11/7

Interval information

Ratio	11/7
Factorization	7-1 × 11
Monzo	[0 0 0 -1 1⟩
Size in cents	782.492¢
Names	undecimal minor sixth, undecimal augmented fifth
Color name	1or5, loru 5th
FJS name	[math]\displaystyle{ \text{P5}^{11}_{7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	6.26679
Weil norm (log2 max(n, d))	6.91886
Wilson norm (sopfr(nd))	18
[sound info]
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In 11-limit just intonation, 11/7 is an undecimal minor sixth, measuring about 782.5¢. It is the inversion of 14/11, the undecimal major third.

11/7 is flat of the Pythagorean minor sixth of 128/81 (about 792.2¢) by a pentacircle comma, 896/891. It is flat of the 5-limit minor sixth of 8/5 (about 813.7¢) by 56/55. It is sharp of the 7-limit subminor sixth of 14/9 (about 764.9¢) by a mothwellsma, 99/98. And finally, it is sharp of the classic augmented fifth of 25/16 (about 772.6¢) by a valinorsma, 176/175.

11/7 is 22/21 (about 80.5¢) above the 3/2 perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2.

Approximations by EDOs

Following EDOs (up to 200) contain good approximations of the interval 11/7. Errors are given by magnitude, the arrows in the table show if the EDO representation is sharp (↑) or flat (↓).

EDO	deg\edo	Absolute error (¢)	Relative error (r¢)	↕	Equally acceptable multiples
20	13\20	2.4920	4.1534	↓
23	15\23	0.1167	0.2236	↑	30\46, 45\69, 60\92, 75\115, 90\138, 105\161, 120\184
26	17\26	2.1233	4.6006	↑
43	28\43	1.0967	3.9298	↓
49	32\49	1.1814	4.8242	↑
66	43\66	0.6739	3.7062	↓
72	47\72	0.8413	5.0478	↑
89	58\89	0.4696	3.4826	↓	116\178
95	62\95	0.6659	5.2714	↑
112	73\112	0.3492	3.2590	↓
118	77\118	0.5588	5.4950	↑
135	88\135	0.2698	3.0354	↓
141	92\141	0.4867	5.7186	↑
158	103\158	0.2136	2.8118	↓
164	107\164	0.4348	5.9422	↑
181	118\181	0.1716	2.5882	↓
187	122\187	0.3957	6.1658	↑

See also

• 14/11 – its octave complement
• Gallery of just intervals
• File:Ji-11-7-csound-foscil-220hz.mp3 – another sound example