71edt
| ← 70edt | 71edt | 72edt → |
71EDT is the equal division of the third harmonic into 71 parts of 26.7881 cents each, corresponding to 44.7960 edo (45edo with 5.4644 cents octave stretch). It is related to the 13-limit temperament which tempers out 540/539, 1575/1573, 2200/2197, and 4375/4374, which is supported by 45edo (45ef val), 179edo (179ef val), 224edo, 269edo (269ce val), and 403edo (403def val).
71EDT is the 13th no-twos zeta peak EDT.
Theory
71edt is a remarkably strong 3.5.11 subgroup microtemperament with sub-cent accuracy on the 5th and 11th harmonics. It supports the delta centauri temperament in the 3.5.11 subgroup, equating a stack of 9 5/3s tritave-reduced to 11/9. Its 7th harmonic is decent, though much worse than the 5th and 11th harmonics.
71edt can be considered as 45edo with an octave stretch, but it is definitely a significant stretch because 45edo completely looses the extreme accuracy on the 5th and 11th harmonics, being a dual-5/4 system.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.5 | +0.0 | -0.4 | +6.5 | +0.8 | +6.3 | -2.7 | -7.8 | +9.7 | +10.2 | +1.9 |
| Relative (%) | +20.4 | +0.0 | -1.3 | +24.2 | +3.1 | +23.5 | -10.2 | -29.0 | +36.2 | +38.2 | +7.2 | |
| Steps (reduced) |
45 (45) |
71 (0) |
104 (33) |
126 (55) |
155 (13) |
166 (24) |
183 (41) |
190 (48) |
203 (61) |
218 (5) |
222 (9) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.7 | +0.1 | -2.0 | +4.7 | +11.0 | +12.9 | +8.7 | +7.1 | -13.0 | -7.5 | -10.3 |
| Relative (%) | -36.3 | +0.3 | -7.5 | +17.7 | +41.2 | +48.1 | +32.7 | +26.3 | -48.4 | -27.9 | -38.4 | |
| Steps (reduced) |
233 (20) |
240 (27) |
243 (30) |
249 (36) |
257 (44) |
264 (51) |
266 (53) |
272 (59) |
275 (62) |
277 (64) |
282 (69) | |
Intervals
| Degree | Cents | Hekts | Corresponding JI intervals |
Comments |
|---|---|---|---|---|
| 0 | exact 1/1 | |||
| 1 | 26.7881 | 18.3099 | 66/65 | |
| 2 | 53.5762 | 36.6197 | 65/63 | |
| 3 | 80.3643 | 54.9296 | 22/21 | |
| 4 | 107.1524 | 73.2394 | 117/110 | |
| 5 | 133.9405 | 91.5493 | 27/25 | |
| 6 | 160.7286 | 109.85915 | 169/154 | |
| 7 | 187.5167 | 128.169 | 39/35 | |
| 8 | 214.3048 | 146.4789 | 147/130, 198/175 | |
| 9 | 241.0929 | 164.7887 | 169/147 | |
| 10 | 267.8810 | 183.0986 | 7/6 | |
| 11 | 294.6691 | 201.40845 | 77/65 | |
| 12 | 321.4572 | 219.7183 | 65/54 | |
| 13 | 348.2453 | 238.0282 | 11/9 | |
| 14 | 375.0334 | 256.338 | 273/220 | |
| 15 | 401.8215 | 274.6479 | 63/50 | |
| 16 | 428.6096 | 292.95775 | 169/132 | |
| 17 | 455.3977 | 311.2676 | 13/10 | |
| 18 | 482.1858 | 329.5775 | 33/25 | |
| 19 | 508.9739 | 347.8873 | 169/126 | |
| 20 | 535.7620 | 366.1972 | 15/11 | |
| 21 | 562.5501 | 384.507 | 18/13 | |
| 22 | 589.3382 | 402.8169 | (45/32) | |
| 23 | 616.1263 | 421.1268 | 10/7 | |
| 24 | 642.9144 | 439.4366 | 132/91 | |
| 25 | 669.7025 | 457.7465 | 22/15 | |
| 26 | 696.4906 | 476.0563 | 486/325, 220/147 | pseudo-3/2 |
| 27 | 723.2787 | 494.3662 | 50/33 | |
| 28 | 750.0668 | 512.6761 | 54/35 | |
| 29 | 776.8549 | 530.9859 | 264/169 | |
| 30 | 803.643 | 549.2958 | 35/22 | |
| 31 | 830.4311 | 567.6056 | 21/13 | |
| 32 | 857.2192 | 585.9155 | 18/11 | |
| 33 | 884.0073 | 604.22535 | 5/3 | |
| 34 | 910.7954 | 622.5352 | 22/13 | |
| 35 | 937.5835 | 640.8451 | 12/7 | |
| 36 | 964.3715 | 659.1549 | 7/4 | |
| 37 | 991.1596 | 677.4648 | 39/22 | |
| 38 | 1017.9477 | 695.77465 | 9/5 | |
| 39 | 1044.7358 | 714.0845 | 11/6 | |
| 40 | 1071.5239 | 732.3944 | 13/7 | |
| 41 | 1098.312 | 750.7042 | 66/35 | |
| 42 | 1125.1001 | 769.0141 | 21/11 | |
| 43 | 1151.8882 | 787.3239 | 35/18 | |
| 44 | 1178.6763 | 805.6338 | 22/13 | |
| 45 | 1205.4644 | 823.9437 | 441/220, 325/162 | pseudo-octave |
| 46 | 1232.2525 | 842.2535 | 45/22 | |
| 47 | 1259.0406 | 860.5634 | 91/44 | |
| 48 | 1285.8287 | 878.8732 | 21/10 | |
| 49 | 1312.6168 | 897.1831 | (32/15) | |
| 50 | 1339.4049 | 915.493 | 13/6 | |
| 51 | 1366.193 | 933.8028 | 11/5 | |
| 52 | 1392.9811 | 952.1127 | 378/169 | |
| 53 | 1419.7692 | 970.4225 | 25/11 | |
| 54 | 1446.5573 | 988.7324 | 30/13 | |
| 55 | 1473.3454 | 1007.04225 | 396/169 | |
| 56 | 1500.1335 | 1025.3521 | 50/21 | |
| 57 | 1526.9216 | 1043.662 | 220/91 | |
| 58 | 1553.7097 | 1061.9718 | 27/11 | |
| 59 | 1580.4978 | 1080.2817 | 162/65 | |
| 60 | 1607.2859 | 1098.59155 | 195/77 | |
| 61 | 1634.0740 | 1161.9014 | 18/7 | |
| 62 | 1660.8621 | 1135.2113 | 441/169 | |
| 63 | 1687.6502 | 1153.5211 | 175/66, 130/49 | |
| 64 | 1714.4383 | 1171.831 | 35/13, 132/49 | |
| 65 | 1741.2264 | 1190.14085 | 462/169 | |
| 66 | 1768.0145 | 1208.4507 | 25/9 | |
| 67 | 1794.8026 | 1226.7606 | 110/39 | |
| 68 | 1821.5907 | 1245.0704 | 63/22 | |
| 69 | 1848.3788 | 1263.3803 | 189/65 | |
| 70 | 1875.1669 | 1281.6901 | 65/22 | |
| 71 | 1901.9550 | 1300 | exact 3/1 | just perfect fifth plus an octave |