21edo: Difference between revisions
CompactStar (talk | contribs) I think ultraminor would be low neutral 3rds |
Add 13-limit uniform maps |
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The subset 2 5 5 6 3 of 21 EDO is a good tuning for the [[Aurora scale]]. | The subset 2 5 5 6 3 of 21 EDO is a good tuning for the [[Aurora scale]]. | ||
== | == Regular temperament properties == | ||
The [[patent val]] for 21 EDO 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. | The [[patent val]] for 21 EDO 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 map|13|20.5|21.5}} | |||
{| | |||
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=== Commas === | === Commas === | ||
21edo [[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" | ||
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|} | |} | ||
<references/> | <references/> | ||
=== Rank-2 temperaments === | |||
[[List of 21edo rank two temperaments by badness]] | |||
{| class="wikitable" | |||
|- | |||
! Periods per octave | |||
! Generator | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 1\21 | |||
| [[Escapade_family#Escapade|Escapade]] | |||
|- | |||
| 1 | |||
| 2\21 | |||
| [[Gamelismic_clan#Miracle|Miracle]] | |||
|- | |||
| 1 | |||
| 4\21 | |||
| [[Slendric]]/[[Gamelismic_clan#Gorgo|Gorgo]]/[[Gamelismic_clan#Gidorah|Gidorah]] | |||
|- | |||
| 1 | |||
| 5\21 | |||
| [[Mint_temperaments#Subklei|Subklei]] | |||
|- | |||
| 1 | |||
| 8\21 | |||
| [[Chromatic_pairs#Tridec|Tridec]] | |||
|- | |||
| 1 | |||
| 10\21 | |||
| [[Marvel_temperaments#Triton|Triton]] | |||
|- | |||
| 3 | |||
| 1\21 | |||
| | |||
|- | |||
| 3 | |||
| 2\21 | |||
| [[Augmented_family|Augmented]]/[[August]] | |||
|- | |||
| 3 | |||
| 3\21 | |||
| [[Oodako]] | |||
|- | |||
| 7 | |||
| 1\21 | |||
| [[Apotome_family|Whitewood]] | |||
|} | |||
== Approaches == | == Approaches == | ||