2048edo: Difference between revisions
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{{Infobox ET}} | |||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
2048edo has an excellent [[3/2|perfect fifth]], which derives from [[1024edo]]. It [[tempering out|tempers out]] the breedsma ([[2401/2400]]) in the 7-limit, and supports the rank-3 breed temperament. | |||
2048edo has an excellent perfect fifth, which derives from 1024edo. It tempers out the breedsma (2401/2400) in the 7-limit, and supports the rank 3 breed temperament. | |||
2048edo is usable as high as 43-limit, with the 2048f val regular temperament having an error of 0.023 cents (0.04 edosteps) per octave, and the no- | 2048edo is usable as high as 43-limit, with the 2048f val regular temperament having an error of 0.023 cents (0.04 edosteps) per octave, and the no-13's limit patent val is unambiguous and has an error of only 0.019 cents/octave. | ||
2048edo | In the 5-limit, it supports [[monzismic]] temperament. In the 11-limit, 2048edo tempers out the [[quartisma]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|2048}} | |||
=== Subsets and supersets === | |||
2048edo is the 11th-power-of-two edo, with subset edos {{EDOs| 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024 }}. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! rowspan="2" | [[Subgroup]] | ||
![[TE simple badness|Relative]] (%) | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve Stretch (¢) | |||
! colspan="2" | Tuning Error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|54 | | {{monzo| 54 -37 2 }}, {{monzo| -111 -12 56 }} | ||
| | | {{mapping| 2048 3246 4755 }} | ||
|0.0264 | | +0.0264 | ||
|0.0364 | | 0.0364 | ||
|6.22 | | 6.22 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|2401/2400, {{monzo|-18 | | 2401/2400, {{monzo| -18 -13 13 3 }}, {{monzo| 49 -38 0 4 }} | ||
| | | {{mapping| 2048 3246 4755 5749 }} | ||
|0.0439 | | +0.0439 | ||
|0.0438 | | 0.0438 | ||
|7.48 | | 7.48 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179 | | 2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179 | ||
| | | {{mapping| 2048 3246 4755 5749 7085 }} | ||
|0.0323 | | +0.0323 | ||
|0.0456 | | 0.0456 | ||
|7.78 | | 7.78 | ||
|} | |} | ||
[[ | == Scales == | ||
* [[MET-24]] | |||