97/84: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = homothetic semifourth | | Name = nonacesimoseptimal semifourth, homothetic semifourth | ||
| Color name = 97or2 | |||
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'''97/84''' is the arithmetic mean of [[7/6]] and [[8/7]], which closely approximates their geometric mean, that is, the square root of [[4/3]], categorizing it as a very exact [[JI]] semifourth, as it is also a convergent of the square root of 4/3. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma [[S-expression|S97]] = [[9409/9408]]. Therefore, 97/84 is approximated well in any [[ET]] with a good approximation of 4/3 by an even number of steps, such as by [[24edo|5\24]] or [[53edo|11\53]]. It is closely related to [[97/56]], a semitritave. | |||
{{Todo|improve synopsis}} | |||
Latest revision as of 14:13, 12 June 2026
| Interval information |
homothetic semifourth
97/84 is the arithmetic mean of 7/6 and 8/7, which closely approximates their geometric mean, that is, the square root of 4/3, categorizing it as a very exact JI semifourth, as it is also a convergent of the square root of 4/3. Two instances of 97/84 differ from 4/3 by the 0.18-cent comma S97 = 9409/9408. Therefore, 97/84 is approximated well in any ET with a good approximation of 4/3 by an even number of steps, such as by 5\24 or 11\53. It is closely related to 97/56, a semitritave.