768/625: Difference between revisions

Interval information
Ratio	768/625
Factorization	28 × 3 × 5-4
Monzo	[8 1 -4⟩
Size in cents	356.7001¢
Names	(greater) pental neutral third,; tetraptolemaic double-diminished fourth
Color name	quadgu 4th, g^44
FJS name	[math]\displaystyle{ \text{dd4}_{5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	18.8727
Weil norm (log2 max(n, d))	19.1699
Wilson norm (sopfr(nd))	39
	https://en.xen.wiki/w/File:Audacity_pluck_768_625.wav; [sound info]
	Open this interval in xen-calc

Latest revision as of 10:33, 4 October 2024

768/625, the (greater) pental neutral third or tetraptolemaic double-diminished fourth is a 5-limit interval of about 356.7 cents. It is sharp of the Pythagorean double-diminished fourth by four syntonic commas. Equivalently, it is equal to a fifth minus an octave-reduced stack of four classical major thirds, or equal to a classical minor third plus a diesis. In the 11-limit it is 6912/6875 sharp of 11/9, and 5632/5625 sharp of 27/22. In the 13-limit it is 625/624 flat of 16/13.

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = (greater) 5-limit neutral third
+| Name = (greater) pental neutral third, tetraptolemaic double-diminished fourth
 | Color name = quadgu 4th, g^44
-| Sound = audacity_pluck_625_512.wav
+| Sound = audacity_pluck_768_625.wav
 }}
-'''768/625''', the '''(greater) 5-limit neutral third''' is a [[128/125|diesis]] sharp of [[6/5]] and 6912/6875 sharp of [[11/9]].
+'''768/625''', the '''(greater) pental neutral third''' or '''tetraptolemaic double-diminished fourth''' is a [[5-limit]] [[interval]] of about 356.7 [[cent]]s. It is sharp of the Pythagorean double-diminished fourth by four [[81/80|syntonic comma]]s. Equivalently, it is equal to a [[3/2|fifth]] minus an [[octave reduction|octave-reduced]] stack of four [[5/4|classical major thirds]], or equal to a [[6/5|classical minor third]] plus a [[128/125|diesis]]. In the 11-limit it is 6912/6875 sharp of [[11/9]], and [[5632/5625]] sharp of [[27/22]]. In the 13-limit it is [[625/624]] flat of [[16/13]].
-[[Category:Stub]]
+== See also ==
+* [[625/384]] – its [[octave complement]]
+* [[625/512]] – its [[fifth complement]]
+* [[24edo]]
+* [[Iceface tuning]]
+[[Category:Third]]
+[[Category:Fourth]]
+[[Category:Neutral third]]
+[[Category:Diminished fourth]]