1920edo: Difference between revisions
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br>per 8ve | ! Periods<br />per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br />Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 31: | Line 31: | ||
|- | |- | ||
| 30 | | 30 | ||
| 583\1920<br>(7\1920) | | 583\1920<br />(7\1920) | ||
| 364.375<br>(4.375) | | 364.375<br />(4.375) | ||
| 216/175<br>(385/384) | | 216/175<br />(385/384) | ||
| [[Zinc]] | | [[Zinc]] | ||
|- | |- | ||
| 60 | | 60 | ||
| 583\1920<br>(7\1920) | | 583\1920<br />(7\1920) | ||
| 364.375<br>(4.375) | | 364.375<br />(4.375) | ||
| 216/175<br>(385/384) | | 216/175<br />(385/384) | ||
| [[Neodymium]] / [[neodymium magnet]] | | [[Neodymium]] / [[neodymium magnet]] | ||
|} | |} | ||
{{orf}} | |||
== Music == | == Music == | ||
Revision as of 01:04, 16 November 2024
| ← 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) | |
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 |
Music
- Jazz Improvisation (2023)