22/21

Interval information

Ratio	22/21
Factorization	2 × 3-1 × 7-1 × 11
Monzo	[1 -1 0 -1 1⟩
Size in cents	80.53704¢
Names	small undecimal semitone, undecimal minor semitone, pentacircle minor second
Color name	1or1, loru unison
FJS name	[math]\displaystyle{ \text{P1}^{11}_{7} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	8.85175
Weil height (log2 max(n, d))	8.91886
Wilson height (sopfr(nd))	23
Comma size	medium
[sound info]
Open this interval in xen-calc

22/21 is a small superparticular semitone of about 80.5¢ that appears in 11-limit just intonation, commonly known as the small undecimal semitone, or undecimal minor semitone. It is the difference between 12/11 and 8/7, or between 7/6 and 11/9.

In many notation systems (e.g. FJS, HEJI), it is an imperfect unison, as it is the stack 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 flat of the Pythagorean minor second (256/243) by a pentacircle comma (896/891). For this reason it could be called the pentacircle minor second.

Furthermore, it is close in size to 21/20, a 7-limit superparticular interval most commonly treated as a minor second, differing from it by 441/440, about 3.9¢. The single degree of 88cET can function as both 21/20 and 22/21, thus tempering out 441/440.

Approximation

10 steps of 149edo appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using relative cents.

See also

• 21/11 – its octave complement
• Gallery of just intervals
• List of superparticular intervals