121edo: Difference between revisions
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=== Prime harmonics === | === Prime harmonics === | ||
{{Primes in edo|121|columns=10}} | {{Primes in edo|121|columns=10}} | ||
== 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| 192 -121 }} | |||
| [{{val| 121 192 }}] | |||
| -0.687 | |||
| 0.687 | |||
| 6.93 | |||
|- | |||
| 2.3.5 | |||
| 15625/15552, {{monzo| 31 -21 1 }} | |||
| [{{val| 121 192 281 }}] | |||
| -0.524 | |||
| 0.606 | |||
| 6.11 | |||
|- | |||
| 2.3.5.7 | |||
| 4000/3969, 6144/6125, 10976/10935 | |||
| [{{val| 121 192 281 340 }}] | |||
| -0.667 | |||
| 0.580 | |||
| 5.85 | |||
|- | |||
| 2.3.5.7.11 | |||
| 540/539, 896/891, 1375/1372, 4375/4356 | |||
| [{{val| 121 192 281 340 419 }}] | |||
| -0.768 | |||
| 0.556 | |||
| 5.61 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 325/324, 352/351, 364/363, 540/539, 625/624 | |||
| [{{val| 121 192 281 340 419 448 }}] | |||
| -0.750 | |||
| 0.510 | |||
| 5.14 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 256/255, 325/324, 352/351, 364/363, 442/441, 540/539 | |||
| [{{val| 121 192 281 340 419 448 }}] | |||
| -0.787 | |||
| 0.480 | |||
| 4.85 | |||
|} | |||
=== 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 | |||
| 9\121 | |||
| 89.26 | |||
| 21/20 | |||
| [[Slithy]] | |||
|- | |||
| 1 | |||
| 12\121 | |||
| 119.01 | |||
| 15/14 | |||
| [[Subsedia]] | |||
|- | |||
| 1 | |||
| 16\121 | |||
| 158.68 | |||
| 35/32 | |||
| [[Hemikleismic]] | |||
|- | |||
| 1 | |||
| 27\121 | |||
| 267.77 | |||
| 7/6 | |||
| [[Hemimaquila]] | |||
|- | |||
| 1 | |||
| 32\121 | |||
| 317.36 | |||
| 6/5 | |||
| [[Hanson]] / [[metakleismic]] | |||
|- | |||
| 1 | |||
| 39\121 | |||
| 386.78 | |||
| 5/4 | |||
| [[Grendel]] | |||
|- | |||
| 1 | |||
| 40\121 | |||
| 396.69 | |||
| 98304/78125 | |||
| [[Squarschmidt]] | |||
|- | |||
| 1 | |||
| 42\121 | |||
| 416.53 | |||
| 14/11 | |||
| [[Sqrtphi]] | |||
|- | |||
| 1 | |||
| 46/121 | |||
| 456.20 | |||
| 125/96 | |||
| [[Qak]] | |||
|- | |||
| 1 | |||
| 47/121 | |||
| 466.12 | |||
| 55/42 | |||
| [[Hemiseptisix]] | |||
|- | |||
| 1 | |||
| 48/121 | |||
| 476.03 | |||
| 21/16 | |||
| [[Subfourth]] | |||
|- | |||
| 1 | |||
| 50\121 | |||
| 495.87 | |||
| 4/3 | |||
| [[Leapday]] / [[polypyth]] | |||
|- | |||
| 1 | |||
| 51\121 | |||
| 505.79 | |||
| 75/56 | |||
| [[Marfifths]] / marf / diatessic | |||
|- | |||
| 1 | |||
| 54\121 | |||
| 535.54 | |||
| 512/375 | |||
| [[Maquila]] | |||
|- | |||
| 1 | |||
| 59\121 | |||
| 585.12 | |||
| 7/5 | |||
| [[Pluto]] | |||
|- | |||
| 11 | |||
| 50\121<br>(5\121) | |||
| 495.87<br>(49.59) | |||
| 4/3<br>(36/35) | |||
| [[Hendecatonic]] | |||
|} | |||
== 13-limit detempering of 121et == | == 13-limit detempering of 121et == | ||