Bird's eye view of temperaments by accuracy: Difference between revisions
→7-limit focus: add garibaldi |
→No-3's focus: add didacus and mediantone |
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== No-2's focus == | == No-2's focus == | ||
== No-3's focus == | == No-3's focus == | ||
=== [[Didacus]] === | |||
Note counts: | |||
* 10 for {5, 7, 11, 25, 35, 55} ([[6L 7s]]) | |||
* 15 for {5, 7, 11, 25, 35, 49, 55, 77} ([[6L 13s]]) | |||
Bound-violating intervals: [[35/22]], [[49/44]] | |||
Didacus is a uniquely efficient no-3's focus temperament, mapping the no-3's 11-limit with ease and at the cost of accuracy admitting an extension to the no-3's 19-limit called [[#Mediantone]]. | |||
Its generator is [[~]][[28/25]] slightly flattened; two make [[~]][[5/4]], three make [[~]][[7/5]], four make a slightly flattened [[~]][[11/7]] (which is thus a sharp [[~]][[25/16]]), thus five make [[~]][[7/4]] and nine make [[~]][[11/4]] so that seven make [[~]][[11/5]]. | |||
[[37edo]] is a good tuning for its size and is practically equivalent to the pure-11's tuning, though for less damage on 5 and 7, [[68edo]] is a good tuning that much better targets composite harmonies, so might be advised as the first edo tuning to try. | |||
=== [[Mediantone]] === | |||
Note count: 29 for {5, 7, 11, 13, 17, 19, 25, 55, 65, 91} ([[6L 25s]]) | |||
Bound-violating intervals: [[25/17]], [[28/17]], [[55/34]] (all intervals of 17; note odd 35 can be added but is high error) | |||
Though not quite as accurate as [[#Didacus]], mediantone is notable for extending didacus to the full no-3's 19-limit. It does well in an optimized tuning, though if one wants to use an edo tuning, the main tuning of interest is [[80edo]], which finds primes 3 and 23 as well. | |||
== No-5's focus == | == No-5's focus == | ||
=== 2.3.7 [[Buzzard]] === | === 2.3.7 [[Buzzard]] === | ||