1920edo: Difference between revisions
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The '''1920 division''' divides the octave into 1920 equal parts of exactly 0.625 cents each. It is distinctly consistent through the 25 limit, and in terms of 23-limit [[Tenney- | The '''1920 division''' divides the octave into 1920 equal parts of exactly 0.625 cents each. It 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]]. | ||
1920 = 2 | === Prime harmonics === | ||
{{Harmonics in equal|1920|columns=11}} | |||
=== Miscellany === | |||
1920 = 2<sup>7</sup> × 3 × 5; some of its divisors 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]]. | |||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
Revision as of 08:26, 24 November 2022
| ← 1919edo | 1920edo | 1921edo → |
The 1920 division divides the octave into 1920 equal parts of exactly 0.625 cents each. It 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.080 | -0.064 | -0.076 | -0.068 | +0.097 | +0.045 | -0.013 | -0.149 | -0.202 | -0.036 |
| Relative (%) | +0.0 | -12.8 | -10.2 | -12.1 | -10.9 | +15.6 | +7.1 | -2.1 | -23.9 | -32.4 | -5.7 | |
| Steps (reduced) |
1920 (0) |
3043 (1123) |
4458 (618) |
5390 (1550) |
6642 (882) |
7105 (1345) |
7848 (168) |
8156 (476) |
8685 (1005) |
9327 (1647) |
9512 (1832) | |
Miscellany
1920 = 27 × 3 × 5; some of its divisors are 10, 12, 15, 16, 24, 60, 80, 96, 128, 240, 320 and 640.