1920edo: Difference between revisions
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{{EDO intro|1920}} | {{EDO intro|1920}} | ||
== Theory == | == Theory == | ||
1920edo is distinctly [[consistent]] through the 25-odd-limit, and in terms of 23-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], only [[1578edo|1578]] and [[1889edo|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 === | === Prime harmonics === | ||
Revision as of 15:14, 8 December 2022
| ← 1919edo | 1920edo | 1921edo → |
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) | |
Miscellany
1920 = 27 × 3 × 5; some of its divisors are 10, 12, 15, 16, 24, 60, 80, 96, 128, 240, 320 and 640.