364edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 577 -364 }}
| {{monzo| 577 -364 }}
| {{mapping| 364 577 }}
| {{mapping| 364 577 }}
| -0.0766
| &minus;0.0766
| 0.0766
| 0.0766
| 2.32
| 2.32
Line 42: Line 34:
| 65625/65536, 390625/388962, 420125/419904
| 65625/65536, 390625/388962, 420125/419904
| {{mapping| 364 577 845 1022 }}
| {{mapping| 364 577 845 1022 }}
| -0.0098
| &minus;0.0098
| 0.1662
| 0.1662
| 5.04
| 5.04
Line 73: Line 65:
| 0.1620
| 0.1620
| 4.91
| 4.91
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 121: Line 107:
|-
|-
| 13
| 13
| 151\364<br>(11\364)
| 151\364<br />(11\364)
| 497.80<br>(36.26)
| 497.80<br />(36.26)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Aluminium]]
| [[Aluminium]]
|-
|-
| 26
| 26
| 151\364<br>(11\364)
| 151\364<br />(11\364)
| 497.80<br>(36.26)
| 497.80<br />(36.26)
| 4/3<br>(?)
| 4/3<br />(?)
| [[Iron]]
| [[Iron]]
|-
|-
| 28
| 28
| 151\364<br>(5\364)
| 151\364<br />(5\364)
| 497.80<br>(16.48)
| 497.80<br />(16.48)
| 4/3<br>(105/104)
| 4/3<br />(105/104)
| [[Oquatonic]]
| [[Oquatonic]]
|-
|-
| 91
| 91
| 151\364<br>(3\364)
| 151\364<br />(3\364)
| 497.80<br>(3.30)
| 497.80<br />(3.30)
| 4/3<br>(176/175)
| 4/3<br />(176/175)
| [[Protactinium]]
| [[Protactinium]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Scales ==
== Scales ==
* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30
* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30

Revision as of 05:22, 16 November 2024

← 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. The equal temperament tempers out 1600000/1594323 (amity comma) and [-65 0 28⟩ (oquatonic comma) in the 5-limit; 65625/65536 (horwell comma), 390625/388962 (dimcomp comma), 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.

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)

Subsets and supersets

Since 364 factors into 22 × 7 × 13, 364edo has subset edos 2, 4, 7, 13, 14, 26, 28, 52, 91, 182.

Miscellaneous properties

364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of 11edo, 12edo, 13edo and 14edo. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these edos are sought after.

Regular temperament properties

Template:Comma basis begin |- | 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 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 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 |- | 13 | 151\364
(11\364) | 497.80
(36.26) | 4/3
(?) | Aluminium |- | 26 | 151\364
(11\364) | 497.80
(36.26) | 4/3
(?) | Iron |- | 28 | 151\364
(5\364) | 497.80
(16.48) | 4/3
(105/104) | Oquatonic |- | 91 | 151\364
(3\364) | 497.80
(3.30) | 4/3
(176/175) | Protactinium Template:Rank-2 end Template:Orf

Scales

  • WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30
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