48edo: Difference between revisions

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If 48 is treated as a no-fives system, it still tempers out 99/98 and 243/242 in the 11-limit, leading to a no-fives version of squares for which it does well as a tuning. In the 13 no-fives limit, we can add 144/143 to the list of commas, and we get the no-fives version of 13-limit squares, for which 48 actually defines the [[optimal patent val]]. No-fives squares should probably be considered by anyone interested in 48edo; the generator is 17\48, a 425{{c}} interval serving as both [[9/7]] and [[14/11]].

Something close to 48edo is what you get if you cross 16edo with pure fifths, for instance, on a 16-tone guitar. The presence of 12/11 in 16edo allows a string offset of 11/8 to also work for producing perfect fifths.

Something close to 48edo is what you get if you cross [[16edo]] with pure fifths, for instance, on a 16-tone guitar. The presence of 12/11 in 16edo allows a string offset of 11/8 to also work for producing perfect fifths. Since 16edo supports [[mavila]] temperament, and 48edo has two viable major and minor thirds, 48edo could be used for an unexplored system of "adaptive mavila".

=== Odd harmonics ===

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 If 48 is treated as a no-fives system, it still tempers out 99/98 and 243/242 in the 11-limit, leading to a no-fives version of squares for which it does well as a tuning. In the 13 no-fives limit, we can add 144/143 to the list of commas, and we get the no-fives version of 13-limit squares, for which 48 actually defines the [[optimal patent val]]. No-fives squares should probably be considered by anyone interested in 48edo; the generator is 17\48, a 425{{c}} interval serving as both [[9/7]] and [[14/11]].
-Something close to 48edo is what you get if you cross 16edo with pure fifths, for instance, on a 16-tone guitar. The presence of 12/11 in 16edo allows a string offset of 11/8 to also work for producing perfect fifths.
+Something close to 48edo is what you get if you cross [[16edo]] with pure fifths, for instance, on a 16-tone guitar. The presence of 12/11 in 16edo allows a string offset of 11/8 to also work for producing perfect fifths. Since 16edo supports [[mavila]] temperament, and 48edo has two viable major and minor thirds, 48edo could be used for an unexplored system of "adaptive mavila".
 === Odd harmonics ===