22/21
| Ratio | 22/21 |
| Factorization | 2 × 3-1 × 7-1 × 11 |
| Monzo | [1 -1 0 -1 1⟩ |
| Size in cents | 80.537035¢ |
| Names | small undecimal semitone, undecimal minor semitone, pentacircle minor second |
| Color name | 1or1, loru unison |
| FJS name | [math]\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 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.32833 bits |
| 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 makes the difference between the 21st and 22nd harmonics.
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.