161edo: Difference between revisions
Adopt new template, +links, +categories, and misc |
+RTT table and rank-2 temperaments |
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| Line 3: | Line 3: | ||
== Prime harmonics == | == Prime harmonics == | ||
161edo is notable as being low in [[29-limit]] relative error in the 100 to 200 range. | 161edo is notable as being low in [[29-limit]] relative error in the 100 to 200 range. | ||
{{Harmonics in equal|161}} | |||
{{ | == 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| -255 161 }} | |||
| [{{val| 161 255 }}] | |||
| +0.421 | |||
| 0.421 | |||
| 5.65 | |||
|- | |||
| 2.3.5 | |||
| 393216/390625, {{monzo| -17 21 -7 }} | |||
| [{{val| 161 255 374 }}] | |||
| +0.099 | |||
| 0.570 | |||
| 7.65 | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 3136/3125, 177147/175000 | |||
| [{{val| 161 255 374 452 }}] | |||
| +0.064 | |||
| 0.498 | |||
| 6.67 | |||
|- | |||
| 2.3.5.7.11 | |||
| 243/242, 441/440, 3136/3125, 35937/35840 | |||
| [{{val| 161 255 374 452 557 }}] | |||
| +0.037 | |||
| 0.448 | |||
| 6.01 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 243/242, 351/350, 441/440, 847/845, 3136/3125 | |||
| [{{val| 161 255 374 452 557 596 }}] | |||
| -0.046 | |||
| 0.449 | |||
| 6.03 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 243/242, 351/350, 441/440, 561/560, 847/845, 1089/1088 | |||
| [{{val| 161 255 374 452 557 596 658 }}] | |||
| -0.018 | |||
| 0.422 | |||
| 5.66 | |||
|- | |||
| 2.3.5.7.11.13.17.19 | |||
| 243/242, 324/323, 351/350, 441/440, 456/455, 495/494, 513/512 | |||
| [{{val| 161 255 374 452 557 596 658 684 }}] | |||
| -0.034 | |||
| 0.397 | |||
| 5.32 | |||
|} | |||
=== 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 | |||
| 15\161 | |||
| 111.80 | |||
| 16/15 | |||
| [[Vavoom]] | |||
|- | |||
| 1 | |||
| 17\161 | |||
| 126.71 | |||
| 14/13 | |||
| [[Mowglic]] | |||
|- | |||
| 1 | |||
| 25\161 | |||
| 186.34 | |||
| 10/9 | |||
| [[Mintone]] | |||
|- | |||
| 1 | |||
| 26\161 | |||
| 193.79 | |||
| 28/25 | |||
| [[Hemiwürschmidt]] | |||
|- | |||
| 1 | |||
| 38\161 | |||
| 283.23 | |||
| 33/28 | |||
| [[Neominor]] (161f) | |||
|- | |||
| 1 | |||
| 52\161 | |||
| 387.58 | |||
| 5/4 | |||
| [[Würschmidt]] (5-limit) | |||
|- | |||
| 1 | |||
| 79\161 | |||
| 588.82 | |||
| 45/32 | |||
| [[Aufo]] | |||
|- | |||
| 7 | |||
| 67\161<br>(2\161) | |||
| 499.38<br>(14.91) | |||
| 4/3<br>(81/80) | |||
| [[Absurdity]] | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Mintone]] | [[Category:Mintone]] | ||