57edo: Difference between revisions

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→Intervals: Removed pions column
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|-
|-
! rowspan="2" | [[Degree|Degree]]
! rowspan="2" | [[Degree|Degree]]
! colspan="3" | Size
! colspan="2" | Size
|-
|-
![[cent|Cents]]
![[cent|Cents]]
!pions
!7mus
!7mus
|-
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
|0.0000
|0.0000
|0
|0
|0
|-
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:right;" | 21.0526
| style="text-align:right;" | 21.0526
|22.3158
|26.9474 (1A.F287<sub>16</sub>)
|26.9474 (1A.F287<sub>16</sub>)
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:right;" | 42.1053
| style="text-align:right;" | 42.1053
|44.6316
|53.8947 (35.E50E<sub>16</sub>)
|53.8947 (35.E50E<sub>16</sub>)
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:right;" | 63.1579
| style="text-align:right;" | 63.1579
|66.9474
|80.8421 (50.D794<sub>16</sub>)
|80.8421 (50.D794<sub>16</sub>)
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:right;" | 84.2105
| style="text-align:right;" | 84.2105
|89.2632
|107.7895 (6B.CA1B<sub>16</sub>)
|107.7895 (6B.CA1B<sub>16</sub>)
|-
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:right;" | 105.2632
| style="text-align:right;" | 105.2632
|111.57895
|134.7368 (86.BCA2<sub>16</sub>)
|134.7368 (86.BCA2<sub>16</sub>)
|-
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| style="text-align:right;" | 126.3158
| style="text-align:right;" | 126.3158
|133.8947
|161.6842 (A1.AF29<sub>16</sub>)
|161.6842 (A1.AF29<sub>16</sub>)
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| style="text-align:right;" | 147.3684
| style="text-align:right;" | 147.3684
|156.2105
|188.6316 (BC.A1AF<sub>16</sub>)
|188.6316 (BC.A1AF<sub>16</sub>)
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:right;" | 168.42105
| style="text-align:right;" | 168.42105
|178.5263
|215.57895 (D7.9436<sub>16</sub>)
|215.57895 (D7.9436<sub>16</sub>)
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| style="text-align:right;" | 189.4737
| style="text-align:right;" | 189.4737
|200.8421
|242.5263 (F2.86BD<sub>16</sub>)
|242.5263 (F2.86BD<sub>16</sub>)
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| style="text-align:right;" | 210.5263
| style="text-align:right;" | 210.5263
|223.1579
|269.4737 (10D.7943<sub>16</sub>)
|269.4737 (10D.7943<sub>16</sub>)
|-
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| style="text-align:right;" | 231.57895
| style="text-align:right;" | 231.57895
|245.4737
|296.42105 (128.6BCA<sub>16</sub>)
|296.42105 (128.6BCA<sub>16</sub>)
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| style="text-align:right;" | 252.6316
| style="text-align:right;" | 252.6316
|267.7895
|323.3684 (143.5E51<sub>16</sub>)
|323.3684 (143.5E51<sub>16</sub>)
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| style="text-align:right;" | 273.6842
| style="text-align:right;" | 273.6842
|290.1053
|350.3158 (15E.50D7<sub>16</sub>)
|350.3158 (15E.50D7<sub>16</sub>)
|-
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| style="text-align:right;" | 294.7368
| style="text-align:right;" | 294.7368
|312.42105
|377.2632 (17B.435E<sub>16</sub>)
|377.2632 (17B.435E<sub>16</sub>)
|-
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 15
