21/19

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.

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
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Approximation

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

See also

• 38/21 – its octave complement
• 19/14 – its fifth complement
• Gallery of just intervals