95ed5
| ← 94ed5 | 95ed5 | 96ed5 → |
Division of the 5th harmonic into 95 equal parts (95ed5) is related to 41 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 2.5143 cents stretched and the step size is about 29.3296 cents. This tuning has a generally sharp tendency for harmonics up to 12. Unlike 41edo, it is only consistent up to the 12-integer-limit, with discrepancy for the 13th harmonic.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 29.3296 | ||
| 2 | 58.6592 | 931/900 | |
| 3 | 87.9889 | 81/77, 20/19 | |
| 4 | 117.3185 | 1280/1197 | |
| 5 | 146.6481 | 209/192, 49/45 | |
| 6 | 175.9777 | 448/405 | |
| 7 | 205.3073 | ||
| 8 | 234.6369 | 63/55, 55/48 | |
| 9 | 263.9666 | 220/189 | |
| 10 | 293.2962 | ||
| 11 | 322.6258 | 135/112 | |
| 12 | 351.9554 | 60/49, 256/209 | |
| 13 | 381.2850 | 399/320 | pseudo-5/4 |
| 14 | 410.6147 | 19/15 | |
| 15 | 439.9443 | 1200/931 | |
| 16 | 469.2739 | 21/16 | |
| 17 | 498.6035 | 4/3 | |
| 18 | 527.9331 | ||
| 19 | 557.2627 | 243/176 | |
| 20 | 586.5924 | 108/77, 275/196, 80/57 | |
| 21 | 615.9220 | ||
| 22 | 645.2516 | 209/144, 196/135 | |
| 23 | 674.5812 | 2025/1372 | |
| 24 | 703.9108 | 1539/1024 | pseudo-3/2 |
| 25 | 733.2405 | 171/112, 84/55, 55/36 | |
| 26 | 762.5701 | ||
| 27 | 791.8997 | ||
| 28 | 821.2293 | 45/28 | |
| 29 | 850.5589 | 1024/627 | |
| 30 | 879.8885 | 133/80 | pseudo-5/3 |
| 31 | 909.2182 | 1232/729, 3645/2156, 225/133 | |
| 32 | 938.5478 | ||
| 33 | 967.8774 | 7/4 | |
| 34 | 997.2070 | 16/9 | |
| 35 | 1026.5366 | ||
| 36 | 1055.8662 | 81/44 | |
| 37 | 1085.1959 | 144/77, 275/147, 320/171 | |
| 38 | 1114.5255 | ||
| 39 | 1143.8551 | 209/108, 405/209 | |
| 40 | 1173.1847 | 675/343 | |
| 41 | 1202.5143 | 513/256, 441/220 | pseudo-octave |
| 42 | 1231.8440 | 57/28, 112/55, 55/27 | |
| 43 | 1261.1736 | ||
| 44 | 1290.5032 | ||
| 45 | 1319.8328 | 15/7 | |
| 46 | 1349.1624 | ||
| 47 | 1378.4920 | 133/60, 539/243 | |
| 48 | 1407.8217 | 1215/539, 300/133 | |
| 49 | 1437.1513 | ||
| 50 | 1466.4809 | 7/3 | |
| 51 | 1495.8105 | ||
| 52 | 1525.1401 | ||
| 53 | 1554.4698 | 27/11, 275/112, 140/57 | |
| 54 | 1583.7994 | 1100/441, 1280/513 | pseudo-5/2 |
| 55 | 1613.1290 | 343/135 | |
| 56 | 1642.4586 | 209/81, 540/209 | |
| 57 | 1671.7882 | ||
| 58 | 1701.1178 | 171/64, 147/55, 385/144 | |
| 59 | 1730.4475 | 220/81 | |
| 60 | 1759.7771 | ||
| 61 | 1789.1067 | 45/16 | |
| 62 | 1818.4363 | 20/7 | |
| 63 | 1847.7659 | ||
| 64 | 1877.0956 | 133/45, 2156/729, 3645/1232 | |
| 65 | 1906.4252 | 400/133 | pseudo-3/1 |
| 66 | 1935.7548 | 3135/1024 | |
| 67 | 1965.0844 | 28/9 | |
| 68 | 1994.4140 | ||
| 69 | 2023.7436 | ||
| 70 | 2053.0733 | 36/11, 275/84, 560/171 | |
| 71 | 2082.4029 | 5120/1539 | pseudo-10/3 |
| 72 | 2111.7325 | 1372/405 | |
| 73 | 2141.0621 | 675/196, 720/209 | |
| 74 | 2170.3917 | ||
| 75 | 2199.7214 | 57/16, 196/55, 385/108 | |
| 76 | 2229.0510 | 880/243 | |
| 77 | 2258.3806 | ||
| 78 | 2287.7102 | 15/4 | |
| 79 | 2317.0398 | 80/21 | |
| 80 | 2346.3694 | 931/240 | |
| 81 | 2375.6991 | 75/19 | |
| 82 | 2405.0287 | 1600/399 | pseudo-4/1 |
| 83 | 2434.3583 | 1045/256, 49/12 | |
| 84 | 2463.6879 | 112/27 | |
| 85 | 2493.0175 | ||
| 86 | 2522.3472 | 189/44 | |
| 87 | 2551.6768 | 48/11, 275/63 | |
| 88 | 2581.0064 | ||
| 89 | 2610.3360 | 2025/448 | |
| 90 | 2639.6656 | 225/49, 960/209 | |
| 91 | 2668.9952 | 1197/256 | |
| 92 | 2698.3249 | 19/4, 385/81 | |
| 93 | 2727.6545 | 4500/931 | |
| 94 | 2756.9841 | ||
| 95 | 2786.3137 | exact 5/1 | just major third plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.5 | +4.5 | +5.0 | +0.0 | +7.0 | +4.1 | +7.5 | +8.9 | +2.5 | +13.5 | +9.5 |
| Relative (%) | +8.6 | +15.2 | +17.1 | +0.0 | +23.8 | +13.9 | +25.7 | +30.5 | +8.6 | +46.0 | +32.4 | |
| Steps (reduced) |
41 (41) |
65 (65) |
82 (82) |
95 (0) |
106 (11) |
115 (20) |
123 (28) |
130 (35) |
136 (41) |
142 (47) |
147 (52) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.8 | +6.6 | +4.5 | +10.1 | -6.9 | +11.5 | +5.8 | +5.0 | +8.6 | -13.3 | -2.3 |
| Relative (%) | -40.1 | +22.5 | +15.2 | +34.3 | -23.6 | +39.1 | +19.9 | +17.1 | +29.2 | -45.4 | -7.8 | |
| Steps (reduced) |
151 (56) |
156 (61) |
160 (65) |
164 (69) |
167 (72) |
171 (76) |
174 (79) |
177 (82) |
180 (85) |
182 (87) |
185 (90) | |
95ed5 as a generator
95ed5 can also be thought of as a generator of the 2.3.5.7.11.19 subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a cluster temperament with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384 ~ 441/440 ~ 1479016/1476225 ~ 194579/194400 ~ 204800/204687 ~ 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by 41edo, 491edo (491e val), and 532edo (532d val) among others.