65/63: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
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..."
 
Jdood (talk | contribs)
Added a name (feel free to change it)
 
Line 2: Line 2:
| Comma = yes
| Comma = yes
| Color name = 3ory1, thoruyo unison
| Color name = 3ory1, thoruyo unison
}}
|Name=Radius of Tolerance}}


'''65/63''' is a [[13-limit]] quartertone measuring about 54.1 [[cent]]s. 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>.
'''65/63''' is a [[13-limit]] quartertone measuring about 54.1 [[cent]]s. 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>.

Latest revision as of 09:25, 23 October 2025

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 Radius of Tolerance
Color name 3ory1, thoruyo unison
FJS name [math]\displaystyle{ \text{P1}^{5,13}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 11.9996
Weil norm (log2 max(n, d)) 12.0447
Wilson norm (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