54edo: Difference between revisions

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The immediate close presence of [[53edo]] obscures 54edo and puts this temperament out of popular usage.

== Theory ==

54edo is suitable for usage with [[dual-fifth tuning]] systems, or alternately, no-fifth tuning systems.

It's a rare temperament which adds approximations of the 11th and 15th harmonics.

It's a rare temperament which adds better approximations of the 11th and 15th harmonics from [[27edo]], which it doubles. 54edo contains an alternate (flat) mapping of the fifth and an "extreme bayati" 6 6 10 10 2 10 10 diatonic scale.

~~From [[27edo]] which it doubles, 54edo contains an alternate (flat) mapping of the fifth and an "extreme bayati" 6 6 10 10 2 10 10 diatonic scale.~~

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]], while the bdf val does higher limit [[Magic family #Muggles|muggles]] about as well as it can be tuned.

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]].

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|+Table of intervals

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 The immediate close presence of [[53edo]] obscures 54edo and puts this temperament out of popular usage.
+{{primes in edo|54}}
 == Theory ==
 edo is suitable for usage with [[dual-fifth tuning]] systems, or alternately, no-fifth tuning systems.
-It's a rare temperament which adds approximations of the 11th and 15th harmonics.
+It's a rare temperament which adds better approximations of the 11th and 15th harmonics from [[27edo]], which it doubles. 54edo contains an alternate (flat) mapping of the fifth and an "extreme bayati" 6 6 10 10 2 10 10 diatonic scale.
-From [[27edo]] which it doubles, 54edo contains an alternate (flat) mapping of the fifth and an "extreme bayati" 6 6 10 10 2 10 10 diatonic scale.
+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]], while the bdf val does higher limit [[Magic family #Muggles|muggles]] about as well as it can be tuned.
-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]].
 {| class="wikitable"
 |+Table of intervals