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| Consistency = 21
| Consistency = 21
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The '''364 equal divisions of the octave''' ('''364edo'''), or the '''364(-tone) equal temperament''' ('''364tet''', '''364et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 364 parts of about 3.30 [[cent]]s each.
{{EDO intro|364}}


== Theory ==
== Theory ==
364edo is consistent through the [[21-odd-limit]], [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo| -65 0 28 }}; (28-5-comma) in the [[5-limit]]; 65625/65536 (horwell), 390625/388962 ([[Dimcomp comma|dimcomp]]), and 420175/419904 (wizma) in the [[7-limit]] (supporting [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[19712/19683]], and 41503/41472 in the [[11-limit]] (as well as [[9801/9800]]); [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], and 14641/14625 in the [[13-limit]] (as well as [[4096/4095]], [[4225/4224]], and [[10985/10976]]); [[715/714]], [[1089/1088]], [[1225/1224]], 1275/1274, 2025/2023, and 8624/8619 in the [[17-limit]] (as well as 2431/2430, 4914/4913, and [[5832/5831]]); [[1216/1215]], 1331/1330, 1540/1539, and [[1729/1728]] in the [[19-limit]].
364edo is consistent through the [[21-odd-limit]], [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo| -65 0 28 }}; (28-5-comma) in the [[5-limit]]; 65625/65536 (horwell), 390625/388962 ([[Dimcomp comma|dimcomp]]), and 420175/419904 (wizma) in the [[7-limit]] (supporting [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[19712/19683]], and 41503/41472 in the [[11-limit]] (as well as [[9801/9800]]); [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], and 14641/14625 in the [[13-limit]] (as well as [[4096/4095]], [[4225/4224]], and [[10985/10976]]); [[715/714]], [[1089/1088]], [[1225/1224]], 1275/1274, 2025/2023, and 8624/8619 in the [[17-limit]] (as well as 2431/2430, 4914/4913, and [[5832/5831]]); [[1216/1215]], 1331/1330, 1540/1539, and [[1729/1728]] in the [[19-limit]].


364 is divisible by, and thus contains sub-edos {{EDOs|1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182.}}
364 is divisible by, and thus contains sub-edos {{EDOs|1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182}}.


=== Prime harmonics ===
=== Prime harmonics ===
{{Primes in edo|364}}
{{Harmonics in equal|364|columns=11}}


== Regular temperament properties ==
== Regular temperament properties ==
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| [[Semiwitch]]
| [[Semiwitch]]
|-
|-
|4
| 4
|30\364
| 30\364
|98.90
| 98.90
|18/17
| 18/17
|[[World Calendar]]
| [[World calendar]]
|-
|-
| 28
| 28

Revision as of 14:20, 1 June 2022

← 363edo 364edo 365edo →
Prime factorization 22 × 7 × 13
Step size 3.2967 ¢ 
Fifth 213\364 (702.198 ¢)
Semitones (A1:m2) 35:27 (115.4 ¢ : 89.01 ¢)
Consistency limit 21
Distinct consistency limit 21

Template:EDO intro

Theory

364edo is consistent through the 21-odd-limit, tempering out 1600000/1594323 (amity comma) and [-65 0 28⟩; (28-5-comma) in the 5-limit; 65625/65536 (horwell), 390625/388962 (dimcomp), and 420175/419904 (wizma) in the 7-limit (supporting fifthplus and oquatonic); 1375/1372, 6250/6237, 19712/19683, and 41503/41472 in the 11-limit (as well as 9801/9800); 625/624, 1716/1715, 2080/2079, 2200/2197, and 14641/14625 in the 13-limit (as well as 4096/4095, 4225/4224, and 10985/10976); 715/714, 1089/1088, 1225/1224, 1275/1274, 2025/2023, and 8624/8619 in the 17-limit (as well as 2431/2430, 4914/4913, and 5832/5831); 1216/1215, 1331/1330, 1540/1539, and 1729/1728 in the 19-limit.

364 is divisible by, and thus contains sub-edos 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182.

Prime harmonics

Approximation of prime harmonics in 364edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.24 -0.60 +0.40 -0.77 +0.13 +0.54 -0.81 +1.40 -1.01 -1.08
Relative (%) +0.0 +7.4 -18.2 +12.3 -23.3 +4.0 +16.4 -24.6 +42.3 -30.5 -32.7
Steps
(reduced) 		364
(0) 		577
(213) 		845
(117) 		1022
(294) 		1259
(167) 		1347
(255) 		1488
(32) 		1546
(90) 		1647
(191) 		1768
(312) 		1803
(347)

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [577 -364⟩ [⟨364 577]] -0.0766 0.0766 2.32
2.3.5 1600000/1594323, [-65 0 28⟩ [⟨364 577 845]] +0.0350 0.1698 5.15
2.3.5.7 65625/65536, 390625/388962, 420125/419904 [⟨364 577 845 1022]] -0.0098 0.1662 5.04
2.3.5.7.11 1375/1372, 6250/6237, 19712/19683, 41503/41472 [⟨364 577 845 1022 1259]] +0.0366 0.1753 5.32
2.3.5.7.11.13 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625 [⟨364 577 845 1022 1259 1347]] +0.0245 0.1622 4.92
2.3.5.7.11.13.17 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197 [⟨364 577 845 1022 1259 1347 1488]] +0.0022 0.1599 4.85
2.3.5.7.11.13.17.19 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728 [⟨364 577 845 1022 1259 1347 1488 1546]] +0.0257 0.1620 4.91

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperaments
1 103\364 339.56 243/200 Amity / paramity
1 125\364 412.09 80/63 Witch
1 149\364 491.21 3645/2744 Fifthplus
1 151\364 497.80 4/3 Gary
2 57\364 187.91 49/44 Semiwitch
4 30\364 98.90 18/17 World calendar
28 151\364
(5\364) 		497.80
(16.48) 		4/3
(105/104) 		Oquatonic
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