| style="text-align:right;" | 315.7895
| style="text-align:right;" | 315.7895
|334.7368
|404.2105 (194.35E5<sub>16</sub>)
|404.2105 (194.35E5<sub>16</sub>)
|-
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| style="text-align:right;" | 336.8421
| style="text-align:right;" | 336.8421
|357.0526
|431.1579 (1AF.286C<sub>16</sub>)
|431.1579 (1AF.286C<sub>16</sub>)
|-
|-
| style="text-align:center;" | 17
| style="text-align:center;" | 17
| style="text-align:right;" | 357.8947
| style="text-align:right;" | 357.8947
|379.3684
|458.1053 (1CA.1AF2<sub>16</sub>)
|458.1053 (1CA.1AF2<sub>16</sub>)
|-
|-
| style="text-align:center;" | 18
| style="text-align:center;" | 18
| style="text-align:right;" | 378.9474
| style="text-align:right;" | 378.9474
|401.6842
|485.0526 (1E5.0D79<sub>16</sub>)
|485.0526 (1E5.0D79<sub>16</sub>)
|-
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 19
| style="text-align:right;" | 400
| style="text-align:right;" | 400
|424
|512 (200<sub>16</sub>)
|512 (200<sub>16</sub>)
|-
|-
| style="text-align:center;" | 20
| style="text-align:center;" | 20
| style="text-align:right;" | 421.0526
| style="text-align:right;" | 421.0526
|446.3158
|538.9474 (21A.F287<sub>16</sub>)
|538.9474 (21A.F287<sub>16</sub>)
|-
|-
| style="text-align:center;" | 21
| style="text-align:center;" | 21
| style="text-align:right;" | 442.1053
| style="text-align:right;" | 442.1053
|468.6316
|565.8947 (235.E50E<sub>16</sub>)
|565.8947 (235.E50E<sub>16</sub>)
|-
|-
| style="text-align:center;" | 22
| style="text-align:center;" | 22
| style="text-align:right;" | 463.1579
| style="text-align:right;" | 463.1579
|490.9474
|592.8421 (250.D794<sub>16</sub>)
|592.8421 (250.D794<sub>16</sub>)
|-
|-
| style="text-align:center;" | 23
| style="text-align:center;" | 23
| style="text-align:right;" | 484.2105
| style="text-align:right;" | 484.2105
|513.2632
|619.7895 (26B.CA1B<sub>16</sub>)
|619.7895 (26B.CA1B<sub>16</sub>)
|-
|-
| style="text-align:center;" | 24
| style="text-align:center;" | 24
| style="text-align:right;" | 505.2632
| style="text-align:right;" | 505.2632
|535.57895
|646.7368 (286.BCA2<sub>16</sub>)
|646.7368 (286.BCA2<sub>16</sub>)
|-
|-
| style="text-align:center;" | 25
| style="text-align:center;" | 25
| style="text-align:right;" | 526.3158
| style="text-align:right;" | 526.3158
|557.8947
|673.6842 (2A1.AF29<sub>16</sub>)
|673.6842 (2A1.AF29<sub>16</sub>)
|-
|-
| style="text-align:center;" | 26
| style="text-align:center;" | 26
| style="text-align:right;" | 547.3684
| style="text-align:right;" | 547.3684
|580.2105
|700.6316 (2BC.A1AF<sub>16</sub>)
|700.6316 (2BC.A1AF<sub>16</sub>)
|-
|-
| style="text-align:center;" | 27
| style="text-align:center;" | 27
| style="text-align:right;" | 568.42105
| style="text-align:right;" | 568.42105
|602.5263
|727.57895 (2D7.9436<sub>16</sub>)
|727.57895 (2D7.9436<sub>16</sub>)
|-
|-
| style="text-align:center;" | 28
| style="text-align:center;" | 28
| style="text-align:right;" | 589.4737
| style="text-align:right;" | 589.4737
|624.8421
|754.5263 (2F2.86BD<sub>16</sub>)
|754.5263 (2F2.86BD<sub>16</sub>)
|-
|-
| style="text-align:center;" | 29
| style="text-align:center;" | 29
| style="text-align:right;" | 610.5263
| style="text-align:right;" | 610.5263
|647.1579
