442/441
Ratio | 442/441 |
Factorization | 2 × 3^{-2} × 7^{-2} × 13 × 17 |
Monzo | [1 -2 0 -2 0 1 1⟩ |
Size in cents | 3.9212566¢ |
Name | seminaiadma |
Color name | 17o3orr1, Sothoruru 1sn Sothoruru comma |
FJS name | [math]\text{d1}^{13,17}_{7,7}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 17.5725 |
Weil height (log_{2} max(n, d)) | 17.5758 |
Wilson height (sopfr (nd)) | 52 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.34133 bits |
Comma size | small |
open this interval in xen-calc |
442/441, the seminaiadma, is a small 17-limit superparticular comma about 3.9 cents in size. It is the difference between 21/17 and 26/21, and forms the amount by which a stack consisting of 13/8 and 17/16 exceeds a stack of two 21/16s. It differs from 441/440 (werckisma) by 194481/194480 (scintillisma) – an unnoticeable comma measuring ~0.0089 cents. By tempering it out is defined the seminaiadmic temperament, which enables the seminaiadmic chords.
Commatic relations
This comma identifies itself as the difference between the following superparticular pairs:
- 85/84 and 105/104
- 136/135 and 196/195
- 169/168 and 273/272
- 221/220 and 441/440
- 289/288 and 833/832
- 325/324 and 1225/1224
- 351/350 and 1701/1700
- 364/363 and 2058/2057
- 441/440 and 194481/194480
It factors into the following superparticular pairs:
- 540/539 and 2431/2430
- 561/560 and 2080/2079
- 595/594 and 1716/1715
- 676/675 and 1275/1274
- 715/714 and 1156/1155
Etymology
The name seminaiadma was named by Xenllium in 2023, for the following reasons - its size is about a half of minor naiadma, 221/220 (similar to semicomma, whose size is about a half of syntonic comma). Tempering it out leads equating 21/17 and 26/21 into a single submajor third interval, two of which give an interseptimal interval, 26/17 (octave complement of a naiadic interval, 17/13).