44edf
| ← 43edf | 44edf | 45edf → |
44 equal divisions of the perfect fifth (abbreviated 44edf or 44ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 44 equal parts of about 16 ¢ each. Each step represents a frequency ratio of (3/2)1/44, or the 44th root of 3/2.
Theory
44edf corresponds to 75.2185edo. It is related to the regular temperament which tempers out [183 -51 -44⟩ in the 5-limit, which is supported by 301-, 376-, 677-, 1053-, 1429-, 1730-, 2407-, and 2783edo.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.49 | -3.49 | +5.55 | -2.63 | -3.40 | -5.45 | -7.22 | +7.61 | -4.08 | -6.54 | +5.63 |
| Relative (%) | -21.8 | -21.8 | +34.8 | -16.5 | -21.3 | -34.2 | -45.3 | +47.7 | -25.6 | -41.0 | +35.3 | |
| Steps (reduced) |
75 (31) |
119 (31) |
175 (43) |
211 (35) |
260 (40) |
278 (14) |
307 (43) |
320 (12) |
340 (32) |
365 (13) |
373 (21) | |
Related regular temperaments
5-limit 677&1053
Comma: |183 -51 -44>
POTE generator: ~|-104 29 25> = 15.9540
Mapping: [<1 1 3|, <0 44 -51|]
EDOs: 75, 301, 376, 677, 978, 1053, 1429, 1730, 2407, 2783, 3836
2.3.5.11 677&1053
Commas: 184549376/184528125, 38084983750656/38060880859375
POTE generator: ~|-104 29 25> = 15.9535
Mapping: [<1 1 3 1|, <0 44 -51 185|]
EDOs: 301, 376, 677, 978, 1053, 1429, 1730, 2407, 2783, 3084
13-limit 677&1053
Commas: 6656/6655, 184549376/184528125, 1162261467/1161875000
POTE generator: ~|-104 29 25> = 15.9540
Mapping: [<1 1 3 1 -3|, <0 44 -51 185 504|]
EDOs: 677, 1053, 1730, 2407, 3084, 4137
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 15.9535 | ||
| 2 | 31.907 | ||
| 3 | 47.8606 | ||
| 4 | 63.8141 | ||
| 5 | 79.7676 | 22/21 | |
| 6 | 95.7211 | 37/35 | |
| 7 | 111.6747 | 16/15 | |
| 8 | 127.6282 | 14/13 | |
| 9 | 143.5817 | 25/23 | |
| 10 | 159.5352 | 34/31 | |
| 11 | 175.48875 | 31/28 | |
| 12 | 191.4423 | 19/17 | |
| 13 | 207.3958 | 62/55 | |
| 14 | 223.3493 | 33/29 | |
| 15 | 239.3028 | 31/27 | |
| 16 | 255.2564 | 51/44 | |
| 17 | 271.2099 | 62/53 | |
| 18 | 287.1634 | ||
| 19 | 303.1169 | 81/68 | |
| 20 | 319.0705 | 6/5 | |
| 21 | 335.024 | ||
| 22 | 350.9775 | 60/49, 49/40 | |
| 23 | 366.931 | ||
| 24 | 382.8845 | 5/4 | |
| 25 | 398.8381 | 34/27 | |
| 26 | 414.7916 | 14/11 | |
| 27 | 430.7451 | 9/7 | |
| 28 | 446.6986 | 22/17 | |
| 29 | 462.6522 | ||
| 30 | 478.6057 | ||
| 31 | 494.5592 | 4/3 | |
| 32 | 510.5127 | ||
| 33 | 526.46625 | 42/31, 27/20 | |
| 34 | 542.4198 | ||
| 35 | 558.3733 | ||
| 36 | 574.3268 | ||
| 37 | 590.2803 | 45/32 | |
| 38 | 606.2339 | ||
| 39 | 622.1874 | 63/44 | |
| 40 | 638.1409 | 81/56 | |
| 41 | 654.0944 | ||
| 42 | 670.048 | ||
| 43 | 686.0015 | 40/27 | |
| 44 | 701.955 | exact 3/2 | just perfect fifth |
| 45 | 717.8985 | 243/160 | |
| 46 | 733.862 | ||
| 47 | 749.8156 | ||
| 48 | 765.7691 | 14/9 | |
| 49 | 781.7226 | 11/7 | |
| 50 | 797.6761 | ||
| 51 | 813.6297 | 8/5 | |
| 52 | 829.5832 | ||
| 53 | 845.5367 | ||
| 54 | 861.4902 | ||
| 55 | 877.44375 | 5/3 | |
| 56 | 893.3973 | ||
| 57 | 909.3508 | 27/16 | |
| 58 | 925.3043 | ||
| 59 | 941.2578 | ||
| 60 | 957.2184 | 153/88 | |
| 61 | 973.1649 | 7/4 | |
| 62 | 989.1184 | 99/56 | |
| 63 | 1005.0719 | 243/136 | |
| 64 | 1021.0255 | 9/5 | |
| 65 | 1036.979 | ||
| 66 | 1052.9325 | ||
| 67 | 1068.886 | 13/7 | |
| 68 | 1084.89355 | 15/8 | |
| 69 | 1100.7931 | ||
| 70 | 1116.7466 | ||
| 71 | 1132.7001 | ||
| 72 | 1148.6536 | ||
| 73 | 1164.9072 | ||
| 74 | 1180.5607 | 160/81 | |
| 75 | 1196.5142 | 2/1 | |
| 76 | 1212.4677 | ||
| 77 | 1228.42125 | ||
| 78 | 1244.3748 | ||
| 79 | 1260.3283 | ||
| 80 | 1276.2818 | ||
| 81 | 1292.2353 | ||
| 82 | 1308.1889 | ||
| 83 | 1324.1424 | ||
| 84 | 1340.0959 | ||
| 85 | 1356.0494 | ||
| 86 | 1372.003 | ||
| 87 | 1387.9565 | 20/9 | |
| 88 | 1403.91 | exact 9/4 | |