19/14

19/14, the hendrix fourth, is 19-limit interval that is a hendrix comma (57/56) sharp of the just perfect fourth (4/3). It an octave higher, 19/7, is a convergent in the continued fraction to Euler's number.

Interval information

Ratio	19/14
Factorization	2-1 × 7-1 × 19
Monzo	[-1 0 0 -1 0 0 0 1⟩
Size in cents	528.6871¢
Name	hendrix fourth
Color name	19or4, noru 4th
FJS name	[math]\displaystyle{ \text{P4}^{19}_{7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.05528
Weil norm (log2 max(n, d))	8.49586
Wilson norm (sopfr(nd))	28
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Approximation

Edo approximations for 19/14 (528.69 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
7	3\7	514.29	-14.40	-8.40
9	4\9	533.33	+4.65	+3.48
16	7\16	525.00	-3.69	-4.92
18	8\18	533.33	+4.65	+6.97
25	11\25	528.00	-0.69	-1.43
32	14\32	525.00	-3.69	-9.83
34	15\34	529.41	+0.72	+2.05
41	18\41	526.83	-1.86	-6.35
43	19\43	530.23	+1.55	+5.54
50	22\50	528.00	-0.69	-2.86
52	23\52	530.77	+2.08	+9.02
59	26\59	528.81	+0.13	+0.62
66	29\66	527.27	-1.41	-7.78
68	30\68	529.41	+0.72	+4.11
75	33\75	528.00	-0.69	-4.29
77	34\77	529.87	+1.18	+7.59

See also

• 28/19 – its octave complement
• 19/17 – one octave higher
• 57/56, the hendrix comma

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