Bird's eye view of temperaments by accuracy: Difference between revisions
m →7-limit focus: revert some of the wording to be clearer, also clarify some of the terms |
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[[#Generator tunings|Generator tunings]]: 24\31, 31\53, 55\94 | [[#Generator tunings|Generator tunings]]: 24\31, 31\53, 55\94 | ||
Garibaldi is a very natural and very efficient (for its accuracy) way of | Garibaldi is a very natural and very efficient (for its accuracy) way of bestowing prime 7 upon [[#Schismic]], at the cost of accuracy as needing a slightly sharper fifth tunes the 5-limit worse so that it is no longer a microtemperament. This is done by interpreting ([[9/8]])<sup>3</sup> as [[~]][[10/7]] by tempering out [[5120/5103|S8/S9]] so that 8/7 and 10/9 are equidistant from 9/8, with the step being a convenient tempered comma-sized interval that simultaneously not only represents not only [[64/63]] = S8 and [[81/80]] = S9 but also the [[Pythagorean comma]] (as per schismic), equal to (9/8)<sup>6</sup> / (2/1). [[41edo]] and [[53edo]] are slightly overtempered and undertempered for it respectively, so that [[94edo]] is pretty close to optimal, though it has a (barely) inconsistently flat [[~]][[25/16]] which is unbefitting of schismic. 94 + 53 = [[147edo]] also supports it but with yet more inconsistencies due to the finer gamut. | ||
Extensions include: | Extensions include: | ||