61ed7
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Prime factorization
61 (prime)
Step size
55.2267¢
Octave
22\61ed7 (1214.99¢)
Twelfth
34\61ed7 (1877.71¢)
Consistency limit
2
Distinct consistency limit
2
| ← 60ed7 | 61ed7 | 62ed7 → |
Division of the 7th harmonic into 61 equal parts (61ed7) is related to the alphaquarter temperament, which tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit; 325/324, 364/363, 1001/1000, and 4096/4095 in the 13-limit. The step size is about 55.2267 cents, corresponding to 21.7286 edo.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 55.2267 | 33/32 | |
| 2 | 110.4533 | 16/15 | |
| 3 | 165.6800 | 11/10 | |
| 4 | 220.9066 | 25/22 | |
| 5 | 276.1333 | 88/75 | |
| 6 | 331.3599 | 40/33 | |
| 7 | 386.5866 | 5/4 | |
| 8 | 441.8132 | (49/38) | |
| 9 | 497.0399 | 4/3 | |
| 10 | 552.2665 | 11/8 | |
| 11 | 607.4932 | (91/64), 64/45 | |
| 12 | 662.7199 | 22/15 | |
| 13 | 717.9465 | 50/33 | |
| 14 | 773.1732 | 25/16 | |
| 15 | 828.3998 | ||
| 16 | 883.6265 | 5/3 | |
| 17 | 938.8531 | 55/32 | |
| 18 | 994.0798 | 16/9 | |
| 19 | 1049.3064 | 11/6 | |
| 20 | 1104.5331 | ||
| 21 | 1159.7597 | ||
| 22 | 1214.9864 | ||
| 23 | 1270.2130 | 25/12 | |
| 24 | 1325.4397 | ||
| 25 | 1380.6664 | 20/9 | |
| 26 | 1435.8930 | 55/24 | |
| 27 | 1491.1197 | ||
| 28 | 1546.3463 | ||
| 29 | 1601.5730 | 63/25 | |
| 30 | 1656.7996 | ||
| 31 | 1712.0263 | ||
| 32 | 1767.2529 | 25/9 | |
| 33 | 1822.4796 | ||
| 34 | 1877.7062 | ||
| 35 | 1932.9329 | ||
| 36 | 1988.1596 | ||
| 37 | 2043.3862 | 88/27 | |
| 38 | 2098.6129 | 84/25 | |
| 39 | 2153.8395 | ||
| 40 | 2209.0662 | (68/19) | |
| 41 | 2264.2928 | 100/27 | |
| 42 | 2319.5195 | 42/11 | |
| 43 | 2374.7461 | 63/16 | |
| 44 | 2429.9728 | (57/14), 224/55, 110/27 | |
| 45 | 2485.1994 | 21/5 | |
| 46 | 2540.4261 | (13/3) | |
| 47 | 2595.6527 | ||
| 48 | 2650.8794 | ||
| 49 | 2706.1061 | 105/22 | |
| 50 | 2761.3327 | (64/13) | |
| 51 | 2816.5594 | 56/11 | |
| 52 | 2871.7860 | 21/4 | |
| 53 | 2927.0127 | (38/7) | |
| 54 | 2982.2393 | 28/5 | |
| 55 | 3037.4660 | (52/9) | |
| 56 | 3092.6926 | ||
| 57 | 3147.9193 | (80/13) | |
| 58 | 3203.1459 | 70/11 | |
| 59 | 3258.3726 | 105/16 | |
| 60 | 3313.5993 | (88/13) | |
| 61 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +15.0 | -24.2 | -25.3 | -25.0 | -9.3 | +0.0 | -10.3 | +6.7 | -10.0 | -9.3 | +5.7 |
| Relative (%) | +27.1 | -43.9 | -45.7 | -45.2 | -16.8 | +0.0 | -18.6 | +12.2 | -18.1 | -16.9 | +10.4 | |
| Steps (reduced) |
22 (22) |
34 (34) |
43 (43) |
50 (50) |
56 (56) |
61 (0) |
65 (4) |
69 (8) |
72 (11) |
75 (14) |
78 (17) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -22.4 | +15.0 | +6.0 | +4.7 | +10.2 | +21.7 | -16.7 | +5.0 | -24.2 | +5.7 | -16.1 |
| Relative (%) | -40.6 | +27.1 | +10.9 | +8.5 | +18.5 | +39.3 | -30.2 | +9.0 | -43.9 | +10.3 | -29.1 | |
| Steps (reduced) |
80 (19) |
83 (22) |
85 (24) |
87 (26) |
89 (28) |
91 (30) |
92 (31) |
94 (33) |
95 (34) |
97 (36) |
98 (37) | |