|781.4737 (30D.7943<sub>16</sub>)
|781.4737 (30D.7943<sub>16</sub>)
|-
|-
| style="text-align:center;" | 30
| style="text-align:center;" | 30
| style="text-align:right;" | 631.57895
| style="text-align:right;" | 631.57895
|669.4737
|808.42105 (328.6BCA<sub>16</sub>)
|808.42105 (328.6BCA<sub>16</sub>)
|-
|-
| style="text-align:center;" | 31
| style="text-align:center;" | 31
| style="text-align:right;" | 652.6316
| style="text-align:right;" | 652.6316
|691.7895
|835.3684 (343.5E51<sub>16</sub>)
|835.3684 (343.5E51<sub>16</sub>)
|-
|-
| style="text-align:center;" | 32
| style="text-align:center;" | 32
| style="text-align:right;" | 673.6842
| style="text-align:right;" | 673.6842
|714.1053
|862.3158 (35E.50D7<sub>16</sub>)
|862.3158 (35E.50D7<sub>16</sub>)
|-
|-
| style="text-align:center;" | 33
| style="text-align:center;" | 33
| style="text-align:right;" | 694.7368
| style="text-align:right;" | 694.7368
|736.42105
|889.2632 (37B.435E<sub>16</sub>)
|889.2632 (37B.435E<sub>16</sub>)
|-
|-
| style="text-align:center;" | 34
| style="text-align:center;" | 34
| style="text-align:right;" | 715.7895
| style="text-align:right;" | 715.7895
|758.7368
|916.2105 (394.35E5<sub>16</sub>)
|916.2105 (394.35E5<sub>16</sub>)
|-
|-
| style="text-align:center;" | 35
| style="text-align:center;" | 35
| style="text-align:right;" | 736.8421
| style="text-align:right;" | 736.8421
|781.0526
|943.1579 (3AF.286C<sub>16</sub>)
|943.1579 (3AF.286C<sub>16</sub>)
|-
|-
| style="text-align:center;" | 36
| style="text-align:center;" | 36
| style="text-align:right;" | 757.8947
| style="text-align:right;" | 757.8947
|803.3684
|970.1053 (3CA.1AF2<sub>16</sub>)
|970.1053 (3CA.1AF2<sub>16</sub>)
|-
|-
| style="text-align:center;" | 37
| style="text-align:center;" | 37
| style="text-align:right;" | 778.9474
| style="text-align:right;" | 778.9474
|825.6842
|997.0526 (3E5.0D79<sub>16</sub>)
|997.0526 (3E5.0D79<sub>16</sub>)
|-
|-
| style="text-align:center;" | 38
| style="text-align:center;" | 38
| style="text-align:right;" | 800
| style="text-align:right;" | 800
|848
|1024 (400<sub>16</sub>)
|1024 (400<sub>16</sub>)
|-
|-
| style="text-align:center;" | 39
| style="text-align:center;" | 39
| style="text-align:right;" | 821.0526
| style="text-align:right;" | 821.0526
|870.3158
|1050.9474 (41A.F287<sub>16</sub>)
|1050.9474 (41A.F287<sub>16</sub>)
|-
|-
| style="text-align:center;" | 40
| style="text-align:center;" | 40
| style="text-align:right;" | 842.1053
| style="text-align:right;" | 842.1053
|892.6316
|1077.8947 (435.E50E<sub>16</sub>)
|1077.8947 (435.E50E<sub>16</sub>)
|-
|-
| style="text-align:center;" | 41
| style="text-align:center;" | 41
| style="text-align:right;" | 863.1579
| style="text-align:right;" | 863.1579
|914.9474
|1104.8421 (450.D794<sub>16</sub>)
|1104.8421 (450.D794<sub>16</sub>)
|-
|-
| style="text-align:center;" | 42
| style="text-align:center;" | 42
| style="text-align:right;" | 884.2105
| style="text-align:right;" | 884.2105
|937.2632
|1131.7895 (46B.CA1B<sub>16</sub>)
|1131.7895 (46B.CA1B<sub>16</sub>)
|-
|-
| style="text-align:center;" | 43
| style="text-align:center;" | 43
| style="text-align:right;" | 905.2632
| style="text-align:right;" | 905.2632
|959.57895
|1158.7368 (486.BCA2<sub>16</sub>)
|1158.7368 (486.BCA2<sub>16</sub>)
