21/11
| Ratio | 21/11 |
| Factorization | 3 × 7 × 11-1 |
| Monzo | [0 1 0 1 -1⟩ |
| Size in cents | 1119.463¢ |
| Names | large undecimal diminished octave, undecimal major seventh, pentacircle major seventh |
| Color name | 1uz8, luzo 8ve |
| FJS name | [math]\text{P8}^{7}_{11}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 7.85175 |
| Weil height (log2 max(n, d)) | 8.78463 |
| Wilson height (sopfr(nd)) | 21 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.25633 bits |
[sound info] | |
| open this interval in xen-calc | |
21/11, commonly known as the large undecimal diminished octave, is an 11-limit interval, and the octave complement of 22/21.
In many notation systems (e.g. FJS, HEJI), it is an imperfect octave, as it is the octave minus a stack consisting 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 sharp of the Pythagorean major seventh (243/128) by a pentacircle comma (896/891). For this reason it could be called the pentacircle major seventh.
Of note is that the Huygens-Fokker Foundation dubs this interval the undecimal major seventh, which also makes sense, resulting in this interval being perhaps best classified as a "sevtave" – a type of cross between a seventh and an octave.
See also
- 22/21 – its octave complement