DKW theory: Difference between revisions
| Line 39: | Line 39: | ||
Below are commas with simple expressions in terms of these intervals, with "complexity" measured as the sum of the absolute values of powers of '''A''', '''B''', and '''C'''. | Below are commas with simple expressions in terms of these intervals, with "complexity" measured as the sum of the absolute values of powers of '''A''', '''B''', and '''C'''. | ||
Note all commas considered here (aside from complexity-1) are those that contain at least one minus sign in their signature expression. | |||
{| class="wikitable center-1 center-2 center-3 center-4" | |||
|- | |||
! rowspan="2" | Comma | |||
! rowspan="2" | Defined temperament | |||
! rowspan="2" | Complexity | |||
! rowspan="2" | Smonzo (9/8.16/15.25/24) | |||
|- | |||
! | |||
|- | |||
| [[9/8]] | |||
| [[Very_low_accuracy_temperaments#Antitonic|Antitonic]] | |||
| 1 | |||
| {{monzo| 1 0 0 }} | |||
|- | |||
| [[16/15]] | |||
| [[Father]] | |||
| 1 | |||
| {{monzo| 0 1 0 }} | |||
|- | |||
| [[25/24]] | |||
| [[Dicot]] | |||
| 1 | |||
| {{monzo| 0 0 1 }} | |||
|- | |||
| [[27/25]] | |||
| [[Bug]] | |||
| 2 | |||
| {{monzo| 1 0 -1 }} | |||
|- | |||
| [[135/128]] | |||
| [[Mavila]] | |||
| 2 | |||
| {{monzo| 1 -1 0 }} | |||
|- | |||
| [[128/125]] | |||
| [[Augmented]] | |||
| 2 | |||
| {{monzo| 0 1 -1 }} | |||
|- | |||
| [[648/625]] | |||
| [[Dimipent]] | |||
| 3 | |||
| {{monzo| 1 0 -2 }} | |||
|- | |||
| [[2048/2025]] | |||
| [[Diaschismic]] | |||
| 3 | |||
| {{monzo| -1 2 0 }} | |||
|- | |||
| [[3125/3072]] | |||
| [[Magic]] | |||
| 3 | |||
| {{monzo| 0 -1 2 }} | |||
|- | |||
| [[81/80]] | |||
| [[Meantone]] | |||
| 3 | |||
| {{monzo| 1 -1 -1 }} | |||
|} | |||
[[Category:Regular temperament tuning]] | [[Category:Regular temperament tuning]] | ||
[[Category:Diamond]] | [[Category:Diamond]] | ||
{{Todo| add examples }} | {{Todo| add examples }} | ||