221/220
Ratio | 221/220 |
Factorization | 2^{-2} × 5^{-1} × 11^{-1} × 13 × 17 |
Monzo | [-2 0 -1 0 -1 1 1⟩ |
Size in cents | 7.851415¢ |
Name | minor naiadma |
Color name | 17o3o1ug2, Sotholugu 2nd Sotholugu comma |
FJS name | [math]\text{d2}^{13,17}_{5,11}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 15.5693 |
Weil height (log_{2} max(n, d)) | 15.5758 |
Wilson height (sopfr (nd)) | 50 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.65546 bits |
Comma size | small |
open this interval in xen-calc |
221/220, the minor naiadma, is a small 17-limit superparticular comma about 7.9 cents in size. It forms the difference between 13/10 (tridecimal semisixth) and 22/17 (small septendecimal semisixth). It is also the amount by which a stack consisting of 13/10 and 17/10 exceeds 11/5 (11/10 plus an octave). The name minor naiadma is contrast to the major naiadma, 170/169, measuring about 10.2¢, which is the difference between 13/10 and 17/13 (large septendecimal semisixth). They are so named because 13/10, 17/13 and 22/17 are naiadic interseptimal intervals, and 221/220 is smaller than 170/169 by a 13-limit unnoticeable comma, 2200/2197 (petrma).
Commatic relations
This comma identifies itself as the difference between the following superparticular pairs:
- 34/33 and 40/39
- 51/50 and 66/65
- 78/77 and 120/119
- 91/90 and 154/153
- 136/135 and 352/351
- 169/168 and 715/714
It factors into the following superparticular pairs:
- 225/224 and 12376/12375
- 243/242 and 2431/2430
- 273/272 and 1156/1155
- 289/288 and 936/935
- 351/350 and 595/594
- 364/363 and 561/560
- 441/440 and 442/441