1920edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{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]]. | 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]]. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
1920 | Since 1920 factors into 2<sup>7</sup> × 3 × 5, 1920edo has subset edos {{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 == | == Regular temperament properties == | ||
1920edo has the lowest relative error in the 31-, 37-, 41-, and 47- limit. | 1920edo has the lowest relative error in the 31-, 37-, 41-, and 47-limit. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods<br>per 8ve | ! Periods<br>per 8ve | ||
!Generator | ! Generator* | ||
!Cents | ! Cents* | ||
!Associated<br> | ! Associated<br>Ratio | ||
!Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|179\1920 | | 179\1920 | ||
|111.875 | | 111.875 | ||
|16/15 | | 16/15 | ||
|[[Vavoom]] | | [[Vavoom]] | ||
|- | |- | ||
|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>(?) | | 216/175<br>(?) | ||
|[[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>(?) | | 216/175<br>(?) | ||
|[[Neodymium]] / [[neodymium magnet]] | | [[Neodymium]] / [[neodymium magnet]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
==Music== | == Music == | ||
; [[Eliora]] | ; [[Eliora]] | ||
* [https://www.youtube.com/watch?v=ShbfCHv8Lj0 Jazz Improvisation ( | * [https://www.youtube.com/watch?v=ShbfCHv8Lj0 ''Jazz Improvisation''] (2023) | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 14:07, 15 October 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) | |
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 (?) |
Zinc |
| 60 | 583\1920 (7\1920) |
364.375 (4.375) |
216/175 (?) |
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)