|-
|-
| style="text-align:center;" | 44
| style="text-align:center;" | 44
| style="text-align:right;" | 926.3158
| style="text-align:right;" | 926.3158
|981.8947
|1175.6842 (4A1.AF29<sub>16</sub>)
|1175.6842 (4A1.AF29<sub>16</sub>)
|-
|-
| style="text-align:center;" | 45
| style="text-align:center;" | 45
| style="text-align:right;" | 947.3684
| style="text-align:right;" | 947.3684
|1004.2105
|1212.6316 (4BC.A1AF<sub>16</sub>)
|1212.6316 (4BC.A1AF<sub>16</sub>)
|-
|-
| style="text-align:center;" | 46
| style="text-align:center;" | 46
| style="text-align:right;" | 968.42105
| style="text-align:right;" | 968.42105
|1026.5263
|1239.57895 (4D7.9436<sub>16</sub>)
|1239.57895 (4D7.9436<sub>16</sub>)
|-
|-
| style="text-align:center;" | 47
| style="text-align:center;" | 47
| style="text-align:right;" | 989.4737
| style="text-align:right;" | 989.4737
|1048.8421
|1266.5263 (4F2.86BD<sub>16</sub>)
|1266.5263 (4F2.86BD<sub>16</sub>)
|-
|-
| style="text-align:center;" | 48
| style="text-align:center;" | 48
| style="text-align:right;" | 1010.5263
| style="text-align:right;" | 1010.5263
|1071.1579
|1293.4737 (50D.7943<sub>16</sub>)
|1293.4737 (50D.7943<sub>16</sub>)
|-
|-
| style="text-align:center;" | 49
| style="text-align:center;" | 49
| style="text-align:right;" | 1031.57895
| style="text-align:right;" | 1031.57895
|1093.4737
|1320.42105 (528.6BCA<sub>16</sub>)
|1320.42105 (528.6BCA<sub>16</sub>)
|-
|-
| style="text-align:center;" | 50
| style="text-align:center;" | 50
| style="text-align:right;" | 1052.6316
| style="text-align:right;" | 1052.6316
|1115.7895
|1347.3684 (543.5E51<sub>16</sub>)
|1347.3684 (543.5E51<sub>16</sub>)
|-
|-
| style="text-align:center;" | 51
| style="text-align:center;" | 51
| style="text-align:right;" | 1073.6842
| style="text-align:right;" | 1073.6842
|1138.1053
|1374.3158 (55E.50D7<sub>16</sub>)
|1374.3158 (55E.50D7<sub>16</sub>)
|-
|-
| style="text-align:center;" | 52
| style="text-align:center;" | 52
| style="text-align:right;" | 1094.7368
| style="text-align:right;" | 1094.7368
|1160.42105
|1401.2632 (57B.435E<sub>16</sub>)
|1401.2632 (57B.435E<sub>16</sub>)
|-
|-
| style="text-align:center;" | 53
| style="text-align:center;" | 53
| style="text-align:right;" | 1115.7895
| style="text-align:right;" | 1115.7895
|1182.7368
|1428.2105 (594.35E5<sub>16</sub>)
|1428.2105 (594.35E5<sub>16</sub>)
|-
|-
| style="text-align:center;" | 54
| style="text-align:center;" | 54
| style="text-align:right;" | 1136.8421
| style="text-align:right;" | 1136.8421
|1205.0526
|1455.1579 (5AF.286C<sub>16</sub>)
|1455.1579 (5AF.286C<sub>16</sub>)
|-
|-
| style="text-align:center;" | 55
| style="text-align:center;" | 55
| style="text-align:right;" | 1157.8947
| style="text-align:right;" | 1157.8947
|1227.3684
|1482.1053 (5CA.1AF2<sub>16</sub>)
|1482.1053 (5CA.1AF2<sub>16</sub>)
|-
|-
| style="text-align:center;" | 56
| style="text-align:center;" | 56
| style="text-align:right;" | 1178.9474
| style="text-align:right;" | 1178.9474
|1249.6842
|1509.0526 (5E5.0D79<sub>16</sub>)
|1509.0526 (5E5.0D79<sub>16</sub>)
|-
|-
| style="text-align:center;" | 57
| style="text-align:center;" | 57
| style="text-align:right;" | 1200
| style="text-align:right;" | 1200
|1272
|1536 (600<sub>16</sub>)
|1536 (600<sub>16</sub>)
|}
|}

