171edo: Difference between revisions
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== Intervals == | == Intervals == | ||
{{Main| 171edo/Intervals }} | {{Main| 171edo/Intervals }} | ||
== 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| -271 171 }} | |||
| [{{val| 171 271 }}] | |||
| +0.063 | |||
| 0.0633 | |||
| 0.90 | |||
|- | |||
| 2.3.5 | |||
| 32805/32768, {{monzo| 1 -27 18 }} | |||
| [{{val| 171 271 397 }}] | |||
| +0.092 | |||
| 0.0660 | |||
| 0.94 | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 4375/4374, 32805/32768 | |||
| [{{val| 171 271 397 480 }}] | |||
| +0.105 | |||
| 0.0614 | |||
| 0.87 | |||
|- | |||
| 2.3.5.7.11 | |||
| 243/242, 441/440, 4375/4356, 16384/16335 | |||
| [{{val| 171 271 397 480 592 }}] (171) | |||
| -0.093 | |||
| 0.401 | |||
| 5.71 | |||
|- | |||
| 2.3.5.7.11 | |||
| 385/384, 1331/1323, 1375/1372, 4375/4374 | |||
| [{{val| 171 271 397 480 591 }}] (171e) | |||
| +0.312 | |||
| 0.418 | |||
| 5.96 | |||
|} | |||
=== 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 | |||
| 5\171 | |||
| 35.09 | |||
| 234375/229376 | |||
| [[Gammic]] | |||
|- | |||
| 1 | |||
| 20\171 | |||
| 140.35 | |||
| 243/224 | |||
| [[Tsaharuk]] | |||
|- | |||
| 1 | |||
| 25\171 | |||
| 175.44 | |||
| 448/405 | |||
| [[Sesquiquartififths]] / [[sesquart]] | |||
|- | |||
| 1 | |||
| 26\171 | |||
| 182.46 | |||
| 10/9 | |||
| [[Minortone]] / [[mitonic]] / [[mineral]] (171) / [[ore]] (171e) | |||
|- | |||
| 1 | |||
| 34\171 | |||
| 238.60 | |||
| 147/128 | |||
| [[Tokko]] | |||
|- | |||
| 1 | |||
| 46\171 | |||
| 322.81 | |||
| 3087/2560 | |||
| [[Senior]] / [[seniority]] | |||
|- | |||
| 1 | |||
| 62\171 | |||
| 435.09 | |||
| 9/7 | |||
| [[Supermajor]] | |||
|- | |||
| 1 | |||
| 64\171 | |||
| 449.12 | |||
| 35/27 | |||
| [[Semidimi]] | |||
|- | |||
| 1 | |||
| 65\171 | |||
| 456.14 | |||
| 125/96 | |||
| [[Qak]] | |||
|- | |||
| 1 | |||
| 71\171 | |||
| 498.25 | |||
| 4/3 | |||
| [[Helmholtz]] / [[pontiac]] | |||
|- | |||
| 1 | |||
| 83\171 | |||
| 582.46 | |||
| 7/5 | |||
| [[Neptune]] | |||
|- | |||
| 3 | |||
| 20\171 | |||
| 140.35 | |||
| 243/224 | |||
| [[Septichrome]] | |||
|- | |||
| 3 | |||
| 23\171 | |||
| 161.40 | |||
| 192/175 | |||
| [[Pnict]] | |||
|- | |||
| 3 | |||
| 71\171<br>(2\171) | |||
| 385.96<br>(14.04) | |||
| 5/4<br>(126/125) | |||
| [[Mutt]] | |||
|- | |||
| 3 | |||
| 55\171<br>(2\171) | |||
| 498.25<br>(98.25) | |||
| 4/3<br>(200/189) | |||
| [[Term]] / [[terminal]] | |||
|- | |||
| 9 | |||
| 7\171 | |||
| 49.12 | |||
| 36/35 | |||
| [[Ennealimmal]] (171e) / [[Ennealimmia]] (171) / [[Ennealimnic]] (171) / [[Ennealiminal]] (171e) | |||
|- | |||
| 19 | |||
| 71\171<br>(1\171) | |||
| 498.25<br>(7.02) | |||
| 4/3<br>(225/224) | |||
| [[Enneadecal]] | |||
|} | |||
== Scales == | == Scales == | ||