24/19

24/19, the small undevicesimal major third or Boethius' major third, is a 19-limit interval that is very close to the major third of 12edo (400 cents). It is an undevicesimal comma aka Boethius' comma (513/512) below the Pythagorean major third (81/64).

Interval information

Ratio	24/19
Subgroup monzo	2.3.19 [3 1 -1⟩
Size in cents	404.442¢
Names	small undevicesimal major third, Boethius' major third
Color name	19u3, inu 3rd
FJS name	[math]\displaystyle{ \text{M3}_{19} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.83289
Weil norm (log2 max(n, d))	9.16993
Wilson norm (sopfr(nd))	28
[sound info]
Open this interval in xen-calc

Approximation

Edo approximations for 24/19 (404.44 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
3	1\3	400.00	-4.44	-1.11
6	2\6	400.00	-4.44	-2.22
9	3\9	400.00	-4.44	-3.33
12	4\12	400.00	-4.44	-4.44
15	5\15	400.00	-4.44	-5.55
18	6\18	400.00	-4.44	-6.66
21	7\21	400.00	-4.44	-7.77
24	8\24	400.00	-4.44	-8.88
27	9\27	400.00	-4.44	-9.99
65	22\65	406.15	+1.71	+9.27
68	23\68	405.88	+1.44	+8.16
71	24\71	405.63	+1.19	+7.05
74	25\74	405.41	+0.96	+5.94
77	26\77	405.19	+0.75	+4.83
80	27\80	405.00	+0.56	+3.72

See also

• 19/12 – its octave complement
• 19/16 – its fifth complement
• 19/15 – the large undevicesimal major third
• Gallery of just intervals