58edf
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Prime factorization
2 × 29
Step size
12.1027¢
Octave
99\58edf (1198.16¢)
Twelfth
157\58edf (1900.12¢)
Consistency limit
12
Distinct consistency limit
9
← 57edf | 58edf | 59edf → |
Division of the just perfect fifth into 58 equal parts (58EDF) is related to 99edo, 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.
Intervals
todo: mapping for 11 and 13 should differ from 99edo
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 | |
3 | 36.308 | 128/125 | 49/48 | ||
4 | 48.4107 | 250/243 | 36/35 | 33/32 | |
5 | 60.5134 | 648/625 | 28/27 | 26/25 | |
6 | 72.616 | 25/24 | 22/21 | ||
7 | 84.7187 | 256/243 | 21/20 | ||
8 | 96.8214 | 135/128 | 81/77 | 52/49 | |
9 | 108.92405 | 16/15 | |||
10 | 121.0267 | 2187/2048 | 15/14 | ||
11 | 133.1294 | 27/25 | 13/12 | ||
12 | 145.2321 | 625/576 | 49/45 | ||
13 | 157.3347 | 800/729 | 35/32 | 11/10 | |
14 | 169.4374 | 1125/1024 | 54/49 | ||
15 | 181.54 | 10/9 | 10/9 | ||
16 | 193.6428 | 4096/3645 | 28/25 | ||
17 | 205.7454 | 9/8 | |||
18 | 217.8481 | 256/225 | 245/216 | 112/99 | 91/80 |
19 | 229.9508 | 729/640 | 8/7 | ||
20 | 242.05345 | 144/125 | 63/55 | 52/45 | |
21 | 254.1561 | 125/108 | 81/70 | 15/13 | |
22 | 266.2587 | 729/625 | 7/6 | ||
23 | 278.3615 | 75/64 | 33/28 | ||
24 | 290.4641 | 32/27 | 32/27 | 13/11 | |
25 | 302.5668 | 1215/1024 | 25/21 | ||
26 | 314.6695 | 6/5 | |||
27 | 326.7722 | 3125/2592 | 98/81 | 91/75 | |
28 | 338.8748 | 243/200 | 128/105 | 11/9 | |
29 | 350.9775 | 625/512 | 49/40 | ||
30 | 363.0802 | 100/81 | 27/22 | 16/13 | |
31 | 375.18285 | 3888/3125 | 56/45 | ||
32 | 387.2855 | 5/4 | |||
33 | 399.3882 | 512/405 | 63/50 | 49/39 | |
34 | 411.4909 | 81/64 | 80/63 | 33/26 | |
35 | 423.5935 | 32/25 | 14/11 | ||
36 | 435.6962 | 625/486 | 9/7 | ||
37 | 447.7989 | 162/125 | 35/27 | 13/10 | |
38 | 459.90155 | 125/96 | 64/49 | 55/42 | |
39 | 472.0042 | 320/243 | 21/16 | ||
40 | 484.1069 | 675/512 | 250/189 | 65/49 | |
41 | 469.2096 | 4/3 | |||
42 | 508.3122 | 8192/6075 | 75/56 | 66/49 | |
43 | 520.4149 | 27/20 | |||
44 | 532.5176 | 512/375 | 49/36 | ||
45 | 544.6203 | 1000/729 | 48/35 | 11/8 | |
46 | 556.7229 | 864/625 | 112/81 | 91/66 | |
47 | 568.8256 | 25/18 | 18/13 | ||
48 | 580.9283 | 1024/729 | 7/5 | ||
49 | 593.03095 | 45/32 | |||
50 | 605.1336 | 64/45 | |||
51 | 617.2362 | 729/512 | 10/7 | ||
52 | 629.339 | 36/25 | 13/9 | ||
53 | 641.4416 | 625/432 | 81/56 | 75/52 | |
