58edf: Difference between revisions

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Created page with "'''Division of the just perfect fifth into 58 equal parts''' (58EDF) is related to 99 edo, but with the 3/2 rather than the 2/1 being just. The octave is abo..."
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Lookalikes: [[99edo]], [[157edt]]
Lookalikes: [[99edo]], [[157edt]]
 
{| class="wikitable"
|-
! |Degrees
! |Cents Value
|Five limit
|Seven limit
|Eleven limit
|Thirteen limit
|-
| |1
| |12.1027
|2048/2025
|126/125
|99/98
|91/90
|-
| |2
| |24.2053
|81/80
|64/63
|55/54
|55/54
|-
| |3
| |36.308
|128/125
|49/48
|49/48
|49/48
|-
| |4
| |48.4107
|250/243
|36/35
|33/32
|33/32
|-
| |5
| |60.5134
|648/625
|28/27
|28/27
|26/25
|-
| |6
| |72.616
|25/24
|25/24
|22/21
|22/21
|-
| |7
| |84.7187
|256/243
|21/20
|21/20
|21/20
|-
| |8
| |96.8214
|135/128
|135/128
|81/77
|52/49
|-
| |9
| |108.92405
|16/15
|16/15
|16/15
|16/15
|-
| |10
| |121.0267
|2187/2048
|15/14
|15/14
|15/14
|-
| |11
| |133.1294
|27/25
|27/25
|27/25
|13/12
|-
| |12
| |145.2321
|625/576
|49/45
|49/45
|49/45
|-
| |13
| |157.3347
|800/729
|35/32
|11/10
|11/10
|-
| |14
| |169.4374
|1125/1024
|54/49
|54/49
|54/49
|-
| |15
| |181.54
|10/9
|10/9
|10/9
|10/9
|-
| |16
| |193.6428
|4096/3645
|28/25
|28/25
|28/25
|-
| |17
| |205.7454
|9/8
|9/8
|9/8
|9/8
|-
| |18
| |217.8481
|256/225
|245/216
|112/99
|91/80
|-
| |19
| |229.9508
|729/640
|8/7
|8/7
|8/7
|-
| |20
| |242.05345
|144/125
|144/125
|63/55
|52/45
|-
| |21
| |254.1561
|125/108
|81/70
|81/70
|15/13
|-
| |22
| |266.2587
|729/625
|7/6
|7/6
|7/6
|-
| |23
| |278.3615
|75/64
|75/64
|33/28
|33/28
|-
| |24
| |290.4641
|32/27
|32/27
|32/27
|13/11
|-
| |25
| |302.5668
|1215/1024
|25/21
|25/21
|25/21
|-
| |26
| |314.6695
|6/5
|6/5
|6/5
|6/5
|-
| |27
| |326.7722
|3125/2592
|98/81
|98/81
|91/75
|-
| |28
| |338.8748
|243/200
|128/105
|11/9
|11/9
|-
| |29
| |350.9775
|625/512
|49/40
|49/40
|49/40
|-
| |30
| |363.0802
|100/81
|100/81
|27/22
|16/13
|-
| |31
| |375.18285
|3888/3125
|56/45
|56/45
|56/45
|-
| |32
| |387.2855
|5/4
|5/4
|5/4
|5/4
|-
| |33
| |399.3882
|512/405
|63/50
|63/50
|49/39
|-
| |34
| |411.4909
|81/64
|80/63
|80/63
|33/26
|-
| |35
| |423.5935
|32/25
|32/25
|14/11
|14/11
|-
| |36
| |435.6962
|625/486
|9/7
|9/7
|9/7
|-
| |37
| |447.7989
|162/125
|35/27
|35/27
|13/10
|-
| |38
| |459.90155
|125/96
|64/49
|55/42
|55/42
|-
| |39
| |472.0042
|320/243
|21/16
|21/16
|21/16
|-
| |40
| |484.1069
|675/512
|250/189
|250/189
|65/49
|-
| |41
| |469.2096
|4/3
|4/3
|4/3
|4/3
|-
| |42
| |508.3122
|8192/6075
|75/56
|66/49
|66/49
|-
| |43
| |520.4149
|27/20
|27/20
|27/20
|27/20
|-
| |44
| |532.5176
|512/375
|49/36
|49/36
|49/36
|-
| |45
| |544.6203
|1000/729
|48/35
|11/8
|11/8
|-
