299edo: Difference between revisions
Expansion and +categories |
Expansion (+infobox; +prime error table; +RTT table and rank-2 temperaments) |
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{{Infobox ET | |||
| Prime factorization = 13 × 23 | |||
| Step size = 4.01338¢ | |||
| Fifth = 175\299 (702.34¢) | |||
| Semitones = 29:22 (116.39¢ : 88.29¢) | |||
| Consistency = 7 | |||
}} | |||
{{EDO intro|299}} | |||
== Theory == | |||
In the 5-limit, 299et tempers out the [[kleisma]], 15625/15552, in the 7-limit [[10976/10935]], in the 11-limit [[385/384]]; and in the 13-limit [[325/324]], [[625/624]] and [[676/675]]. It provides the [[optimal patent val]] for the 13-limit rank-3 [[enlil]] temperament, and the rank-4 temperament tempering out 325/324 and 385/384. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|299}} | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" | Subgroup | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| 474 -299 }} | |||
| [{{val| 299 474 }}] | |||
| -0.1218 | |||
| 0.1218 | |||
| 3.04 | |||
|- | |||
| 2.3.5 | |||
| 15625/15552, {{monzo| 80 -49 -1 }} | |||
| [{{val| 299 474 694 }}] | |||
| +0.0665 | |||
| 0.2844 | |||
| 7.09 | |||
|- | |||
| 2.3.5.7 | |||
| 10976/10935, 15625/15552, 823543/819200 | |||
| [{{val| 299 474 694 839 }}] | |||
| +0.1925 | |||
| 0.3291 | |||
| 8.20 | |||
|- | |||
| 2.3.5.7.11 | |||
| 385/384, 6250/6237, 10976/10935, 12005/11979 | |||
| [{{val| 299 474 694 839 1034 }}] | |||
| +0.2399 | |||
| 0.3092 | |||
| 7.70 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 325/324, 385/384, 676/675, 10648/10647, 10976/10935 | |||
| [{{val| 299 474 694 839 1034 1106 }}] | |||
| +0.2779 | |||
| 0.2948 | |||
| 7.34 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 325/324, 385/384, 595/594, 625/624, 2058/2057, 8624/8619 | |||
| [{{val| 299 474 694 839 1034 1106 1222 }}] | |||
| +0.2595 | |||
| 0.2767 | |||
| 6.89 | |||
|- | |||
| 2.3.5.7.11.13.17.19 | |||
| 325/324, 343/342, 385/384, 595/594, 625/624, 1216/1215, 1445/1444 | |||
| [{{val| 299 474 694 839 1034 1106 1222 1270 }}] | |||
| +0.2424 | |||
| 0.2627 | |||
| 6.54 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per octave | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 79\299 | |||
| 317.06 | |||
| 6/5 | |||
| [[Hanson]] | |||
|- | |||
| 1 | |||
| 124\299 | |||
| 505.69 | |||
| 75/56 | |||
| [[Marfifths]] | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Enlil]] | [[Category:Enlil]] | ||
[[Category:Keenanismic]] | [[Category:Keenanismic]] | ||