23edo and octave stretching: Difference between revisions

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[[23edo|23edo]] is not typically taken seriously as a tuning except by those interested in extreme xenharmony. Its fifths are significantly flat, and is neighbors 22edo and 24edo generally get more attention.

However, when using a slightly [[~~Wikipedia:Stretched~~ tuning|stretched octave]] of around 1216 cents, 23edo looks much better, and it approximates the perfect fifth (and various other intervals involving the 5th, 7th, 11th, and 13th harmonics) to within 18 cents or so. If we can tolerate errors around this size in 12edo, we can probably tolerate them in stretched-23edo as well.

However, when using a slightly [[stretched tuning|stretched octave]] of around 1216 cents, 23edo looks much better, and it approximates the perfect fifth (and various other intervals involving the 5th, 7th, 11th, and 13th harmonics) to within 18 cents or so. If we can tolerate errors around this size in 12edo, we can probably tolerate them in stretched-23edo as well.

The perfect fifth is sharper than it is in 7edo, and thus the width of the perfect fifth falls within the syntonic temperament's tuning range. However, stretched-23 is ''not'' a syntonic temperament; using the perfect fifth as generator results in a [[Pelogic_family|pelogic]] ("mavila" or "antidiatonic") scale. Because of this, stretched-23 is not an extension of or replacement for 12edo, but rather an alternative to it; its strengths tend to be 12edo's weaknesses and vice versa, so they complement each other.

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 [[23edo|23edo]] is not typically taken seriously as a tuning except by those interested in extreme xenharmony. Its fifths are significantly flat, and is neighbors 22edo and 24edo generally get more attention.
-However, when using a slightly [[Wikipedia:Stretched tuning|stretched octave]] of around 1216 cents, 23edo looks much better, and it approximates the perfect fifth (and various other intervals involving the 5th, 7th, 11th, and 13th harmonics) to within 18 cents or so. If we can tolerate errors around this size in 12edo, we can probably tolerate them in stretched-23edo as well.
+However, when using a slightly [[stretched tuning|stretched octave]] of around 1216 cents, 23edo looks much better, and it approximates the perfect fifth (and various other intervals involving the 5th, 7th, 11th, and 13th harmonics) to within 18 cents or so. If we can tolerate errors around this size in 12edo, we can probably tolerate them in stretched-23edo as well.
 The perfect fifth is sharper than it is in 7edo, and thus the width of the perfect fifth falls within the syntonic temperament's tuning range. However, stretched-23 is ''not'' a syntonic temperament; using the perfect fifth as generator results in a [[Pelogic_family|pelogic]] ("mavila" or "antidiatonic") scale. Because of this, stretched-23 is not an extension of or replacement for 12edo, but rather an alternative to it; its strengths tend to be 12edo's weaknesses and vice versa, so they complement each other.