Bird's eye view of temperaments by accuracy: Difference between revisions
→Higher-limit focus: add sendai |
→7-limit focus: add superpyth |
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== 5-limit focus == | == 5-limit focus == | ||
== 7-limit focus == | == 7-limit focus == | ||
=== [[Superpyth]] === | |||
Note counts: | |||
* 4 for {3, 7} ([[2L 3s]]) | |||
* 12 for {3, 5, 7, 9, 15} ([[5L 7s]] and [[5L 12s]]) | |||
Superpyth is the natural "opposite" of [[#Septimal meantone]] in a surprisingly large number of surprisingly exact senses; the main ones of note are that the [[3/2|fifth]] is mistuned in opposite directions (sharp in superpyth), and that superpyth makes prime 7 most immediately accessible on the chain of fifths with prime 5 requiring more complex movements (when measured in number of fifths), while septimal meantone does the opposite. Superpyth makes the major third [[~]][[9/7]], the minor third [[~]][[7/6]], the major second a blend between a sharp [[~]][[9/8]] and a flat [[~]][[8/7]] and the minor second [[~]][[28/27]], which is tuned very flat so that it becomes a quarter-tone in any good tuning of superpyth. Superpyth finds [[~]][[5/4]] as the augmented second and [[~]][[6/5]] correspondingly as the diminished fourth. | |||
Superpyth is a common choice for a beginner, with [[22edo]] and [[27edo]] having different advantages and 22edo the most explored by far, though the number of unique advantages and opportunities in 27edo make it formidable as a competitor. [[22edo]] is approximately the pure-[[9/7]]'s tuning while [[27edo]] is approximately the pure-[[7/6]]'s tuning. For 5 more notes, 27edo has the advantage of not equating [[7/5]] and [[10/7]] and having a more accurate [[8/7]] and [[7/4]]. A more optimized edo tuning is [[49edo]] but that comes at the cost of a lot of notes if you aren't merely looking to take a [[MOS]] scale subset of it. | |||
== 11-limit focus == | == 11-limit focus == | ||
=== [[Mohaha]] === | === [[Mohaha]] === | ||