77/72: Difference between revisions
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'''77/72''', the '''undecimal secor''', lies between the 3\31 [[secor]] of [[31edo]] and the 10\103 secor of [[103edo]]. It is [[385/384]] (4.5 cents) sharper than [[16/15]] and [[540/539]] (3.2 cents) flatter than [[15/14]]. In 11-limit JI scales it often appears, being the interval between [[12/11]] and [[7/6]], [[8/7]] and [[11/9]], [[9/7]] and [[11/8]], and their inversions. Tempering out 385/384 equates it with [[16/15]], tempering out 540/539 equates it with [[15/14]], and tempering out both makes it the marvel secor. | '''77/72''', the '''undecimal secor''', lies between the 3\31 [[secor]] of [[31edo]] and the 10\103 secor of [[103edo]]. It is [[385/384]] (4.5 cents) sharper than [[16/15]] and [[540/539]] (3.2 cents) flatter than [[15/14]]. In 11-limit JI scales it often appears, being the interval between [[12/11]] and [[7/6]], [[8/7]] and [[11/9]], [[9/7]] and [[11/8]], and their inversions. | ||
77/72 is extremely close to the [[mediant]] of 16/15 and 15/14, [[31/29]], differing only by [[2233/2232]] (0.7 cents). | |||
== Approximation == | |||
Tempering out [[385/384]] equates it with [[16/15]], tempering out [[540/539]] equates it with [[15/14]], and tempering out both makes it the marvel secor. | |||
Tempering out [[19712/19683]] instead equates it with the [[apotome]], with better accuracy than the former (2.5 cents). | |||
== See also == | == See also == | ||
Latest revision as of 08:20, 28 September 2026
| Interval information |
[sound info]
77/72, the undecimal secor, lies between the 3\31 secor of 31edo and the 10\103 secor of 103edo. It is 385/384 (4.5 cents) sharper than 16/15 and 540/539 (3.2 cents) flatter than 15/14. In 11-limit JI scales it often appears, being the interval between 12/11 and 7/6, 8/7 and 11/9, 9/7 and 11/8, and their inversions.
77/72 is extremely close to the mediant of 16/15 and 15/14, 31/29, differing only by 2233/2232 (0.7 cents).
Approximation
Tempering out 385/384 equates it with 16/15, tempering out 540/539 equates it with 15/14, and tempering out both makes it the marvel secor.
Tempering out 19712/19683 instead equates it with the apotome, with better accuracy than the former (2.5 cents).