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2048edo: Difference between revisions

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{{EDO intro|2048}}
{{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 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.
In the 5-limit, it supports [[monzismic]] temperament. In the 11-limit, 2048edo tempers out the [[quartisma]].
=== Prime harmonics ===
{{Harmonics in equal|2048}}
{{Harmonics in equal|2048}}
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-13s limit patent val has an error of only 0.019 cents/octave.
=== 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 ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! 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
| {{monzo| 54 -37 2 }}, {{monzo| -111 -12 56 }}
| {{mapping| 2048 3246 4755 }}
| +0.0264
| 0.0364
| 6.22
|-
| 2.3.5.7
| 2401/2400, {{monzo| -18 -13 13 3 }}, {{monzo| 49 -38 0 4 }}
| {{mapping| 2048 3246 4755 5749 }}
| +0.0439
| 0.0438
| 7.48
|-
| 2.3.5.7.11
| 2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179
| {{mapping| 2048 3246 4755 5749 7085 }}
| +0.0323
| 0.0456
| 7.78
|}


2048edo is the 11th power of two EDO.
== Scales ==
* [[MET-24]]
Retrieved from "https://en.xen.wiki/w/2048edo"