54edo: Difference between revisions
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'''54-EDO''' is an equal temperament that divides the octave into 54 equal parts, each 22.2222 [[cent]]s in size. It's a rare temperament which adds approximations of the 11th and 15th harmonics, as well as an alternate (flat) mapping for the 5th, to [[27edo]] which it doubles. It is the highest [[EDO]] in which the best mappings of the major 3rd ([[5/4]]) and harmonic 7th ([[7/4]]), 17\54 and 44\54, are exactly 600 cents apart, making them suitable for harmonies using tritone substitutions. The 54cd val makes for an excellent tuning of 7-limit [[Augmented_family#Hexe|hexe temperament]]. | '''54-EDO''' is an equal temperament that divides the octave into 54 equal parts, each 22.2222 [[cent]]s in size. It's a rare temperament which adds approximations of the 11th and 15th harmonics, as well as an alternate (flat) mapping for the 5th, to [[27edo]] which it doubles. It is the highest [[EDO]] in which the best mappings of the major 3rd ([[5/4]]) and harmonic 7th ([[7/4]]), 17\54 and 44\54, are exactly 600 cents apart, making them suitable for harmonies using tritone substitutions. The 54cd val makes for an excellent tuning of 7-limit [[Augmented_family#Hexe|hexe temperament]]. | ||
[[Category: | [[Category:Equal divisions of the octave]] | ||
Revision as of 23:13, 4 December 2020
54-EDO is an equal temperament that divides the octave into 54 equal parts, each 22.2222 cents in size. It's a rare temperament which adds approximations of the 11th and 15th harmonics, as well as an alternate (flat) mapping for the 5th, to 27edo which it doubles. It is the highest EDO in which the best mappings of the major 3rd (5/4) and harmonic 7th (7/4), 17\54 and 44\54, are exactly 600 cents apart, making them suitable for harmonies using tritone substitutions. The 54cd val makes for an excellent tuning of 7-limit hexe temperament.