1920edo: Difference between revisions
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{{Harmonics in equal|1920|columns=15}} | {{Harmonics in equal|1920|columns=15}} | ||
=== | === Divisors === | ||
1920 = 2<sup>7</sup> × 3 × 5; some of its | 1920 = 2<sup>7</sup> × 3 × 5; some of its subset EDOs are [[10edo|10]], [[12edo|12]], [[15edo|15]], [[16edo|16]], [[24edo|24]], [[60edo|60]], [[80edo|80]], [[96edo|96]], [[128edo|128]], [[240edo|240]], [[320edo|320]] and [[640edo|640]]. | ||
== Regular temperament properties == | |||
1920edo has the lowest relative error in the 31-, 37-, 41-, and 47- limit. | |||
=== Rank-2 temperaments === | |||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
Revision as of 18:43, 14 January 2023
| ← 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) | |
Divisors
1920 = 27 × 3 × 5; some of its subset EDOs are 10, 12, 15, 16, 24, 60, 80, 96, 128, 240, 320 and 640.
Regular temperament properties
1920edo has the lowest relative error in the 31-, 37-, 41-, and 47- limit.