21/19: Difference between revisions

Interval information
Ratio	21/19
Factorization	3 × 7 × 19-1
Monzo	[0 1 0 1 0 0 0 -1⟩
Size in cents	173.2679¢
Names	hendrix major second,; undevicesimal submajor second,; undevicesimal supraneutral second
Color name	19uz2, nuzo 2nd
FJS name	[math]\displaystyle{ \text{M2}^{7}_{19} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.64024
Weil norm (log2 max(n, d))	8.78463
Wilson norm (sopfr(nd))	29
	https://en.xen.wiki/w/File:Ji-21-19-csound-foscil-220hz.mp3; [sound info]
	Open this interval in xen-calc

Latest revision as of 13:07, 3 November 2025

In 19-limit just intonation, 21/19 is the hendrix major second, also known as the undevicesimal submajor second or undevicesimal supraneutral second, named for falling short of the Pythagorean major second (9/8) by a hendrix comma (57/56). In counterpyth systems, it is equated to the diminished third (the interval formed by two limmas (256/243)). It can also be considered to approximate the tetracot generator.

Edo approximations for 21/19 (173.27 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
7	1\7	171.43	-1.84	-1.07
14	2\14	171.43	-1.84	-2.15
21	3\21	171.43	-1.84	-3.22
28	4\28	171.43	-1.84	-4.29
34	5\34	176.47	+3.20	+9.07
35	5\35	171.43	-1.84	-5.36
41	6\41	175.61	+2.34	+8.00
42	6\42	171.43	-1.84	-6.44
48	7\48	175.00	+1.73	+6.93
49	7\49	171.43	-1.84	-7.51
55	8\55	174.55	+1.28	+5.86
56	8\56	171.43	-1.84	-8.58
62	9\62	174.19	+0.93	+4.78
63	9\63	171.43	-1.84	-9.66
69	10\69	173.91	+0.65	+3.71
76	11\76	173.68	+0.42	+2.64

@@ Line 1: / Line 1: @@
-'''21/19'''
+{{Infobox Interval
-|0 1 0 1 0 0 0 -1&gt;
+| Name = hendrix major second, undevicesimal submajor second, undevicesimal supraneutral second
+| Color name = 19uz2, nuzo 2nd
+| Sound = ji-21-19-csound-foscil-220hz.mp3
+}}
-.26789 cents
+In [[19-limit]] [[just intonation]], '''21/19''' is the '''hendrix major second''', also known as the '''undevicesimal submajor second''' or '''undevicesimal supraneutral second''', named for falling short of the [[9/8|Pythagorean major second (9/8)]] by a [[57/56|hendrix comma (57/56)]]. In [[counterpyth]] systems, it is equated to the diminished third (the interval formed by two [[256/243|limmas (256/243)]]). It can also be considered to approximate the [[tetracot]] generator.
+== Approximation ==
+{{Interval edo approximation|21/19}}
+== See also ==
+* [[38/21]] – its [[octave complement]]
+* [[19/14]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
-[[File:ji-21-19-csound-foscil-220hz.mp3]]  [[:File:ji-21-19-csound-foscil-220hz.mp3|sound sample]]
+[[Category:Second]]
+[[Category:Neutral second]]
-The '''large neutral undevicesimal second''', its inverse is the minor neutral undevicesimal seventh [[38/21|38/21]].
+[[Category:Equable heptatonic]]
+[[Category:Tetracot]]
-See also: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
+[[Category:Hendrix]]