875/864
| Ratio | 875/864 |
| Factorization | 2-5 × 3-3 × 53 × 7 |
| Monzo | [-5 -3 3 1⟩ |
| Size in cents | 21.902045¢ |
| Name | keema |
| Color name | zy31, zotriyo 1sn, Zotriyo comma |
| FJS name | [math]\text{A1}^{5,5,5,7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 19.528 |
| Weil height (log2 max(n, d)) | 19.5463 |
| Wilson height (sopfr(nd)) | 41 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~3.98367 bits |
| Comma size | small |
| S-expression | S5 / S6 |
| open this interval in xen-calc | |
875/864, the keema, is a small 7-limit comma measuring about 21.9 cents. It marks the difference between the septimal minor seventh (7/4) and a stack of three just minor thirds (6/5), or between a septimal major seventh (27/14) and a stack of three just major thirds (5/4). It is also the sum of 245/243 and 225/224, the sum of 100/99 and 385/384, the sum of 105/104 and 325/324, and the difference between 49/48 and 126/125.
Temperaments
Tempering it out leads to the supermagic temperament. See Keemic family for the rank-3 temperament family where it is tempered out. See Keemic temperaments for a collection of rank-2 temperaments where it is tempered out.
Etymology
This comma was first named as supermagic by Gene Ward Smith in 2005 as a contraction of superkleismic and magic[1], hence the name of the corresponding rank-3 temperament. It is not clear how it later became keema, but the root of keema is obvious, being a contraction of keemun and magic.