176/117: Difference between revisions

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+intro; +FJS name; correction of monzo. Name and category: minthmic not gentle
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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = major minthmic fifth
| Ratio = 176/117
| Color name = 3u1o5, thulo 5th
| Monzo = 4 -2 0 0 1 -1
| Cents = 706.88028
| Name = minthmic fifth
| Color name =
| FJS name = P5<sup>11</sup><sub>13</sub>
| Sound = Ji-176-117-csound-foscil-220hz.mp3
| Sound = Ji-176-117-csound-foscil-220hz.mp3
}}
}}


'''176/117''' is a [[13-limit]] [[ratio]] of 706.8 cents. It is [[352/351]] against the just perfect fifth of [[3/2]]. It arises in 13-limit [[just intonation]] by lowering [[22/13]] by [[9/8]] or by stacking [[16/13]] and [[11/9]].  
'''176/117''', the '''major minthmic fifth''', is a [[13-limit]] [[interval]] of 706.8{{cent}}. It is [[352/351]] sharp of the just perfect fifth of [[3/2]]. It arises in 13-limit [[just intonation]] by lowering [[22/13]] by [[9/8]] or by stacking [[16/13]] and [[11/9]].
 
Note that ''major minthmic'' modifies ''fifth'' and that ''major minthmic'' is the name of the temperament that tempers out 352/351. ''Major'' does not specify the size of the interval here.  


== See also ==
== See also ==
* [[182/121]] – another fifth similar in size.
* [[117/88]] – its [[octave complement]]
* [[182/121]] – the minor minthmic fifth
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]


[[Category:13-limit]]
[[Category:Interval ratio]]
[[Category:Fifth]]
[[Category:Fifth]]
[[Category:Minthmic]]
[[Category:Major minthmic]]
[[Category:Listen]]
 
[[Category:Todo:add color name]]
[[Category:Todo:expand]]

Latest revision as of 14:25, 15 January 2024

Interval information
Ratio 176/117
Factorization 24 × 3-2 × 11 × 13-1
Monzo [4 -2 0 0 1 -1⟩
Size in cents 706.8803¢
Name major minthmic fifth
Color name 3u1o5, thulo 5th
FJS name [math]\displaystyle{ \text{P5}^{11}_{13} }[/math]
Special properties reduced
Tenney height (log2 nd) 14.3298
Weil height (log2 max(n, d)) 14.9189
Wilson height (sopfr(nd)) 38

[sound info]
Open this interval in xen-calc

176/117, the major minthmic fifth, is a 13-limit interval of 706.8 ¢. It is 352/351 sharp of the just perfect fifth of 3/2. It arises in 13-limit just intonation by lowering 22/13 by 9/8 or by stacking 16/13 and 11/9.

Note that major minthmic modifies fifth and that major minthmic is the name of the temperament that tempers out 352/351. Major does not specify the size of the interval here.

See also

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