Bird's eye view of temperaments by accuracy: Difference between revisions

Flattone is a low-accuracy [[11-limit|11-]] or [[13-limit]] temperament. It is an alternative extension of [[#Meantone]] of interest because it maps [[7/4]] to the arguably more intuitive diminished seventh and [[11/8]] to the similarly simple augmented fourth (aka tritone). If one maps the 13-limit, the best way is by equating a sharpened [[~]][[16/13]] with the already-very-flat [[~]][[5/4]], continuing the strong flat tendency. It tunes meantone much flatter than usual so that the whole tone is much closer to [[10/9]] than it is to [[9/8]], and is maybe most notable as being supported by [[26edo]], the smallest edo consistent in the [[13-odd-limit]]. Maybe surprisingly, it is one of the most accurate temperaments in this accuracy category; its most off primes are 5 and 13, which are the only ones to meaningfully transgress the 12c bound, along with odd 9 being tuned very flat which has the benefit of causing the tuning of [[6/5]] to be relatively accurate.