4/9-comma meantone: Difference between revisions

Revision as of 06:26, 13 November 2024 view source Lucius Chiaraviglio (talk \| contribs) 1,164 edits Add ragisma = 4375/4374 Tag: Visual edit ← Older edit		Latest revision as of 22:13, 10 August 2025 view source BudjarnLambeth (talk \| contribs) autopatrolled 18,215 edits m Mathematical interest
(One intermediate revision by one other user not shown)
Line 1:		Line 1:
	{{~~Novelty~~}}		{{Mathematical interest}}

	'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only a ragisma ([[4375/4374]], 0.395756¢) sharp of [[8/7]] (231.174094¢).		'''4/9-comma meantone''' is a tuning of [[meantone]] where the [[3/2\|fifth]] is flattened by 4/9 of the [[81/80\|syntonic comma]], producing a fifth of 692.396649¢ cents. This is approximated well by [[26edo]] (15\26 is 692.307692¢, which is flatter by 0.088957¢, for a cumulative error of only 2.312882¢ for proceeding all the way around the 26edo circle of fifths). The [[eigenmonzo]] is [[2500/2187]] (231.569849¢), which is only a ragisma ([[4375/4374]], 0.395756¢) sharp of [[8/7]] (231.174094¢).