57edo: Difference between revisions

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! [[Degree|Degree]]
! [[Degree|Degree]]
![[cent|Cents]]
![[cent|Cents]]
! [[Ups and downs notation]] (flat fifth 11\19)
! [[Ups and downs notation]] (sharp fifth 34\57)
|-
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0
| style="text-align:right;" | 0.0000
| style="text-align:right;" | 0.0000
| {{Ups and downs note name|step=0}}
| {{Ups and downs note name|fifth=34|step=0}}
|-
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:right;" | 21.0526
| style="text-align:right;" | 21.0526
| {{Ups and downs note name|step=1}}
| {{Ups and downs note name|fifth=34|step=1}}
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:right;" | 42.1053
| style="text-align:right;" | 42.1053
| {{Ups and downs note name|step=2}}
| {{Ups and downs note name|fifth=34|step=2}}
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:right;" | 63.1579
| style="text-align:right;" | 63.1579
| {{Ups and downs note name|step=3}}
| {{Ups and downs note name|fifth=34|step=3}}
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:right;" | 84.2105
| style="text-align:right;" | 84.2105
| {{Ups and downs note name|step=4}}
| {{Ups and downs note name|fifth=34|step=4}}
|-
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:right;" | 105.2632
| style="text-align:right;" | 105.2632
| {{Ups and downs note name|step=5}}
| {{Ups and downs note name|fifth=34|step=5}}
|-
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| style="text-align:right;" | 126.3158
| style="text-align:right;" | 126.3158
| {{Ups and downs note name|step=6}}
| {{Ups and downs note name|fifth=34|step=6}}
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| style="text-align:right;" | 147.3684
| style="text-align:right;" | 147.3684
| {{Ups and downs note name|step=7}}
| {{Ups and downs note name|fifth=34|step=7}}
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:right;" | 168.42105
| style="text-align:right;" | 168.42105
| {{Ups and downs note name|step=8}}
| {{Ups and downs note name|fifth=34|step=8}}
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| style="text-align:right;" | 189.4737
| style="text-align:right;" | 189.4737
| {{Ups and downs note name|step=9}}
| {{Ups and downs note name|fifth=34|step=9}}
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| style="text-align:right;" | 210.5263
| style="text-align:right;" | 210.5263
| {{Ups and downs note name|step=10}}
| {{Ups and downs note name|fifth=34|step=10}}
|-
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| style="text-align:right;" | 231.57895
| style="text-align:right;" | 231.57895
| {{Ups and downs note name|step=11}}
| {{Ups and downs note name|fifth=34|step=11}}
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| style="text-align:right;" | 252.6316
| style="text-align:right;" | 252.6316
| {{Ups and downs note name|step=12}}
| {{Ups and downs note name|fifth=34|step=12}}
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| style="text-align:right;" | 273.6842
| style="text-align:right;" | 273.6842
| {{Ups and downs note name|step=13}}
| {{Ups and downs note name|fifth=34|step=13}}
|-
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| style="text-align:right;" | 294.7368
| style="text-align:right;" | 294.7368
| {{Ups and downs note name|step=14}}
| {{Ups and downs note name|fifth=34|step=14}}
|-
