36/19

Interval information

Ratio	36/19
Subgroup monzo	2.3.19 [2 2 -1⟩
Size in cents	1106.397¢
Names	undevicesimal major seventh, Boethius' major seventh
Color name	19u7, inu 7th
FJS name	[math]\displaystyle{ \text{M7}_{19} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.41785
Weil norm (log2 max(n, d))	10.3399
Wilson norm (sopfr(nd))	29
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In 19-limit just intonation, 36/19 is the undevicesimal major seventh or Boethius' major seventh, measuring about 1106.4¢. It is flat of the Pythagorean major seventh (243/128) by 513/512, the undevicesimal comma aka Boethius' comma.

Approximation

Edo approximations for 36/19 (1106.40 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
12	11\12	1100.00	-6.40	-6.40
13	12\13	1107.69	+1.30	+1.40
14	13\14	1114.29	+7.89	+9.20
25	23\25	1104.00	-2.40	-4.99
26	24\26	1107.69	+1.30	+2.81
38	35\38	1105.26	-1.13	-3.59
39	36\39	1107.69	+1.30	+4.21
50	46\50	1104.00	-2.40	-9.99
51	47\51	1105.88	-0.51	-2.19
52	48\52	1107.69	+1.30	+5.61
63	58\63	1104.76	-1.64	-8.58
64	59\64	1106.25	-0.15	-0.78
65	60\65	1107.69	+1.30	+7.02
76	70\76	1105.26	-1.13	-7.18
77	71\77	1106.49	+0.10	+0.62
78	72\78	1107.69	+1.30	+8.42

See also

• 19/18 – its octave complement, the large undevicesimal semitone
• 19/10 – the undevicesimal diminished octave
• Gallery of just intervals