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]]. | ||
The immediate close presence of [[53edo]] obscures 54edo and puts this temperament out of popular usage. | |||
== Theory == | |||
{{primes in edo|54}} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 10:44, 16 October 2021
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.
The immediate close presence of 53edo obscures 54edo and puts this temperament out of popular usage.
Theory
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