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 15
| style="text-align:right;" | 315.7895
| style="text-align:right;" | 315.7895
| {{Ups and downs note name|step=15}}
| {{Ups and downs note name|fifth=34|step=15}}
|-
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| style="text-align:right;" | 336.8421
| style="text-align:right;" | 336.8421
| {{Ups and downs note name|step=16}}
| {{Ups and downs note name|fifth=34|step=16}}
|-
|-
| style="text-align:center;" | 17
| style="text-align:center;" | 17
| style="text-align:right;" | 357.8947
| style="text-align:right;" | 357.8947
| {{Ups and downs note name|step=17}}
| {{Ups and downs note name|fifth=34|step=17}}
|-
|-
| style="text-align:center;" | 18
| style="text-align:center;" | 18
| style="text-align:right;" | 378.9474
| style="text-align:right;" | 378.9474
| {{Ups and downs note name|step=18}}
| {{Ups and downs note name|fifth=34|step=18}}
|-
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 19
| style="text-align:right;" | 400
| style="text-align:right;" | 400
| {{Ups and downs note name|step=19}}
| {{Ups and downs note name|fifth=34|step=19}}
|-
|-
| style="text-align:center;" | 20
| style="text-align:center;" | 20
| style="text-align:right;" | 421.0526
| style="text-align:right;" | 421.0526
| {{Ups and downs note name|step=20}}
| {{Ups and downs note name|fifth=34|step=20}}
|-
|-
| style="text-align:center;" | 21
| style="text-align:center;" | 21
| style="text-align:right;" | 442.1053
| style="text-align:right;" | 442.1053
| {{Ups and downs note name|step=21}}
| {{Ups and downs note name|fifth=34|step=21}}
|-
|-
| style="text-align:center;" | 22
| style="text-align:center;" | 22
| style="text-align:right;" | 463.1579
| style="text-align:right;" | 463.1579
| {{Ups and downs note name|step=22}}
| {{Ups and downs note name|fifth=34|step=22}}
|-
|-
| style="text-align:center;" | 23
| style="text-align:center;" | 23
| style="text-align:right;" | 484.2105
| style="text-align:right;" | 484.2105
| {{Ups and downs note name|step=23}}
| {{Ups and downs note name|fifth=34|step=23}}
|-
|-
| style="text-align:center;" | 24
| style="text-align:center;" | 24
| style="text-align:right;" | 505.2632
| style="text-align:right;" | 505.2632
| {{Ups and downs note name|step=24}}
| {{Ups and downs note name|fifth=34|step=24}}
|-
|-
| style="text-align:center;" | 25
| style="text-align:center;" | 25
| style="text-align:right;" | 526.3158
| style="text-align:right;" | 526.3158
| {{Ups and downs note name|step=25}}
| {{Ups and downs note name|fifth=34|step=25}}
|-
|-
| style="text-align:center;" | 26
| style="text-align:center;" | 26
| style="text-align:right;" | 547.3684
| style="text-align:right;" | 547.3684
| {{Ups and downs note name|step=26}}
| {{Ups and downs note name|fifth=34|step=26}}
|-
|-
| style="text-align:center;" | 27
| style="text-align:center;" | 27
| style="text-align:right;" | 568.42105
| style="text-align:right;" | 568.42105
| {{Ups and downs note name|step=27}}
| {{Ups and downs note name|fifth=34|step=27}}
|-
|-
| style="text-align:center;" | 28
| style="text-align:center;" | 28
| style="text-align:right;" | 589.4737
| style="text-align:right;" | 589.4737
| {{Ups and downs note name|step=28}}
| {{Ups and downs note name|fifth=34|step=28}}
|-
|-
| style="text-align:center;" | 29
| style="text-align:center;" | 29
| style="text-align:right;" | 610.5263
