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¢
Name	small undecimal semitone
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
[sound info]
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22/21 is a small superparticular semitone of about 80.5¢ that appears in 11-limit just intonation. It makes the difference between the 21st and 22nd harmonics. It is close in size to 21/20, a 7-limit superparticular interval, 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.

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