373edo: Difference between revisions

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+RTT table and rank-2 temperaments
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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]].
'''373edo''' is the [[EDO|equal division of the octave]] into 373 parts of 3.21716 [[cent]]s each.  
 
== Theory ==
373edo 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]].


373edo is the 74th [[prime edo]].
373edo is the 74th [[prime edo]].
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=== Prime harmonics ===
=== Prime harmonics ===
{{Primes in edo|373}}
{{Primes in edo|373}}
== 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 }}
| [{{val| 373 591 }}]
| +0.1939
| 0.1939
| 6.03
|-
| 2.3.5
| {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }}
| [{{val| 373 591 866 }}]
| +0.1658
| 0.1632
| 5.07
|-
| 2.3.5.7
| 2401/2400, 65625/65536, 43046721/42875000
| [{{val| 373 591 866 1047 }}]
| +0.1654
| 0.1413
| 4.39
|-
| 2.3.5.7.11
| 2401/2400, 3025/3024, 8019/8000, 65625/65536
| [{{val| 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
| [{{val| 373 591 866 1047 1290 1380 }}]
| +0.2056
| 0.1327
| 4.12
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! 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)
|}


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:Prime EDO]]
[[Category:Prime EDO]]

Revision as of 18:29, 9 January 2022

373edo is the equal division of the octave into 373 parts of 3.21716 cents each.

Theory

373edo is consistent to the 15-odd-limit, tempering out 1224440064/1220703125 (parakleisma) and [-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 hemitert temperament.

373edo is the 74th prime edo.

Prime harmonics

Script error: No such module "primes_in_edo".

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-591 373⟩ [⟨373 591]] +0.1939 0.1939 6.03
2.3.5 [8 14 -13⟩, [-51 19 9⟩ [⟨373 591 866]] +0.1658 0.1632 5.07
2.3.5.7 2401/2400, 65625/65536, 43046721/42875000 [⟨373 591 866 1047]] +0.1654 0.1413 4.39
2.3.5.7.11 2401/2400, 3025/3024, 8019/8000, 65625/65536 [⟨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 [⟨373 591 866 1047 1290 1380]] +0.2056 0.1327 4.12

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
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)
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