| style="text-align:right;" | 610.5263
| {{Ups and downs note name|step=29}}
| {{Ups and downs note name|fifth=34|step=29}}
|-
|-
| style="text-align:center;" | 30
| style="text-align:center;" | 30
| style="text-align:right;" | 631.57895
| style="text-align:right;" | 631.57895
| {{Ups and downs note name|step=30}}
| {{Ups and downs note name|fifth=34|step=30}}
|-
|-
| style="text-align:center;" | 31
| style="text-align:center;" | 31
| style="text-align:right;" | 652.6316
| style="text-align:right;" | 652.6316
| {{Ups and downs note name|step=31}}
| {{Ups and downs note name|fifth=34|step=31}}
|-
|-
| style="text-align:center;" | 32
| style="text-align:center;" | 32
| style="text-align:right;" | 673.6842
| style="text-align:right;" | 673.6842
| {{Ups and downs note name|step=32}}
| {{Ups and downs note name|fifth=34|step=32}}
|-
|-
| style="text-align:center;" | 33
| style="text-align:center;" | 33
| style="text-align:right;" | 694.7368
| style="text-align:right;" | 694.7368
| {{Ups and downs note name|step=33}}
| {{Ups and downs note name|fifth=34|step=33}}
|-
|-
| style="text-align:center;" | 34
| style="text-align:center;" | 34
| style="text-align:right;" | 715.7895
| style="text-align:right;" | 715.7895
| {{Ups and downs note name|step=34}}
| {{Ups and downs note name|fifth=34|step=34}}
|-
|-
| style="text-align:center;" | 35
| style="text-align:center;" | 35
| style="text-align:right;" | 736.8421
| style="text-align:right;" | 736.8421
| {{Ups and downs note name|step=35}}
| {{Ups and downs note name|fifth=34|step=35}}
|-
|-
| style="text-align:center;" | 36
| style="text-align:center;" | 36
| style="text-align:right;" | 757.8947
| style="text-align:right;" | 757.8947
| {{Ups and downs note name|step=36}}
| {{Ups and downs note name|fifth=34|step=36}}
|-
|-
| style="text-align:center;" | 37
| style="text-align:center;" | 37
| style="text-align:right;" | 778.9474
| style="text-align:right;" | 778.9474
| {{Ups and downs note name|step=37}}
| {{Ups and downs note name|fifth=34|step=37}}
|-
|-
| style="text-align:center;" | 38
| style="text-align:center;" | 38
| style="text-align:right;" | 800
| style="text-align:right;" | 800
| {{Ups and downs note name|step=38}}
| {{Ups and downs note name|fifth=34|step=38}}
|-
|-
| style="text-align:center;" | 39
| style="text-align:center;" | 39
| style="text-align:right;" | 821.0526
| style="text-align:right;" | 821.0526
| {{Ups and downs note name|step=39}}
| {{Ups and downs note name|fifth=34|step=39}}
|-
|-
| style="text-align:center;" | 40
| style="text-align:center;" | 40
| style="text-align:right;" | 842.1053
| style="text-align:right;" | 842.1053
| {{Ups and downs note name|step=40}}
| {{Ups and downs note name|fifth=34|step=40}}
|-
|-
| style="text-align:center;" | 41
| style="text-align:center;" | 41
| style="text-align:right;" | 863.1579
| style="text-align:right;" | 863.1579
| {{Ups and downs note name|step=41}}
| {{Ups and downs note name|fifth=34|step=41}}
|-
|-
| style="text-align:center;" | 42
| style="text-align:center;" | 42
| style="text-align:right;" | 884.2105
| style="text-align:right;" | 884.2105
| {{Ups and downs note name|step=42}}
| {{Ups and downs note name|fifth=34|step=42}}
|-
|-
| style="text-align:center;" | 43
| style="text-align:center;" | 43
| style="text-align:right;" | 905.2632
| style="text-align:right;" | 905.2632
| {{Ups and downs note name|step=43}}
