21/11

21/11, commonly known as the large undecimal diminished octave, is an 11-limit interval, and the octave complement of 22/21.

Interval information

Ratio	21/11
Factorization	3 × 7 × 11-1
Monzo	[0 1 0 1 -1⟩
Size in cents	1119.463¢
Names	large undecimal diminished octave, undecimal major seventh, pentacircle major seventh
Color name	1uz8, luzo 8ve
FJS name	[math]\displaystyle{ \text{P8}^{7}_{11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	7.85175
Weil norm (log2 max(n, d))	8.78463
Wilson norm (sopfr(nd))	21
[sound info]
Open this interval in xen-calc

In many notation systems (e.g. FJS, HEJI), it is an imperfect octave, as it is the octave minus a stack consisting of an undecimal quartertone (33/32) and a septimal comma (64/63), neither of which changes the scale degree or quality. However, it is only sharp of the Pythagorean major seventh (243/128) by a pentacircle comma (896/891). For this reason it could be called the pentacircle major seventh.

Of note is that the Huygens-Fokker Foundation dubs this interval the undecimal major seventh, which also makes sense, resulting in this interval being perhaps best classified as a "sevtave" – a type of cross between a seventh and an octave.

Approximation

Edo approximations for 21/11 (1119.46 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
14	13\14	1114.29	-5.18	-6.04
15	14\15	1120.00	+0.54	+0.67
16	15\16	1125.00	+5.54	+7.38
29	27\29	1117.24	-2.22	-5.37
30	28\30	1120.00	+0.54	+1.34
31	29\31	1122.58	+3.12	+8.05
44	41\44	1118.18	-1.28	-4.70
45	42\45	1120.00	+0.54	+2.01
46	43\46	1121.74	+2.28	+8.73
59	55\59	1118.64	-0.82	-4.03
60	56\60	1120.00	+0.54	+2.69
61	57\61	1121.31	+1.85	+9.40
74	69\74	1118.92	-0.54	-3.35
75	70\75	1120.00	+0.54	+3.36

See also

• 22/21 – its octave complement