| |46
| |556.7229
|864/625
|112/81
|112/81
|91/66
|-
| |47
| |568.8256
|25/18
|25/18
|25/18
|18/13
|-
| |48
| |580.9283
|1024/729
|7/5
|7/5
|7/5
|-
| |49
| |593.03095
|45/32
|45/32
|45/32
|45/32
|-
| |50
| |605.1336
|64/45
|64/45
|64/45
|64/45
|-
| |51
| |617.2362
|729/512
|10/7
|10/7
|10/7
|-
| |52
| |629.339
|36/25
|36/25
|36/25
|13/9
|-
| |53
| |641.4416
|625/432
|81/56
|81/56
|75/52
|-
| |54
| |653.5443
|729/500
|35/24
|16/11
|16/11
|-
| |55
| |665.647
|375/256
|72/49
|72/49
|72/49
|-
| |56
| |677.7497
|40/27
|40/27
|40/27
|40/27
|-
| |57
| |689.8523
|6075/4096
|112/75
|49/33
|49/33
|-
| |58
| |701.955
|3/2
|3/2
|3/2
|3/2
|-
| |59
| |714.0577
|1024/675
|189/125
|189/125
|91/60
|-
| |60
| |726.16035
|243/160
|32/21
|32/21
|32/21
|-
| |61
| |738.263
|192/125
|49/32
|49/32
|49/32
|-
| |62
| |750.3657
|125/81
|54/35
|54/35
|20/13
|-
| |63
| |762.4684
|972/625
|14/9
|14/9
|14/9
|-
| |64
| |774.571
|25/16
|25/16
|11/7
|11/7
|-
| |65
| |786.6737
|128/81
|63/40
|63/40
|52/33
|-
| |66
| |798.7764
|405/256
|100/63
|100/63
|78/49
|-
| |67
| |810.87905
|8/5
|8/5
|8/5
|8/5
|-
| |68
| |822.9817
|3125/1944
|45/28
|45/28
|45/28
|-
| |69
| |835.0844
|81/50
|81/50
|44/27
|13/8
|-
| |70
| |847.1871
|625/384
|49/30
|49/30
|49/30
|-
| |71
| |859.2897
|400/243
|105/64
|18/11
|18/11
|-
| |72
| |871.3924
|3375/2048
|81/49
|81/49
|81/49
|-
| |73
| |883.4951
|5/3
|5/3
|5/3
|5/3
|-
| |74
| |895.5978
|2048/1215
|42/25
|42/25
|42/25
|-
| |75
| |907.7004
|27/16
|27/16
|27/16
|22/13
|-
| |76
| |919.8031
|128/75
|128/75
|56/33
|56/33
|-
| |77
| |931.9058
|1250/729
|12/7
|12/7
|12/7
|-
| |78
| |944.00845
|216/125
|140/81
|140/81
|26/15
|-
| |79
| |956.1111
|125/72
|125/72
|110/63
|45/26
|-
| |80
| |968.2138
|1280/729
|7/4
|7/4
|7/4
|-
| |81
| |980.3165
|225/128
|225/128
|99/56
|99/56
|-
|82
|992.4191
|16/9
|16/9
|16/9
|16/9
|-
|83
|1004.5218
|3645/2048
|25/14
|25/14
|25/14
|-
|84
|1016.6245
|9/5
|9/5
|9/5
|9/5
|-
|85
|1028.7272
|2048/1125
|49/27
|49/27
|49/27
|-
|86
|1040.8298
|729/400
|64/35
|11/6
|11/6
|-
|87
|1052.9325
|1152/625
|90/49
|90/49
|90/49
|-
|88
|1065.0352
|50/27
|50/27
|50/27
|13/7
|-
|89
|1077.13785
|4096/2187
|28/15
|28/15
|28/15
|-
|90
|1089.2405
|15/8
|15/8
|15/8
|15/8
|-
|91
|1101.3432
|256/135
|189/100
|154/81
|49/26
|-
|92
|1113.4459
|243/128
|40/21
|40/21
|40/21
|-
|93
|1125.5485
|48/25
|48/25
|21/11
|21/11
|-
|94
|1137.6512
|625/324
|27/14
|27/14
|25/13
|-
|95
|1149.7539
|243/125
|35/18
|35/18
|35/18
|-
|96
|1161.8566
|125/64
|49/25
|49/25
|49/25
|-
|97
|1173.9592
|160/81
|63/32
|63/32
|63/32
|-
|98
|1186.0619
|2025/1024
|125/63
|125/63
|125/63
|-
|99
|1198.1646
|2/1
|2/1
|2/1
|2/1
|}
[[Category:Edf]]
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 02:44, 24 February 2019

