43edt
| ← 42edt | 43edt | 44edt → |
Division of the third harmonic into 43 equal parts (43EDT) is related to 27 EDO, but with the 3/1 rather than the 2/1 being just. The octave is about 5.7492 cents compressed and the step size is about 44.2315 cents. It is consistent to the 10-integer-limit.
Properties
This tuning is related to 27EDO having ~5.7 cent octave compression, a small but significant deviation. This is particularly relevant because 27EDO tunes the 3rd, 5th, 7th and 13th harmonics sharp, thus 43EDT improves those approximations.
However, in addition to its rich octave-based harmony, the 43EDT is also a fine tritave-based tuning: with a 7/3 of 1460 cents and such a near perfect 5/3, Bohlen-Pierce harmony is very clear and hearty, as well as capable of extended enharmonic distinctions that 13EDT is not. The 4L+5s MOS has L=7 s=3.
| degrees | cents value | hekts | corresponding JI intervals |
|---|---|---|---|
| 1 | 44.232 | 30.233 | 40/39, 39/38 |
| 2 | 88.463 | 60.465 | 20/19 |
| 3 | 132.695 | 90.698 | 27/25 |
| 4 | 176.926 | 120.93 | 10/9 |
| 5 | 221.158 | 151.163 | 25/22 |
| 6 | 265.389 | 181.395 | (7/6) |
| 7 | 309.621 | 211.628 | 6/5 |
| 8 | 353.852 | 241.8605 | 27/22 |
| 9 | 398.084 | 272.093 | 24/19 |
| 10 | 442.315 | 302.326 | 9/7 |
| 11 | 486.547 | 332.558 | (45/34) |
| 12 | 530.778 | 362.791 | (34/25) |
| 13 | 575.01 | 393.023 | (39/28) |
| 14 | 619.241 | 423.256 | 10/7 |
| 15 | 663.473 | 453.488 | 22/15 |
| 16 | 707.704 | 483.721 | 3/2 |
| 17 | 751.936 | 513.9535 | 105/68, 20/13 |
| 18 | 796.167 | 544.186 | 19/12 |
| 19 | 840.399 | 574.419 | 13/8 |
| 20 | 884.63 | 604.651 | 5/3 |
| 21 | 928.862 | 634.883 | 12/7 |
| 22 | 973.093 | 665.116 | 7/4 |
| 23 | 1017.325 | 695.349 | 9/5 |
| 24 | 1061.556 | 725.581 | 24/13 |
| 25 | 1105.788 | 755.814 | 36/19 |
| 26 | 1150.019 | 786.0465 | 68/35, 39/20 |
| 27 | 1194.251 | 816.279 | 2/1 |
| 28 | 1238.482 | 846.511 | 45/22 |
| 29 | 1282.713 | 876.744 | (21/10) |
| 30 | 1326.946 | 906.977 | (28/13) |
| 31 | 1371.177 | 937.209 | (75/34) |
| 32 | 1415.408 | 967.442 | (34/15) |
| 33 | 1459.640 | 997.674 | 7/3 |
| 34 | 1503.871 | 1027.907 | 19/8 |
| 35 | 1548.193 | 1058.1395 | 22/9 |
| 36 | 1592.334 | 1088.372 | 5/2 |
| 37 | 1636.566 | 1118.605 | (18/7) |
| 38 | 1680.797 | 1148.837 | 66/25 |
| 39 | 1725.029 | 1179.069 | 27/10 |
| 40 | 1769.261 | 1209.302 | 25/9 |
| 41 | 1813.492 | 1239.5345 | 57/20 |
| 42 | 1857.724 | 1269.767 | 117/40, 38/13 |
| 43 | 1901.955 | 1300 | exact 3/1 |
43EDT as a regular temperament
43EDT tempers out a no-twos comma of |0 63 -43>, leading the regular temperament supported by 27, 190, and 217 EDOs.
27&190 temperament
5-limit
Comma: |0 63 -43>
POTE generator: ~|0 -41 28> = 44.2294
Mapping: [<1 0 0|, <0 43 63|]
EDOs: 27, 190, 217, 407, 597, 624, 841
7-limit
Commas: 4375/4374, 40353607/40000000
POTE generator: ~1029/1000 = 44.2288
Mapping: [<1 0 0 1|, <0 43 63 49|]
Badness: 0.1659
217&407 temperament
7-limit
Commas: 134217728/133984375, 512557306947/512000000000
POTE generator: ~525/512 = 44.2320
Mapping: [<1 0 0 9|, <0 43 63 -168|]
EDOs: 217, 407, 624, 841, 1058, 1465
Badness: 0.3544
11-limit
Commas: 46656/46585, 131072/130977, 234375/234256
POTE generator: ~525/512 = 44.2312
Mapping: [<1 0 0 9 -1|, <0 43 63 -168 121|]
Badness: 0.1129
13-limit
Commas: 2080/2079, 4096/4095, 39366/39325, 109512/109375
POTE generator: ~40/39 = 44.2312
Mapping: [<1 0 0 9 -1 3|, <0 43 63 -168 121 19|]
Badness: 0.0503