Bird's eye view of temperaments by accuracy: Difference between revisions
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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 aguably the simplest way of effectively bestowing prime 7 upon [[#Schismic|schismic]], at the cost of accuracy as needing a slightly sharper, not flatter 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 also tempering out [[5120/5103|S8/S9]] so that 10/9 - 9/8 - 8/7 have equidistant steps, with the step being a convenient tempered comma-sized interval that simultaneously represents [[64/63|S8]], [[81/80|S9]], and the [[Pythagorean comma]] (as per schismic). [[41edo]] and [[53edo]] are slightly overtempered and undertempered for it respectively, so that [[94edo]] is pretty close to optimal, though it has | Garibaldi is aguably the simplest way of effectively bestowing prime 7 upon [[#Schismic|schismic]], at the cost of accuracy as needing a slightly sharper, not flatter 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 also tempering out [[5120/5103|S8/S9]] so that 10/9 - 9/8 - 8/7 have equidistant steps, with the step being a convenient tempered comma-sized interval that simultaneously represents [[64/63|S8]], [[81/80|S9]], and the [[Pythagorean comma]] (as per schismic). [[41edo]] and [[53edo]] are slightly overtempered and undertempered for it respectively, so that [[94edo]] is pretty close to optimal, though it has a slightly 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: | ||