| {{Ups and downs note name|fifth=34|step=43}}
|-
|-
| style="text-align:center;" | 44
| style="text-align:center;" | 44
| style="text-align:right;" | 926.3158
| style="text-align:right;" | 926.3158
| {{Ups and downs note name|step=44}}
| {{Ups and downs note name|fifth=34|step=44}}
|-
|-
| style="text-align:center;" | 45
| style="text-align:center;" | 45
| style="text-align:right;" | 947.3684
| style="text-align:right;" | 947.3684
| {{Ups and downs note name|step=45}}
| {{Ups and downs note name|fifth=34|step=45}}
|-
|-
| style="text-align:center;" | 46
| style="text-align:center;" | 46
| style="text-align:right;" | 968.42105
| style="text-align:right;" | 968.42105
| {{Ups and downs note name|step=46}}
| {{Ups and downs note name|fifth=34|step=46}}
|-
|-
| style="text-align:center;" | 47
| style="text-align:center;" | 47
| style="text-align:right;" | 989.4737
| style="text-align:right;" | 989.4737
| {{Ups and downs note name|step=47}}
| {{Ups and downs note name|fifth=34|step=47}}
|-
|-
| style="text-align:center;" | 48
| style="text-align:center;" | 48
| style="text-align:right;" | 1010.5263
| style="text-align:right;" | 1010.5263
| {{Ups and downs note name|step=48}}
| {{Ups and downs note name|fifth=34|step=48}}
|-
|-
| style="text-align:center;" | 49
| style="text-align:center;" | 49
| style="text-align:right;" | 1031.57895
| style="text-align:right;" | 1031.57895
| {{Ups and downs note name|step=49}}
| {{Ups and downs note name|fifth=34|step=49}}
|-
|-
| style="text-align:center;" | 50
| style="text-align:center;" | 50
| style="text-align:right;" | 1052.6316
| style="text-align:right;" | 1052.6316
| {{Ups and downs note name|step=50}}
| {{Ups and downs note name|fifth=34|step=50}}
|-
|-
| style="text-align:center;" | 51
| style="text-align:center;" | 51
| style="text-align:right;" | 1073.6842
| style="text-align:right;" | 1073.6842
| {{Ups and downs note name|step=51}}
| {{Ups and downs note name|fifth=34|step=51}}
|-
|-
| style="text-align:center;" | 52
| style="text-align:center;" | 52
| style="text-align:right;" | 1094.7368
| style="text-align:right;" | 1094.7368
| {{Ups and downs note name|step=52}}
| {{Ups and downs note name|fifth=34|step=52}}
|-
|-
| style="text-align:center;" | 53
| style="text-align:center;" | 53
| style="text-align:right;" | 1115.7895
| style="text-align:right;" | 1115.7895
| {{Ups and downs note name|step=53}}
| {{Ups and downs note name|fifth=34|step=53}}
|-
|-
| style="text-align:center;" | 54
| style="text-align:center;" | 54
| style="text-align:right;" | 1136.8421
| style="text-align:right;" | 1136.8421
| {{Ups and downs note name|step=54}}
| {{Ups and downs note name|fifth=34|step=54}}
|-
|-
| style="text-align:center;" | 55
| style="text-align:center;" | 55
| style="text-align:right;" | 1157.8947
| style="text-align:right;" | 1157.8947
| {{Ups and downs note name|step=55}}
| {{Ups and downs note name|fifth=34|step=55}}
|-
|-
| style="text-align:center;" | 56
| style="text-align:center;" | 56
| style="text-align:right;" | 1178.9474
| style="text-align:right;" | 1178.9474
| {{Ups and downs note name|step=56}}
| {{Ups and downs note name|fifth=34|step=56}}
|-
|-
| style="text-align:center;" | 57
| style="text-align:center;" | 57
| style="text-align:right;" | 1200
| style="text-align:right;" | 1200
| {{Ups and downs note name|step=57}}
| {{Ups and downs note name|fifth=34|step=57}}
|}
|}


