364edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
+links and +prime error table
+RTT table and rank-2 temperaments
Line 1: Line 1:
'''364edo''' is the [[EDO|equal division of the octave]] into 364 parts of 3.2963 [[cent]]s each.  
'''364edo''' is the [[EDO|equal division of the octave]] into 364 parts of 3.2963 [[cent]]s each.  


== 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]].


=== Prime harmonics ===
=== Prime harmonics ===
{{Primes in edo|364}}
{{Primes in edo|364}}
== 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| 577 -364 }}
| [{{val| 364 577 }}]
| -0.0766
| 0.0766
| 2.32
|-
| 2.3.5
| 1600000/1594323, {{monzo| -65 0 28 }}
| [{{val| 364 577 845 }}]
| +0.0350
| 0.1698
| 5.15
|-
| 2.3.5.7
| 65625/65536, 390625/388962, 420125/419904
| [{{val| 364 577 845 1022 }}]
| -0.0098
| 0.1662
| 5.04
|-
| 2.3.5.7.11
| 1375/1372, 6250/6237, 19712/19683, 41503/41472
| [{{val| 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
| [{{val| 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
| [{{val| 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
| [{{val| 364 577 845 1022 1259 1347 1488 1546 }}]
| +0.0257
| 0.1620
| 4.91
|}
=== 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
| 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]]
|-
| 28
| 151\364<br>(5\364)
| 497.80<br>(16.48)
| 4/3<br>(105/104)
| [[Oquatonic]]
|}


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

Revision as of 16:14, 31 December 2021

364edo is the equal division of the octave into 364 parts of 3.2963 cents each.

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.

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 [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
28 151\364
(5\364) 		497.80
(16.48) 		4/3
(105/104) 		Oquatonic
Retrieved from "https://en.xen.wiki/index.php?title=364edo&oldid=82991"