159edo: Difference between revisions
m →Prime harmonics: prec is now by default 2 between 53 and 526 EDOs |
+RTT table |
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== Notation == | == Notation == | ||
{{main|159edo notation}} | {{main| 159edo notation }} | ||
Because of the complexity of 159edo, notation requires systems that make use of multiple extra pairs of accidentals. This is because at high EDOs, systems with only a single extra accidental pair become unwieldy due to the sheer number of such accidentals required for notating some pitches, which in turn results in high amounts of clutter on scores. So far, several notation systems addressing this problem have been proposed. | Because of the complexity of 159edo, notation requires systems that make use of multiple extra pairs of accidentals. This is because at high EDOs, systems with only a single extra accidental pair become unwieldy due to the sheer number of such accidentals required for notating some pitches, which in turn results in high amounts of clutter on scores. So far, several notation systems addressing this problem have been proposed. | ||
== 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]] (%) | |||
|- | |||
| 2.3.5.7 | |||
| 1029/1024, 10976/10935, 15625/15552 | |||
| [{{val| 159 252 369 446 }}] | |||
| +0.411 | |||
| 0.413 | |||
| 5.47 | |||
|- | |||
| 2.3.5.7.11 | |||
| 385/384, 441/440, 4000/3993, 10976/10935 | |||
| [{{val| 159 252 369 446 550 }}] | |||
| +0.350 | |||
| 0.389 | |||
| 5.15 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 325/324, 364/363, 385/384, 625/624, 10976/10935 | |||
| [{{val| 159 252 369 446 550 588 }}] | |||
| +0.418 | |||
| 0.385 | |||
| 5.11 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 273/272, 325/324, 364/363, 375/374, 385/384, 3773/3757 | |||
| [{{val| 159 252 369 446 550 588 650 }}] | |||
| +0.333 | |||
| 0.412 | |||
| 5.46 | |||
|} | |||
=== Rank-2 temperaments === | |||
Note: Temperaments supported by 53et are not included. | |||
{| class="wikitable center-all right-3 left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per octave | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperament | |||
|- | |||
| 1 | |||
| 2\159 | |||
| 15.094 | |||
| 121/120 | |||
| [[Yarman I]] / [[yarman II]] | |||
|- | |||
| 1 | |||
| 11\159 | |||
| 83.019 | |||
| 21/20 | |||
| [[Sextilififths]] | |||
|- | |||
| 1 | |||
| 22\159 | |||
| 166.038 | |||
| 11/10 | |||
| [[Tertiaschis]] | |||
|- | |||
| 1 | |||
| 31\159 | |||
| 233.962 | |||
| 8/7 | |||
| [[Slendric]] / [[guiron]] | |||
|- | |||
| 1 | |||
| 38\159 | |||
| 286.792 | |||
| 13/11 | |||
| [[Gamity]] | |||
|- | |||
| 1 | |||
| 41\159 | |||
| 309.434 | |||
| 448/375 | |||
| [[Triwell]] | |||
|- | |||
| 1 | |||
| 67\159 | |||
| 505.660 | |||
| 75/56 | |||
| [[Marfifths]] | |||
|- | |||
| 3 | |||
| 8\159 | |||
| 60.377 | |||
| 28/27 | |||
| [[Chromat]] | |||
|- | |||
| 3 | |||
| 42\159<br>(11\159) | |||
| 316.981<br>(83.019) | |||
| 6/5<br>(21/20) | |||
| [[Tritikleismic]] | |||
|- | |||
| 3 | |||
| 66\159<br>(13\159) | |||
| 498.113<br>(98.113) | |||
| 4/3<br>(35/33) | |||
| [[Term]] / [[terminal]] | |||
|- | |||
| 53 | |||
| 31\159<br>(1\159) | |||
| 233.962<br>(7.547) | |||
| 8/7<br>(225/224) | |||
| [[Schismerc]] / [[cartography]] | |||
|} | |||
== Music == | == Music == | ||