87ed7
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Prime factorization
3 × 29
Step size
38.7221¢
Octave
31\87ed7 (1200.39¢)
(semiconvergent)
Twelfth
49\87ed7 (1897.38¢)
Consistency limit
12
Distinct consistency limit
9
| ← 86ed7 | 87ed7 | 88ed7 → |
(semiconvergent)
Division of the 7th harmonic into 87 equal parts (87ed7) is related to 31 edo, but with the 7/1 rather than the 2/1 being just. The octave is slightly stretched (about 0.3862 cents) and the step size is about 38.7221 cents.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 38.7221 | ||
| 2 | 77.4443 | ||
| 3 | 116.1664 | 77/72, 15/14 | |
| 4 | 154.8885 | ||
| 5 | 193.6107 | 19/17, 85/76 | |
| 6 | 232.3328 | 8/7 | |
| 7 | 271.0550 | ||
| 8 | 309.7771 | ||
| 9 | 348.4992 | 11/9, 49/40 | |
| 10 | 387.2214 | 5/4 | |
| 11 | 425.9435 | ||
| 12 | 464.6656 | 98/75 | |
| 13 | 503.3878 | 91/68, 75/56 | |
| 14 | 542.1099 | ||
| 15 | 580.8321 | 7/5 | |
| 16 | 619.5542 | 10/7 | |
| 17 | 658.2763 | ||
| 18 | 696.9985 | 112/75, 121/81, 136/91, 187/125 | |
| 19 | 735.7206 | ||
| 20 | 774.4427 | ||
| 21 | 813.1649 | 8/5 | |
| 22 | 851.8870 | ||
| 23 | 890.6091 | ||
| 24 | 929.3313 | 65/38 | |
| 25 | 968.0534 | ||
| 26 | 1006.7756 | ||
| 27 | 1045.4977 | 64/35 | |
| 28 | 1084.2198 | ||
| 29 | 1122.9420 | ||
| 30 | 1161.6641 | 88/45, 96/49, 49/25 | |
| 31 | 1200.3862 | 2/1 | |
| 32 | 1239.1084 | ||
| 33 | 1277.8305 | 44/21 | |
| 34 | 1316.5527 | ||
| 35 | 1355.2748 | ||
| 36 | 1393.9969 | 38/17, 85/38 | |
| 37 | 1432.7191 | ||
| 38 | 1471.4412 | ||
| 39 | 1510.1633 | ||
| 40 | 1548.8855 | ||
| 41 | 1587.6076 | ||
| 42 | 1626.3297 | 64/25 | |
| 43 | 1665.0519 | ||
| 44 | 1703.7740 | ||
| 45 | 1742.4962 | 52/19 | |
| 46 | 1781.2183 | ||
| 47 | 1819.9404 | ||
| 48 | 1858.6626 | 38/13 | |
| 49 | 1897.3847 | ||
| 50 | 1936.1068 | ||
| 51 | 1974.8290 | 25/8 | |
| 52 | 2013.5511 | ||
| 53 | 2052.2733 | ||
| 54 | 2090.9954 | ||
| 55 | 2129.7175 | ||
| 56 | 2168.4397 | ||
| 57 | 2207.1618 | 68/19 | |
| 58 | 2245.8839 | ||
| 59 | 2284.6061 | ||
| 60 | 2323.3282 | 65/17 | |
| 61 | 2362.0503 | ||
| 62 | 2400.7725 | ||
| 63 | 2439.4946 | 45/11 | |
| 64 | 2478.2168 | ||
| 65 | 2516.9389 | ||
| 66 | 2555.6610 | 35/8 | |
| 67 | 2594.3832 | ||
| 68 | 2633.1053 | ||
| 69 | 2671.8274 | ||
| 70 | 2710.5496 | ||
| 71 | 2749.2717 | ||
| 72 | 2787.9939 | 5/1 | |
| 73 | 2826.7160 | ||
| 74 | 2865.4381 | ||
| 75 | 2904.1603 | 75/14 | |
| 76 | 2942.8824 | ||
| 77 | 2981.6045 | ||
| 78 | 3020.3267 | 40/7, 63/11 | |
| 79 | 3059.0488 | ||
| 80 | 3097.7709 | ||
| 81 | 3136.4931 | 49/8 | |
| 82 | 3175.2152 | ||
| 83 | 3213.9374 | ||
| 84 | 3252.6595 | 98/15, 72/11 | |
| 85 | 3291.3816 | ||
| 86 | 3330.1038 | ||
| 87 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.4 | -4.6 | +1.7 | +0.0 | -8.0 | +12.5 | +12.8 | +13.8 | -7.2 | +17.5 | +18.2 |
| Relative (%) | +1.0 | -11.8 | +4.3 | +0.0 | -20.8 | +32.3 | +32.9 | +35.7 | -18.5 | +45.1 | +46.9 | |
| Steps (reduced) |
31 (31) |
49 (49) |
72 (72) |
87 (0) |
107 (20) |
115 (28) |
127 (40) |
132 (45) |
140 (53) |
151 (64) |
154 (67) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.1 | -1.2 | -6.2 | -5.3 | +19.0 | -11.7 | +8.0 | +0.5 | +16.2 | +6.9 | -13.7 |
| Relative (%) | -44.1 | -3.1 | -16.0 | -13.7 | +49.2 | -30.3 | +20.6 | +1.2 | +41.9 | +17.7 | -35.4 | |
| Steps (reduced) |
161 (74) |
166 (79) |
168 (81) |
172 (85) |
178 (4) |
182 (8) |
184 (10) |
188 (14) |
191 (17) |
192 (18) |
195 (21) | |
 |
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