51/40: Difference between revisions

Interval information
Ratio	51/40
Factorization	2-3 × 3 × 5-1 × 17
Monzo	[-3 1 -1 0 0 0 1⟩
Size in cents	420.5967¢
Name	diatismic major third
Color name	17og4, sogu 4th
FJS name	[math]\displaystyle{ \text{d4}^{17}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	10.9944
Weil norm (log2 max(n, d))	11.3449
Wilson norm (sopfr(nd))	31
	Open this interval in xen-calc

Latest revision as of 12:45, 15 June 2025

In 17-limit just intonation, 51/40 is the diatismic major third. It exceeds the Pythagorean major third (81/64) by a diatisma (136/135), hence the name.

It is approximated by:

@@ Line 1: / Line 1: @@
-'''51/40'''
+{{Infobox Interval
-|-8 1 -1 0 0 0 1&gt;
+| Name = diatismic major third
+| Color name = 17og4, sogu 4th
+}}
-.597 [[cent|cents]]
+In [[17-limit]] [[just intonation]], '''51/40''' is the '''diatismic major third'''.  It exceeds the [[81/64|Pythagorean major third (81/64)]] by a [[136/135|diatisma (136/135)]], hence the name.
-[[File:ji-51-40-csound-foscil-220hz.mp3]]
+It is approximated by:
+* [[20edo|7\20]] (420 cents)
+* [[3edo|1\3]] ([[12edo|4\12]]) (400 cents)
+* [[17edo|6\17]] ([[34edo|12\34]]) (423.529 cents)
+* [[37edo|13\37]] (421.622 cents)
-[[:File:ji-51-40-csound-foscil-220hz.mp3|ji-51-40-csound-foscil-220hz.mp3]]
+== See also ==
+* [[80/51]] – its [[octave complement]]
+* [[20/17]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
-Approximated by
+[[Category:Third]]
+[[Category:Major third]]
-<ul><li>[[20edo|7\20]] (420 cents)</li><li>[[3edo|1\3]] ([[12edo|4\12]]) (400 cents)</li><li>[[17edo|6\17]] ([[34edo|12\34]]) (423.529 cents)</li><li>[[Gallery_of_Just_Intervals|Gallery of Just Intervals]]</li></ul>      [[Category:17-limit]]
+[[Category:Supermajor third]]
-[[Category:major_third]]
-[[Category:septendecimal]]
-[[Category:supermajor]]