Division of the just perfect fifth into 58 equal parts (58EDF) is related to 99 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). It is consistent to the 12-integer-limit. In comparison, 99edo is only consistent up to the 10-integer-limit.

Lookalikes: 99edo, 157edt

Degrees Cents Value Five limit Seven limit Eleven limit Thirteen limit
1 12.1027 2048/2025 126/125 99/98 91/90
2 24.2053 81/80 64/63 55/54 55/54
3 36.308 128/125 49/48 49/48 49/48
4 48.4107 250/243 36/35 33/32 33/32
5 60.5134 648/625 28/27 28/27 26/25
6 72.616 25/24 25/24 22/21 22/21
7 84.7187 256/243 21/20 21/20 21/20
8 96.8214 135/128 135/128 81/77 52/49
9 108.92405 16/15 16/15 16/15 16/15
10 121.0267 2187/2048 15/14 15/14 15/14
11 133.1294 27/25 27/25 27/25 13/12
12 145.2321 625/576 49/45 49/45 49/45
13 157.3347 800/729 35/32 11/10 11/10
14 169.4374 1125/1024 54/49 54/49 54/49
15 181.54 10/9 10/9 10/9 10/9
16 193.6428 4096/3645 28/25 28/25 28/25
17 205.7454 9/8 9/8 9/8 9/8
18 217.8481 256/225 245/216 112/99 91/80
19 229.9508 729/640 8/7 8/7 8/7
20 242.05345 144/125 144/125 63/55 52/45
21 254.1561 125/108 81/70 81/70 15/13
22 266.2587 729/625 7/6 7/6 7/6
23 278.3615 75/64 75/64 33/28 33/28
24 290.4641 32/27 32/27 32/27 13/11
25 302.5668 1215/1024 25/21 25/21 25/21
26 314.6695 6/5 6/5 6/5 6/5
27 326.7722 3125/2592 98/81 98/81 91/75
28 338.8748 243/200 128/105 11/9 11/9
29 350.9775 625/512 49/40 49/40 49/40
30 363.0802 100/81 100/81 27/22 16/13
31 375.18285 3888/3125 56/45 56/45 56/45
32 387.2855 5/4 5/4 5/4 5/4
33 399.3882 512/405 63/50 63/50 49/39
34 411.4909 81/64 80/63 80/63 33/26
35 423.5935 32/25 32/25 14/11 14/11
36 435.6962 625/486 9/7 9/7 9/7
37 447.7989 162/125 35/27 35/27 13/10
38 459.90155 125/96 64/49 55/42 55/42
39 472.0042 320/243 21/16 21/16 21/16
40 484.1069 675/512 250/189 250/189 65/49
41 469.2096 4/3 4/3 4/3 4/3
42 508.3122 8192/6075 75/56 66/49 66/49
43 520.4149 27/20 27/20 27/20 27/20
44 532.5176 512/375 49/36 49/36 49/36
45 544.6203 1000/729 48/35 11/8 11/8
46 556.7229 864/625 112/81 112/81 91/66
47 568.8256 25/18 25/18 25/18 18/13
48 580.9283 1024/729 7/5 7/5 7/5
49 593.03095 45/32 45/32 45/32 45/32
50 605.1336 64/45 64/45 64/45 64/45
51 617.2362 729/512 10/7 10/7 10/7
52 629.339 36/25 36/25 36/25 13/9
53 641.4416 625/432 81/56 81/56 75/52
54 653.5443 729/500 35/24 16/11 16/11
55 665.647 375/256 72/49 72/49 72/49
56 677.7497 40/27 40/27 40/27 40/27
57 689.8523 6075/4096 112/75 49/33 49/33
58 701.955 3/2 3/2 3/2 3/2
59 714.0577 1024/675 189/125 189/125 91/60
60 726.16035 243/160 32/21 32/21 32/21
61 738.263 192/125 49/32 49/32 49/32
62 750.3657 125/81 54/35 54/35 20/13
63 762.4684 972/625 14/9 14/9 14/9
64 774.571 25/16 25/16 11/7 11/7
65 786.6737 128/81 63/40 63/40 52/33
66 798.7764 405/256 100/63 100/63 78/49
67 810.87905 8/5 8/5 8/5 8/5
68 822.9817 3125/1944 45/28 45/28 45/28
69 835.0844 81/50 81/50 44/27 13/8
70 847.1871 625/384 49/30 49/30 49/30
71 859.2897 400/243 105/64 18/11 18/11
72 871.3924 3375/2048 81/49 81/49 81/49
73 883.4951 5/3 5/3 5/3 5/3
74 895.5978 2048/1215 42/25 42/25 42/25
75 907.7004 27/16 27/16 27/16 22/13
76 919.8031 128/75 128/75 56/33 56/33
77 931.9058 1250/729 12/7 12/7 12/7
78 944.00845 216/125 140/81 140/81 26/15
79 956.1111 125/72 125/72 110/63 45/26
80 968.2138 1280/729 7/4 7/4 7/4
81 980.3165 225/128 225/128 99/56 99/56
82 992.4191 16/9 16/9 16/9 16/9
83 1004.5218 3645/2048 25/14 25/14 25/14
84 1016.6245 9/5 9/5 9/5 9/5
85 1028.7272 2048/1125 49/27 49/27 49/27
86 1040.8298 729/400 64/35 11/6 11/6
87 1052.9325 1152/625 90/49 90/49 90/49
88 1065.0352 50/27 50/27 50/27 13/7
89 1077.13785 4096/2187 28/15 28/15 28/15
90 1089.2405 15/8 15/8 15/8 15/8
91 1101.3432 256/135 189/100 154/81 49/26
92 1113.4459 243/128 40/21 40/21 40/21
93 1125.5485 48/25 48/25 21/11 21/11
94 1137.6512 625/324 27/14 27/14 25/13
95 1149.7539 243/125 35/18 35/18 35/18
96 1161.8566 125/64 49/25 49/25 49/25
97 1173.9592 160/81 63/32 63/32 63/32
98 1186.0619 2025/1024 125/63 125/63 125/63
99 1198.1646 2/1 2/1 2/1 2/1
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