1920edo
| ← 1919edo | 1920edo | 1921edo → |
1920 equal divisions of the octave (abbreviated 1920edo or 1920ed2), also called 1920-tone equal temperament (1920tet) or 1920 equal temperament (1920et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1920 equal parts of exactly 0.625 ¢ each. Each step represents a frequency ratio of 21/1920, or the 1920th root of 2.
Theory
1920edo is distinctly consistent through the 25-odd-limit, and in terms of 23-limit relative error, only 1578 and 1889 are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31-, 37-, 41-, 43- and 47-limit, nothing beats it. Because of this and because it is a very composite number divisible by 12, it is another candidate for interval size measure.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.080 | -0.064 | -0.076 | -0.068 | +0.097 | +0.045 | -0.013 | -0.149 | -0.202 | -0.036 | -0.094 | -0.312 | -0.268 | +0.118 |
| Relative (%) | +0.0 | -12.8 | -10.2 | -12.1 | -10.9 | +15.6 | +7.1 | -2.1 | -23.9 | -32.4 | -5.7 | -15.0 | -50.0 | -42.8 | +18.9 | |
| Steps (reduced) |
1920 (0) |
3043 (1123) |
4458 (618) |
5390 (1550) |
6642 (882) |
7105 (1345) |
7848 (168) |
8156 (476) |
8685 (1005) |
9327 (1647) |
9512 (1832) |
10002 (402) |
10286 (686) |
10418 (818) |
10665 (1065) | |
Subsets and supersets
Since 1920 factors into 27 × 3 × 5, 1920edo has subset edos 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960.
Regular temperament properties
1920edo has the lowest relative error in the 31-, 37-, 41-, and 47-limit.
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 179\1920 | 111.875 | 16/15 | Vavoom |
| 30 | 583\1920 (7\1920) |
364.375 (4.375) |
216/175 (385/384) |
Zinc |
| 60 | 583\1920 (7\1920) |
364.375 (4.375) |
216/175 (385/384) |
Neodymium / neodymium magnet |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct
Music
- Jazz Improvisation (2023)