1/6-comma meantone: Difference between revisions

'''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. Leopold Mozart and Wolfgang Amadeus Mozart recommended this tuning (implemented as 55edo or something close to it), with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>Chesnut, John (1977) ''Mozart's Teaching of Intonation'', '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref>