176/117: Difference between revisions

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 norm (log2 nd)	14.3298
Weil norm (log2 max(n, d))	14.9189
Wilson norm (sopfr(nd))	38
	https://en.xen.wiki/w/File:Ji-176-117-csound-foscil-220hz.mp3; [sound info]
	Open this interval in xen-calc

Latest revision as of 14:36, 22 July 2026

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.

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = major minthmic fifth
+| Name = major-minthmic fifth
 | Color name = 3u1o5, thulo 5th
 | Sound = Ji-176-117-csound-foscil-220hz.mp3
 }}
+'''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]].
-'''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 ==
 * [[117/88]] – its [[octave complement]]
-* [[182/121]] – the minor minthmic fifth
+* [[182/121]] – the minor-minthmic fifth
 * [[Gallery of just intervals]]
 [[Category:Fifth]]
 [[Category:Major minthmic]]