205edo: Difference between revisions
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+RTT table and rank-2 temperaments |
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The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing [[Wikipedia: Nicola Vicentino|Nicola Vicentino]]'s [http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx adaptive-JI scheme of 1555]. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus. | The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing [[Wikipedia: Nicola Vicentino|Nicola Vicentino]]'s [http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx adaptive-JI scheme of 1555]. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus. | ||
== 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 | |||
| 1600000/1594323, {{monzo| 38 -2 -15 }} | |||
| [{{val| 205 325 476 }}] | |||
| -0.106 | |||
| 0.141 | |||
| 2.41 | |||
|- | |||
| 2.3.5.11 | |||
| 5632/5625, 14641/14580, 1600000/1594323 | |||
| [{{val| 181 287 420 508 }}] | |||
| -0.002 | |||
| 0.218 | |||
| 3.72 | |||
|} | |||
=== 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 | |||
| 6\205 | |||
| 35.122 | |||
| 45/44 | |||
| [[Gammic]] (205e) | |||
|- | |||
| 1 | |||
| 24\205 | |||
| 140.488 | |||
| 13/12 | |||
| [[Quanic]] (205) | |||
|- | |||
| 1 | |||
| 33\205 | |||
| 193.171 | |||
| 28/25 | |||
| [[Luna]] / [[lunatic]] (205) / [[hemithirds]] (205d) | |||
|- | |||
| 1 | |||
| 58\205 | |||
| 339.512 | |||
| 128/105 | |||
| [[Amity]] (205) | |||
|- | |||
| 5 | |||
| 63\205<br>(19\205) | |||
| 368.780<br>(111.220) | |||
| 10125/8192<br>(16/15) | |||
| [[Qintosec]] | |||
|} | |||
== Scales == | == Scales == | ||
=== Quanic (24\205) MOS === | === Quanic (24\205) MOS === | ||
==== 17 note ==== | ==== 17 note ==== | ||
11 13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13 | 11 13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13 | ||