The 11-limit consists of all justly tuned intervals whose numerators and denominators are both products of the primes 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are 14/11, 11/8, 27/22 and 99/98. The 11 odd-limit consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 11. Reduced to an octave, these are the ratios 1/1, 12/11, 11/10, 10/9, 9/8, 8/7, 7/6, 6/5, 11/9, 5/4, 14/11, 9/7, 4/3, 11/8, 7/5, 10/7, 16/11, 3/2, 14/9, 11/7, 8/5, 18/11, 5/3, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 2/1. In an 11-limit system, all the ratios of the 11 odd-limit can be treated as potential consonances.

interval name		ratio	harmonic solfege
1u2	lu 2nd	12/11	fu-sol
1og2	logu 2nd	11/10	mi-fu
y2	yo 2nd	10/9	re-mi
w2	wa 2nd	9/8	do-re
r2	ru 2nd	8/7	ta-do
z3	zo 3rd	7/6	sol-ta
g3	gu 3rd	6/5	mi-sol, ti-re
1o3	ilo 3rd	11/9	re-fu
y3	yo 3rd	5/4	do-mi
1uz4	luzo 4th	14/11	fu-ta
r3	ru 3rd	9/7	ta-re
w4	wa 4th	4/3	do-fa
1o4	ilo 4th	11/8	do-fu
zg5	zogu 5th	7/5	mi-ta
ry4	ruyo 4th	10/7	ta-mi
1u5	lu 5th	16/11	fu-do
w5	wa 5th	3/2	do-sol
z6	zo 6th	14/9	re-ta
1or5	loru 5th	11/7	ta-fu
g6	gu 6th	8/5	mi-do
1u6	lu 6th	18/11	fu-re
y6	yo 6th	5/3	sol-mi
r6	ru 6th	12/7	ta-sol
z7	zo 7th	7/4	do-ta
w7	wa 7th	16/9	re-do
g7	gu 7th	9/5	mi-re
1uy7	luyo 7th	20/11	fu-mi
1o7	ilo 7th	11/6	sol-fu
w8	wa 8ve	2/1	do-do

While the 7-limit introduces subminor and supermajor intervals, which can sound like dramatic inflections of the familiar interval categories of 12edo, the 11-limit introduces neutral intervals, superfourths and subfifths, which fall in between major, minor and perfect interval categories and thus demand new distinctions. It is thus inescapably xenharmonic.

Relative to their size, edos which do (relatively) well in supporting 11-limit intervals are: 1edo, 2edo, 3edo, 4edo, 5edo, 6edo, 7edo, 9edo, 10edo, 12edo, 15edo, 22edo, 26edo, 31edo, 41edo, 63edo, 72edo, 87edo, 109edo, 161edo.

Intervals

Here are all the 15-odd-limit intervals of 11:

Interval name		Ratio	Cents Value
1u2	lu 2nd	12/11	150.637
1og2	logu 2nd	11/10	165.004
1o3	ilo 3rd	11/9	347.408
1uz4	lu 4th	14/11	417.508
1uy4	luyo 4th	15/11	536.951
1o4	ilo 4th	11/8	551.318
1u5	lu 5th	16/11	648.682
1og5	logu 5th	22/15	663.049
1or5	loru 5th	11/7	782.492
1u6	lu 6th	18/11	852.592
1uy7	luyo 7th	20/11	1034.996
1o7	ilo 7th	11/6	1049.363