User:BudjarnLambeth/1ed237.8c
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| ← 0ed187/163 | 1ed187/163 | 2ed187/163 → |
1 equal division of 237.8¢ (1ed237.8c), also known as arithmetic pitch sequence of 237.8¢ (APS237.8¢), is an equal and nonoctave scale generated by making a continuous chain of intervals of exactly 237.8¢.
It is almost exactly 8edt, but retuned to have a slightly more acceptable pseudo-octave. It could be seen as a compromise between 8edt and 5edo, though leaning heavily towards 8edt.
It can also be thought of as 1ed187/163 as 187/163 equals 237.800 cents.
Methodology
Budjarn Lambeth arrived at this scale by looking at every possible 1ed23x.y¢ and 1ed24x.y¢ in Scale Workshop, noodling in each of them, adjusting the generator up and down by 0.1-cent increments until he found the one that sounded most pleasing to his ear.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.0 | +0.4 | -22.0 | +67.3 | -10.6 | -39.6 | -33.0 | +0.9 | +56.3 | -108.7 | -21.6 |
| Relative (%) | -4.6 | +0.2 | -9.3 | +28.3 | -4.4 | -16.7 | -13.9 | +0.4 | +23.7 | -45.7 | -9.1 | |
| Step | 5 | 8 | 10 | 12 | 13 | 14 | 15 | 16 | 17 | 17 | 18 | |
5edo, 8edt, 14ed7 for comparison:
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | +18.0 | +0.0 | +93.7 | +18.0 | -8.8 | +0.0 | +36.1 | +93.7 | -71.3 | +18.0 |
| Relative (%) | +0.0 | +7.5 | +0.0 | +39.0 | +7.5 | -3.7 | +0.0 | +15.0 | +39.0 | -29.7 | +7.5 | |
| Steps (reduced) |
5 (0) |
8 (3) |
10 (0) |
12 (2) |
13 (3) |
14 (4) |
15 (0) |
16 (1) |
17 (2) |
17 (2) |
18 (3) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.3 | +0.0 | -22.6 | +66.6 | -11.3 | -40.4 | -33.8 | +0.0 | +55.3 | -109.7 | -22.6 |
| Relative (%) | -4.7 | +0.0 | -9.5 | +28.0 | -4.7 | -17.0 | -14.2 | +0.0 | +23.3 | -46.1 | -9.5 | |
| Steps (reduced) |
5 (5) |
8 (0) |
10 (2) |
12 (4) |
13 (5) |
14 (6) |
15 (7) |
16 (0) |
17 (1) |
17 (1) |
18 (2) | |
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.2 | +23.1 | +6.3 | +101.3 | +26.2 | +0.0 | +9.5 | +46.2 | +104.4 | -60.6 | +29.4 |
| Relative (%) | +1.3 | +9.6 | +2.6 | +42.1 | +10.9 | +0.0 | +3.9 | +19.2 | +43.4 | -25.2 | +12.2 | |
| Steps (reduced) |
5 (5) |
8 (8) |
10 (10) |
12 (12) |
13 (13) |
14 (0) |
15 (1) |
16 (2) |
17 (3) |
17 (3) |
18 (4) | |
Intervals
| Degree of 1ed65c | Cents Value | Approximate ratio |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 237.8 | 8/7 |
| 2 | 475.6 | 37/28 |
| 3 | 713.4 | 3/2 |
| 4 | 951.2 | 7/4 |
| 5 | 1189.0 | 2/1 |
| 6 | 1426.8 | 16/7 |
| 7 | 1664.6 | 73/28 |
| 8 | 1902.4 | 3/1 |
Scala files
! 1ed237pt8oct.scl ! 1 equal division of 237.8, octave repeating 5 ! 237.800000 475.600000 713.400000 951.200000 1189.000000
! 1ed237pt8tri.scl ! 1 equal division of 237.8, tritave repeating 8 ! 237.800000 475.600000 713.400000 951.200000 1189.000000 1426.800000 1664.600000 1902.400000