65/63

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Revision as of 04:29, 18 May 2025 by Xenllium (talk | contribs) (Created page with "{{Infobox interval | Comma = yes | Color name = 3ory1, thoruyo unison }} '''65/63''' is a 13-limit quartertone measuring about 54.1 cents. It is known as the '''radius of tolerance''' in the Functional Just System<ref>[https://misotanni.github.io/fjs/en/rules.html The Complete Formal FJS Description]</ref>. It arises as the sum of 64/63 and 65/64, the difference between 7/5 (septimal narrow tritone) and 13/9 (tridecimal high tritone), betwee...")
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Interval information
Ratio 65/63
Factorization 3-2 × 5 × 7-1 × 13
Monzo [0 -2 1 -1 0 1⟩
Size in cents 54.10547¢
Name(s) missing ? 
Color name 3ory1, thoruyo unison
FJS name [math]\displaystyle{ \text{P1}^{5,13}_{7} }[/math]
Special properties reduced
Tenney height (log2 nd) 11.9996
Weil height (log2 max(n, d)) 12.0447
Wilson height (sopfr(nd)) 31
Comma size medium
Open this interval in xen-calc

65/63 is a 13-limit quartertone measuring about 54.1 cents. It is known as the radius of tolerance in the Functional Just System[1].

It arises as the sum of 64/63 and 65/64, the difference between 7/5 (septimal narrow tritone) and 13/9 (tridecimal high tritone), between 5/3 and 21/13, between 10/9 and 14/13, and between 13/12 and 21/20.

It differs from the 33/32 semitone by 2080/2079 – an unnoticeable comma measuring about 0.83 cents.

Notes

  1. ↑ The Complete Formal FJS Description
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