59edt
← 58edt | 59edt | 60edt → |
59EDT is the equal division of the third harmonic into 59 parts of 32.2365 cents each, corresponding to 37.2249 edo. It is related to the regular temperament which tempers out |413 -347 59> in the 5-limit, which is supported by 335, 1489, 1824, 2159, 2494, 2829, and 3164 EDOs.
Intervals
Steps | Cents | Hekts | Approximate ratios |
---|---|---|---|
0 | 0 | 0 | 1/1 |
1 | 32.2 | 22 | |
2 | 64.5 | 44.1 | 27/26, 28/27, 29/28 |
3 | 96.7 | 66.1 | 18/17, 19/18 |
4 | 128.9 | 88.1 | 14/13 |
5 | 161.2 | 110.2 | 34/31 |
6 | 193.4 | 132.2 | 19/17, 29/26 |
7 | 225.7 | 154.2 | 33/29 |
8 | 257.9 | 176.3 | 22/19 |
9 | 290.1 | 198.3 | 13/11 |
10 | 322.4 | 220.3 | |
11 | 354.6 | 242.4 | 27/22 |
12 | 386.8 | 264.4 | 5/4 |
13 | 419.1 | 286.4 | 14/11 |
14 | 451.3 | 308.5 | |
15 | 483.5 | 330.5 | |
16 | 515.8 | 352.5 | 31/23 |
17 | 548 | 374.6 | |
18 | 580.3 | 396.6 | |
19 | 612.5 | 418.6 | 27/19 |
20 | 644.7 | 440.7 | |
21 | 677 | 462.7 | 34/23 |
22 | 709.2 | 484.7 | |
23 | 741.4 | 506.8 | 23/15 |
24 | 773.7 | 528.8 | 25/16 |
25 | 805.9 | 550.8 | |
26 | 838.1 | 572.9 | |
27 | 870.4 | 594.9 | |
28 | 902.6 | 616.9 | |
29 | 934.9 | 639 | |
30 | 967.1 | 661 | |
31 | 999.3 | 683.1 | |
32 | 1031.6 | 705.1 | |
33 | 1063.8 | 727.1 | |
34 | 1096 | 749.2 | |
35 | 1128.3 | 771.2 | 23/12 |
36 | 1160.5 | 793.2 | |
37 | 1192.8 | 815.3 | |
38 | 1225 | 837.3 | |
39 | 1257.2 | 859.3 | 29/14, 31/15 |
40 | 1289.5 | 881.4 | 19/9 |
41 | 1321.7 | 903.4 | |
42 | 1353.9 | 925.4 | |
43 | 1386.2 | 947.5 | 29/13 |
44 | 1418.4 | 969.5 | 34/15 |
45 | 1450.6 | 991.5 | |
46 | 1482.9 | 1013.6 | 33/14 |
47 | 1515.1 | 1035.6 | 12/5 |
48 | 1547.4 | 1057.6 | 22/9 |
49 | 1579.6 | 1079.7 | |
50 | 1611.8 | 1101.7 | 33/13 |
51 | 1644.1 | 1123.7 | 31/12 |
52 | 1676.3 | 1145.8 | 29/11 |
53 | 1708.5 | 1167.8 | |
54 | 1740.8 | 1189.8 | |
55 | 1773 | 1211.9 | |
56 | 1805.2 | 1233.9 | 17/6 |
57 | 1837.5 | 1255.9 | 26/9 |
58 | 1869.7 | 1278 | |
59 | 1902 | 1300 | 3/1 |
Prime harmonics
Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -7.2 | +0.0 | -14.0 | +16.0 | +7.2 | +8.1 | -5.0 | -4.1 | -12.5 | +5.2 | -13.5 |
Relative (%) | -22.5 | +0.0 | -43.3 | +49.7 | +22.3 | +25.2 | -15.5 | -12.8 | -38.9 | +16.2 | -41.9 | |
Steps (reduced) |
37 (37) |
59 (0) |
86 (27) |
105 (46) |
129 (11) |
138 (20) |
152 (34) |
158 (40) |
168 (50) |
181 (4) |
184 (7) |
Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +2.5 | -14.0 | +0.3 | +7.5 | -7.1 | +0.6 | +7.4 | +6.1 | +2.5 | -13.4 | +11.0 |
Relative (%) | +7.9 | -43.4 | +0.8 | +23.1 | -22.1 | +1.9 | +22.9 | +19.1 | +7.7 | -41.5 | +34.3 | |
Steps (reduced) |
194 (17) |
199 (22) |
202 (25) |
207 (30) |
213 (36) |
219 (42) |
221 (44) |
226 (49) |
229 (52) |
230 (53) |
235 (58) |
Related regular temperaments
149&186 temperament
5-limit
Comma: |118 12 -59>
POTE generator: ~3125/3072 = 32.2390
Map: [<1 0 2|, <0 59 12|]
EDOs: 37, 149, 186, 335, 484, 521
7-limit 149&186
Commas: 3136/3125, 49433168575/48922361856
POTE generator: ~49/48 = 32.2368
Map: [<1 0 2 2|, <0 59 12 30|]
7-limit 149d&186
Commas: 1280000000/1275989841, 8589934592/8544921875
POTE generator: ~3125/3072 = 32.2456
Map: [<1 0 2 7|, <0 59 12 -156|]
EDOs: 149d, 186, 335d, 521, 707
7-limit 149&186d
Commas: 29360128/29296875, 1937102445/1927561216
POTE generator: ~3125/3072 = 32.2308
Map: [<1 0 2 -2|, <0 59 12 179|]
EDOs: 149, 186d, 335d, 484, 633
335&2159 temperament
5-limit
Comma: |413 -347 59>
POTE generator: ~|-119 100 -17> = 32.2373
Map: [<1 0 -7|, <0 59 347|]