33ed5
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33ED5 is the equal division of the 5th harmonic into 33 parts of 84.4337 cents each (very close to the minor septimal semitone, 21/20, 84.4672 cents). It is related to the 128&270 temperament (Septisemitonic temperament, named by Xenllium), which tempers out 102760448/102515625 and 200120949/200000000 in the 7-limit, supported by 128, 142, 270, 398, 412, 668, and 682 EDOs.
Related regular temperaments
7-limit 128&270
Commas: 102760448/102515625, 200120949/200000000
POTE generator: ~21/20 = 84.4463
Mapping: [<2 5 0 -1|, <0 -13 33 47|]
EDOs: 128, 142, 270, 398, 412, 668, 682
Badness: 0.1661
11-limit 128&270
Commas: 3025/3024, 131072/130977, 422576/421875
POTE generator: ~21/20 = 84.4430
Mapping: [<2 5 0 -1 11|, <0 -13 33 47 -29|]
EDOs: 128, 142, 270, 398, 412, 668, 682
Badness: 0.0583
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 84.4 | 20/19, 23/22 |
| 2 | 168.9 | 11/10 |
| 3 | 253.3 | 15/13, 22/19 |
| 4 | 337.7 | 17/14, 23/19, 28/23 |
| 5 | 422.2 | 14/11 |
| 6 | 506.6 | |
| 7 | 591 | 7/5, 24/17 |
| 8 | 675.5 | 25/17, 28/19 |
| 9 | 759.9 | 17/11 |
| 10 | 844.3 | |
| 11 | 928.8 | 12/7 |
| 12 | 1013.2 | |
| 13 | 1097.6 | |
| 14 | 1182.1 | |
| 15 | 1266.5 | 25/12 |
| 16 | 1350.9 | 24/11 |
| 17 | 1435.4 | 23/10 |
| 18 | 1519.8 | 12/5 |
| 19 | 1604.2 | |
| 20 | 1688.7 | |
| 21 | 1773.1 | |
| 22 | 1857.5 | |
| 23 | 1942 | |
| 24 | 2026.4 | |
| 25 | 2110.8 | 17/5 |
| 26 | 2195.3 | 25/7 |
| 27 | 2279.7 | 26/7 |
| 28 | 2364.1 | |
| 29 | 2448.6 | |
| 30 | 2533 | 13/3 |
| 31 | 2617.4 | |
| 32 | 2701.9 | 19/4 |
| 33 | 2786.3 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -17.9 | +40.0 | -35.9 | +0.0 | +22.1 | +8.5 | +30.7 | -4.4 | -17.9 | -14.1 | +4.2 |
| Relative (%) | -21.2 | +47.4 | -42.5 | +0.0 | +26.2 | +10.1 | +36.3 | -5.2 | -21.2 | -16.7 | +4.9 | |
| Steps (reduced) |
14 (14) |
23 (23) |
28 (28) |
33 (0) |
37 (4) |
40 (7) |
43 (10) |
45 (12) |
47 (14) |
49 (16) |
51 (18) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +34.5 | -9.4 | +40.0 | +12.7 | -7.8 | -22.3 | -31.5 | -35.9 | -35.9 | -32.0 | -24.5 |
| Relative (%) | +40.8 | -11.1 | +47.4 | +15.1 | -9.2 | -26.4 | -37.3 | -42.5 | -42.5 | -37.9 | -29.0 | |
| Steps (reduced) |
53 (20) |
54 (21) |
56 (23) |
57 (24) |
58 (25) |
59 (26) |
60 (27) |
61 (28) |
62 (29) |
63 (30) |
64 (31) | |