54 | 653.5443 | 729/500 | 35/24 | 16/11 | |
55 | 665.647 | 375/256 | 72/49 | ||
56 | 677.7497 | 40/27 | |||
57 | 689.8523 | 6075/4096 | 112/75 | 49/33 | |
58 | 701.955 | 3/2 | |||
59 | 714.0577 | 1024/675 | 189/125 | 91/60 | |
60 | 726.16035 | 243/160 | 32/21 | ||
61 | 738.263 | 192/125 | 49/32 | ||
62 | 750.3657 | 125/81 | 54/35 | 20/13 | |
63 | 762.4684 | 972/625 | 14/9 | ||
64 | 774.571 | 25/16 | 11/7 | ||
65 | 786.6737 | 128/81 | 63/40 | 52/33 | |
66 | 798.7764 | 405/256 | 100/63 | 78/49 | |
67 | 810.87905 | 8/5 | |||
68 | 822.9817 | 3125/1944 | 45/28 | ||
69 | 835.0844 | 81/50 | 44/27 | 13/8 | |
70 | 847.1871 | 625/384 | 49/30 | ||
71 | 859.2897 | 400/243 | 105/64 | 18/11 | |
72 | 871.3924 | 3375/2048 | 81/49 | ||
73 | 883.4951 | 5/3 | |||
74 | 895.5978 | 2048/1215 | 42/25 | ||
75 | 907.7004 | 27/16 | 22/13 | ||
76 | 919.8031 | 128/75 | 56/33 | 56/33 | |
77 | 931.9058 | 1250/729 | 12/7 | ||
78 | 944.00845 | 216/125 | 140/81 | 26/15 | |
79 | 956.1111 | 125/72 | 110/63 | 45/26 | |
80 | 968.2138 | 1280/729 | 7/4 | ||
81 | 980.3165 | 225/128 | 225/128 | 99/56 | |
82 | 992.4191 | 16/9 | |||
83 | 1004.5218 | 3645/2048 | 25/14 | ||
84 | 1016.6245 | 9/5 | |||
85 | 1028.7272 | 2048/1125 | 49/27 | ||
86 | 1040.8298 | 729/400 | 64/35 | 11/6 | |
87 | 1052.9325 | 1152/625 | 90/49 | ||
88 | 1065.0352 | 50/27 | |||
89 | 1077.13785 | 4096/2187 | 28/15 | ||
90 | 1089.2405 | 15/8 | |||
91 | 1101.3432 | 256/135 | 189/100 | 154/81 | 49/26 |
92 | 1113.4459 | 243/128 | 40/21 | ||
93 | 1125.5485 | 48/25 | |||
94 | 1137.6512 | 625/324 | 27/14 | 25/13 | |
95 | 1149.7539 | 243/125 | 35/18 | 35/18 | |
96 | 1161.8566 | 125/64 | 49/25 | 49/25 | |
97 | 1173.9592 | 160/81 | 63/32 | ||
98 | 1186.0619 | 2025/1024 | 125/63 | ||
99 | 1198.1646 | 2/1 | |||
100 | 1210.2672 | 4096/2025 | 252/125 | 99/49 | 91/45 |
101 | 1222.3699 | 81/40 | 128/63 | 55/27 | |
102 | 1234.4726 | 256/125 | 49/24 | ||
103 | 1246.5753 | 500/243 | 72/35 | 33/16 | |
104 | 1258.6779 | 1296/625 | 56/27 | 52/25 | |
105 | 1270.7806 | 25/12 | 44/21 | ||
106 | 1282.8833 | 512/243 | 21/10 | ||
107 | 1294.98595 | 135/64 | 162/77 | 104/49 | |
108 | 1307.0886 | 32/15 | |||
109 | 1319.1913 | 2187/1024 | 15/7 | ||
110 | 1331.294 | 54/25 | 13/6 | ||
111 | 1343.3966 | 625/288 | 98/45 | ||
112 | 1355.4993 | 1600/729 | 35/16 | 11/5 | |
113 | 1367.602 | 1125/512 | 108/49 | ||
114 | 1379.7047 | 20/9 | |||
115 | 1391.8073 | 8192/3645 | 56/25 | ||
116 | 1403.91 | 9/4 |