Revision as of 02:09, 13 June 2023

← 56edo 57edo 58edo →
Prime factorization 3 × 19
Step size 21.0526 ¢ 
Fifth 33\57 (694.737 ¢) (→ 11\19)
Semitones (A1:m2) 3:6 (63.16 ¢ : 126.3 ¢)
Dual sharp fifth 34\57 (715.789 ¢)
Dual flat fifth 33\57 (694.737 ¢) (→ 11\19)
Dual major 2nd 10\57 (210.526 ¢)
Consistency limit 7
Distinct consistency limit 7

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

Just approximation

Script error: No such module "primes_in_edo".

Intervals

Degree Cents Ups and downs notation (flat fifth 11\19) Ups and downs notation (sharp fifth 34\57)
0 0.0000 D D
1 21.0526 ^D, ^E♭♭♭ ^D, E♭
2 42.1053 vD♯, vE♭♭ ^^D, ^E♭
3 63.1579 D♯, E♭♭ ^3D, ^^E♭
4 84.2105 ^D♯, ^E♭♭ ^4D, ^3E♭
5 105.2632 vD𝄪, vE♭ ^5D, ^4E♭
6 126.3158 D𝄪, E♭ v4D♯, v5E
7 147.3684 ^D𝄪, ^E♭ v3D♯, v4E
8 168.42105 vD♯𝄪, vE vvD♯, v3E
9 189.4737 E vD♯, vvE
10 210.5263 ^E, ^F♭♭ D♯, vE
11 231.57895 vE♯, vF♭ E
12 252.6316 E♯, F♭ F
13 273.6842 ^E♯, ^F♭ ^F, G♭
14 294.7368 vE𝄪, vF ^^F, ^G♭
15 315.7895 F ^3F, ^^G♭
16 336.8421 ^F, ^G♭♭♭ ^4F, ^3G♭
17 357.8947 vF♯, vG♭♭ ^5F, ^4G♭
18 378.9474 F♯, G♭♭ v4F♯, v5G
19 400 ^F♯, ^G♭♭ v3F♯, v4G
20 421.0526 vF𝄪, vG♭ vvF♯, v3G
21 442.1053 F𝄪, G♭ vF♯, vvG
22 463.1579 ^F𝄪, ^G♭ F♯, vG
23 484.2105 vF♯𝄪, vG G
24 505.2632 G ^G, A♭
25 526.3158 ^G, ^A♭♭♭ ^^G, ^A♭
26 547.3684 vG♯, vA♭♭ ^3G, ^^A♭
27 568.42105 G♯, A♭♭ ^4G, ^3A♭
28 589.4737 ^G♯, ^A♭♭ ^5G, ^4A♭
29 610.5263 vG𝄪, vA♭ v4G♯, v5A
30 631.57895 G𝄪, A♭ v3G♯, v4A
31 652.6316 ^G𝄪, ^A♭ vvG♯, v3A
32 673.6842 vG♯𝄪, vA vG♯, vvA
33 694.7368 A G♯, vA
34 715.7895 ^A, ^B♭♭♭ A
35 736.8421 vA♯, vB♭♭ ^A, B♭
36 757.8947 A♯, B♭♭ ^^A, ^B♭
37 778.9474 ^A♯, ^B♭♭ ^3A, ^^B♭
38 800 vA𝄪, vB♭ ^4A, ^3B♭
39 821.0526 A𝄪, B♭ ^5A, ^4B♭
40 842.1053 ^A𝄪, ^B♭ v4A♯, v5B
41 863.1579 vA♯𝄪, vB v3A♯, v4B
42 884.2105 B vvA♯, v3B
43 905.2632 ^B, ^C♭♭ vA♯, vvB
44 926.3158 vB♯, vC♭ A♯, vB
45 947.3684 B♯, C♭ B
46 968.42105 ^B♯, ^C♭ C
47 989.4737 vB𝄪, vC ^C, D♭
48 1010.5263 C ^^C, ^D♭
49 1031.57895 ^C, ^D♭♭♭ ^3C, ^^D♭
50 1052.6316 vC♯, vD♭♭ ^4C, ^3D♭
51 1073.6842 C♯, D♭♭ ^5C, ^4D♭
52 1094.7368 ^C♯, ^D♭♭ v4C♯, v5D
53 1115.7895 vC𝄪, vD♭ v3C♯, v4D
54 1136.8421 C𝄪, D♭ vvC♯, v3D
55 1157.8947 ^C𝄪, ^D♭ vC♯, vvD
56 1178.9474 vC♯𝄪, vD C♯, vD
57 1200 D D

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)

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