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]] | ||