]]s each. It is consistent to the 15-odd-limit, tempering out 1224440064/1220703125 ([[parakleisma]]) and {{monzo| -51 19 9 }}; (untritonic comma) in the 5-limit; [[2401/2400]], 65625/65536, 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. It supports the [[Breedsmic temperaments #Hemitert|hemitert temperament]].
+{{Infobox ET}}
+{{ED intro}}
+== Theory ==
+edo 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 ===
 edo is the 74th [[prime edo]].
-=== Prime harmonics ===
+== Intervals ==
-{{Primes in edo|373}}
+{{Main|Table of 373edo intervals}}
+== 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]] (%)
+|-
+| 2.3
+| {{monzo| -591 373 }}
+| {{mapping| 373 591 }}
+| +0.1939
+| 0.1939
+| 6.03
+|-
+| 2.3.5
+| {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }}
+| {{mapping| 373 591 866 }}
+| +0.1658
+| 0.1632
+| 5.07
+|-
+| 2.3.5.7
+| 2401/2400, 65625/65536, 43046721/42875000
+| {{mapping| 373 591 866 1047 }}
+| +0.1654
+| 0.1413
+| 4.39
+|-
+| 2.3.5.7.11
+| 2401/2400, 3025/3024, 8019/8000, 65625/65536
+| {{mapping| 373 591 866 1047 1290 }}
+| +0.2008
+| 0.1449
+| 4.50
+|-
+| 2.3.5.7.11.13
+| 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224
+| {{mapping| 373 591 866 1047 1290 1380 }}
+| +0.2056
+| 0.1327
+| 4.12
+|}
+=== Rank-2 temperaments ===
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
+|-
+| 1
+| 12\373
+| 38.61
+| 45/44
+| [[Hemitert]]
+|-
+| 1
+| 24\373
+| 77.21
+| 256/245
+| [[Tertiaseptal]]
+|-
+| 1
+| 98\373
+| 315.28
+| 6/5
+| [[Parakleismic]] (5-limit)
+|-
+| 1
+| 111\373
+| 357.10
+| 768/625
+| [[Dodifo]] (5-limit)
+|-
+| 1
+| 162\373
+| 521.18
+| 875/648
+| [[Maviloid]]
+|-
+| 1
+| 183\373
+| 588.74
+| 45/32
+| [[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]]