21edo: Difference between revisions
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m →Regular temperament properties: cleanup |
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== Regular temperament properties == | == Regular temperament properties == | ||
The [[patent val]] for | The [[patent val]] for 21edo tempers out [[128/125]] and [[2187/2000]] in the [[5-limit]], and supplies the [[optimal patent val]] for the 5-limit [[laconic]] temperament tempering out 2187/2000, and also the optimal patent val for 7-, 11- and 13-limit [[gorgo]], and 11- and 13-limit spartan. These temperaments lead to some "interesting" mappings, where 10/9 is larger than 9/8, 11/9 is larger than 16/13, and 8/7 maps to the same interval as 10/9, for instance. | ||
=== Uniform maps === | === Uniform maps === | ||
| Line 485: | Line 485: | ||
=== Commas === | === Commas === | ||
21et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 21 33 49 59 73 78 }}.) | |||
{| class="commatable wikitable center-all left-3 right-4 left-6" | {| class="commatable wikitable center-all left-3 right-4 left-6" | ||
| Line 501: | Line 501: | ||
| 113.69 | | 113.69 | ||
| Lawa | | Lawa | ||
| | | Whtiewood comma, apotome, Pythagorean chroma | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 508: | Line 508: | ||
| 41.06 | | 41.06 | ||
| Trigu | | Trigu | ||
| | | Augmented comma, diesis | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 515: | Line 515: | ||
| 31.57 | | 31.57 | ||
| Lala-tribiyo | | Lala-tribiyo | ||
| [[Ampersand]] | | [[Ampersand comma]] | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 522: | Line 522: | ||
| 9.49 | | 9.49 | ||
| Sasa-tritrigu | | Sasa-tritrigu | ||
| [[Escapade]] | | [[Escapade comma]] | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 536: | Line 536: | ||
| 48.77 | | 48.77 | ||
| Rugu | | Rugu | ||
| | | Mint comma, septimal quartertone | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 557: | Line 557: | ||
| 7.71 | | 7.71 | ||
| Ruyoyo | | Ruyoyo | ||
| | | Marvel comma, septimal kleisma | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 564: | Line 564: | ||
| 6.99 | | 6.99 | ||
| Quinru-aquadyo | | Quinru-aquadyo | ||
| Mirkwai | | Mirkwai comma | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 578: | Line 578: | ||
| 0.34 | | 0.34 | ||
| Trisa-seprugu | | Trisa-seprugu | ||
| [[Akjaysma]] | | [[Akjaysma]] | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 599: | Line 599: | ||
| 3.03 | | 3.03 | ||
| Triluyo | | Triluyo | ||
| Wizardharry | | Wizardharry comma | ||
|} | |} | ||
<references/> | <references/> | ||
| Line 608: | Line 608: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Periods per | ! Periods<br>per 8ve | ||
! Generator | ! Generator | ||
! Temperaments | ! Temperaments | ||
| Line 614: | Line 614: | ||
| 1 | | 1 | ||
| 1\21 | | 1\21 | ||
| [[ | | [[Escapade]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 2\21 | | 2\21 | ||
| [[ | | [[Miracle]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 4\21 | | 4\21 | ||
| [[Slendric]]/[[ | | [[Slendric]] / [[gorgo]] / [[gidorah]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 5\21 | | 5\21 | ||
| [[ | | [[Subklei]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 8\21 | | 8\21 | ||
| [[ | | [[Tridec]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 10\21 | | 10\21 | ||
| [[ | | [[Triton]] | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 642: | Line 642: | ||
| 3 | | 3 | ||
| 2\21 | | 2\21 | ||
| [[ | | [[Augmented]] / [[august]] | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 650: | Line 650: | ||
| 7 | | 7 | ||
| 1\21 | | 1\21 | ||
| [[ | | [[Whitewood]] | ||
|} | |} | ||