Revision as of 13:22, 12 December 2019

57 tone equal temperament

57edo divides the octave into 57 parts of size 21.053. It can be used to tune mothra temperament, and is an excellent tuning for the 2.5/3.7.11.13.17.19 just intonation subgroup. One way to describe 57 is that it has a 5-limit part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the 19-limit 46&57 temperament Heinz.

5-limit commas: 81/80, 3125/3072

7-limit commas: 81/80, 3125/3072, 1029/1024

11-limit commas: 99/98, 385/384, 441/440, 625/616

Intervals

Degree Size
Cents 7mus
0 0.0000 0
1 21.0526 26.9474 (1A.F28716)
2 42.1053 53.8947 (35.E50E16)
3 63.1579 80.8421 (50.D79416)
4 84.2105 107.7895 (6B.CA1B16)
5 105.2632 134.7368 (86.BCA216)
6 126.3158 161.6842 (A1.AF2916)
7 147.3684 188.6316 (BC.A1AF16)
8 168.42105 215.57895 (D7.943616)
9 189.4737 242.5263 (F2.86BD16)
10 210.5263 269.4737 (10D.794316)
11 231.57895 296.42105 (128.6BCA16)
12 252.6316 323.3684 (143.5E5116)
13 273.6842 350.3158 (15E.50D716)
14 294.7368 377.2632 (17B.435E16)
15 315.7895 404.2105 (194.35E516)
16 336.8421 431.1579 (1AF.286C16)
17 357.8947 458.1053 (1CA.1AF216)
18 378.9474 485.0526 (1E5.0D7916)
19 400 512 (20016)
20 421.0526 538.9474 (21A.F28716)
21 442.1053 565.8947 (235.E50E16)
22 463.1579 592.8421 (250.D79416)
23 484.2105 619.7895 (26B.CA1B16)
24 505.2632 646.7368 (286.BCA216)
25 526.3158 673.6842 (2A1.AF2916)
26 547.3684 700.6316 (2BC.A1AF16)
27 568.42105 727.57895 (2D7.943616)
28 589.4737 754.5263 (2F2.86BD16)
29 610.5263 781.4737 (30D.794316)
30 631.57895 808.42105 (328.6BCA16)
31 652.6316 835.3684 (343.5E5116)
32 673.6842 862.3158 (35E.50D716)
33 694.7368 889.2632 (37B.435E16)
34 715.7895 916.2105 (394.35E516)
35 736.8421 943.1579 (3AF.286C16)
36 757.8947 970.1053 (3CA.1AF216)
37 778.9474 997.0526 (3E5.0D7916)
38 800 1024 (40016)
39 821.0526 1050.9474 (41A.F28716)
40 842.1053 1077.8947 (435.E50E16)
41 863.1579 1104.8421 (450.D79416)
42 884.2105 1131.7895 (46B.CA1B16)
43 905.2632 1158.7368 (486.BCA216)
44 926.3158 1175.6842 (4A1.AF2916)
45 947.3684 1212.6316 (4BC.A1AF16)
46 968.42105 1239.57895 (4D7.943616)
47 989.4737 1266.5263 (4F2.86BD16)
48 1010.5263 1293.4737 (50D.794316)
49 1031.57895 1320.42105 (528.6BCA16)
50 1052.6316 1347.3684 (543.5E5116)
51 1073.6842 1374.3158 (55E.50D716)
52 1094.7368 1401.2632 (57B.435E16)
53 1115.7895 1428.2105 (594.35E516)
54 1136.8421 1455.1579 (5AF.286C16)
55 1157.8947 1482.1053 (5CA.1AF216)
56 1178.9474 1509.0526 (5E5.0D7916)
57 1200 1536 (60016)

Modes of 57edo

2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)

Retrieved from "https://en.xen.wiki/index.php?title=57edo&oldid=42621"