User:BudjarnLambeth/42ed257/128
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Prime factorization
27
Step size
9.375 ¢
Fifth
75\128 (703.125 ¢)
Semitones (A1:m2)
13:9 (121.9 ¢ : 84.38 ¢)
Consistency limit
7
Distinct consistency limit
7
| ← 127edo | 128 | 129edo → |
42ed257/128 is the equal division of the pseudo-octaveinterval 257/128 into forty-two parts of 28.73 cents each, corresponding to ~41.77edo.
It can be approached as a compressed-octaves version of 42edo, which improves most of 42edo’s JI approximations.
Harmonics
42ed257/128 is a kind of opposite twin to the scale 191zpi. 191zpi makes 42edo into a better 2.3.5.11.13 tuning, while 42ed257/128 makes 42edo into a better 2.3.5.7.17 tuning. They both improve 42edo but in opposite directions.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.7 | -5.6 | +0.7 | -7.2 | -13.9 | +13.0 | +8.2 | -11.9 | +2.1 | +3.0 | +2.5 |
| Relative (%) | +23.5 | -19.6 | +2.4 | -24.9 | -48.3 | +45.1 | +28.7 | -41.5 | +7.3 | +10.6 | +8.8 | |
| Steps (reduced) |
42 (0) |
66 (24) |
97 (13) |
117 (33) |
144 (18) |
155 (29) |
171 (3) |
177 (9) |
189 (21) |
203 (35) |
207 (39) | |
42edo for comparison:
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | +12.3 | +13.7 | +2.6 | -8.5 | -12.0 | +9.3 | -11.8 | +0.3 | -1.0 | -2.2 |
| Relative (%) | +0.0 | +43.2 | +47.9 | +9.1 | -29.6 | -41.8 | +32.7 | -41.3 | +1.0 | -3.5 | -7.6 | |
| Steps (reduced) |
42 (0) |
67 (25) |
98 (14) |
118 (34) |
145 (19) |
155 (29) |
172 (4) |
178 (10) |
190 (22) |
204 (36) |
208 (40) | |
Notation
42ed257/128 can use most notation systems designed for 42edo. See 42edo#Notation.
Scala file
Tuning file for anything that supports Scala. Made with Scale Workshop.
! 42ed257over128.scl ! Created using Scale Workshop 3.0.1 ! ! https://scaleworkshop.plainsound.org/scale/H7mskiu00 ! 42 equal divisions of 257/128 42 ! 28.732130 57.464260 86.196390 114.928520 143.660650 172.392780 201.124910 229.857040 258.589170 287.321300 316.053430 344.785560 373.517690 402.249820 430.981950 459.714080 488.446210 517.178340 545.910470 574.642600 603.374730 632.106859 660.838989 689.571119 718.303249 747.035379 775.767509 804.499639 833.231769 861.963899 890.696029 919.428159 948.160289 976.892419 1005.624549 1034.356679 1063.088809 1091.820939 1120.553069 1149.285199 1178.017329 1206.749459
Instruments
- Lumatone
- 42ed257/128 can use most types of Lumatone mapping for 42edo