97/56: Difference between revisions
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'''97/56''' is the arithmetic mean of [[7/4]] and [[12/7]], which closely approximates their geometric mean, that is, the square root of [[3/1]], categorizing it as a semitwelfth. 3/1 differs from two instances of 97/56 by the 0.18-cent comma [[Square superparticular|S97]] = [[9409/9408]]. Therefore, 97/56 is approximated well in any [[ET]] with a good approximation of 3/1 by an even number of steps (or in even-numbered [[EDT]]s), such as by [[24edo|19\24]] or [[53edo|42\53]]. It is closely related to [[97/84]], a semifourth. | |||
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Revision as of 14:14, 20 January 2025
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homothetic semitwelfth
97/56 is the arithmetic mean of 7/4 and 12/7, which closely approximates their geometric mean, that is, the square root of 3/1, categorizing it as a semitwelfth. 3/1 differs from two instances of 97/56 by the 0.18-cent comma S97 = 9409/9408. Therefore, 97/56 is approximated well in any ET with a good approximation of 3/1 by an even number of steps (or in even-numbered EDTs), such as by 19\24 or 42\53. It is closely related to 97/84, a semifourth.