22/21
Jump to navigation
Jump to search
Ratio | 22/21 |
Factorization | 2 × 3^{-1} × 7^{-1} × 11 |
Monzo | [1 -1 0 -1 1⟩ |
Size in cents | 80.537035¢ |
Name | small undecimal semitone |
Color name | 1or1, loru unison |
FJS name | [math]\text{P1}^{11}_{7}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 8.85175 |
Weil height (log_{2} max(n, d)) | 8.91886 |
Wilson height (sopfr (nd)) | 23 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.32833 bits |
[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. 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.