Bird's eye view of temperaments by accuracy: Difference between revisions
→7-limit focus: add superpyth |
m →Superpyth: note bound-violating intervals |
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Note counts: | Note counts: | ||
* 4 for {3, 7} ([[2L 3s]]) | * 4 for {3, 7} ([[2L 3s]]) | ||
* 12 for {3, 5, 7, 9 | * 12 for {3, 5, 7, 9} ([[5L 7s]] and [[5L 12s]]) | ||
Bound-violating intervals: [[9/8]] (and [[8/7]] in flatter tunings like 22edo) | |||
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 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. | ||