182/121: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Ratio = 182/121
| Ratio = 182/121
| Monzo = 1 0 0 1 -2 1
| Monzo = 1 0 0 1 -2 1
| Cents = 706.71768
| Cents = 706.71768
| Name = tridecimal gentle fifth
| Name = (tridecimal) gentle fifth
| Color name =
| Color name =
| Sound = Ji-182-121-csound-foscil-220hz.mp3
| Sound = Ji-182-121-csound-foscil-220hz.mp3
}}
}}
'''182/121''', 706.7177 cents, is the '''gentle fifth''', found between 11/14 and [[13/11]] (13/11 * [[14/11]] = 182/121).
'''182/121''', the '''(tridecimal) gentle fifth''', is a [[13-limit]] interval measuring about 706.7{{cent}}. It is a gentle comma ([[364/363]]) sharp of the perfect fifth ([[3/2]]). It is found between 11/14 and [[13/11]] (13/11 * [[14/11]] = 182/121).


Rather well approximated by the regular fifths in [[17edo]].
== Approximation ==
The gentle fifth is rather well approximated by the regular fifths in [[17edo]]: 10\17 is 0.8{{cent}} flat of 182/121.


Also incredibly close to another gentle fifth, [[176/117]], 706.8803 cents, found between 13/16 and [[11/9]] (11/9 * [[16/13]] = 176/117).
It is also incredibly close to the minthmic fifth ([[176/117]], 706.8803{{cent}}), found between 13/16 and [[11/9]] (11/9 * [[16/13]] = 176/117).
 
== See also ==
* [[Gallery of just intervals]]


[[Category:13-limit]]
[[Category:13-limit]]
[[Category:Just_interval]]
[[Category:Fifth]]
[[Category:Fifth]]
[[Category:Gentle]]
[[Category:Gentle]]


[[Category:Todo:improve synopsis]]
{{todo|add color name}}
[[Category:Todo:add color name]]
[[Category:Todo:expand]]

Revision as of 18:48, 23 March 2022

Interval information
Ratio 182/121
Factorization 2 × 7 × 11-2 × 13
Monzo [1 0 0 1 -2 1⟩
Size in cents 706.7177¢
Name (tridecimal) gentle fifth
FJS name [math]\displaystyle{ \text{m6}^{7,13}_{11,11} }[/math]
Special properties reduced
Tenney height (log2 nd) 14.4267
Weil height (log2 max(n, d)) 15.0156
Wilson height (sopfr(nd)) 44

[sound info]
Open this interval in xen-calc

182/121, the (tridecimal) gentle fifth, is a 13-limit interval measuring about 706.7 ¢. It is a gentle comma (364/363) sharp of the perfect fifth (3/2). It is found between 11/14 and 13/11 (13/11 * 14/11 = 182/121).

Approximation

The gentle fifth is rather well approximated by the regular fifths in 17edo: 10\17 is 0.8 ¢ flat of 182/121.

It is also incredibly close to the minthmic fifth (176/117, 706.8803 ¢), found between 13/16 and 11/9 (11/9 * 16/13 = 176/117).

See also

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