170/169
Ratio | 170/169 |
Factorization | 2 × 5 × 13^{-2} × 17 |
Monzo | [1 0 1 0 0 -2 1⟩ |
Size in cents | 10.2138¢ |
Name | major naiadma |
Color name | 17o3uuy1, Sothuthuyo 1sn Sothuthuyo comma |
FJS name | [math]\text{A1}^{5,17}_{13,13}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 14.8103 |
Weil height (log_{2} max(n, d)) | 14.8188 |
Wilson height (sopfr (nd)) | 50 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.81925 bits |
Comma size | small |
open this interval in xen-calc |
170/169, the major naiadma, is a small 17-limit superparticular comma about 10.2 cents in size. It forms the difference between 13/10 (tridecimal semisixth) and 17/13 (large septendecimal semisixth). It is also the amount by which a stack of two 13/10s falls short of 17/10 (septendecimal major sixth). The name major naiadma is contrast to the minor naiadma, 221/220, measuring about 7.9¢, which is the difference between 13/10 and 22/17 (small septendecimal semisixth). They are so named because 13/10, 17/13 and 22/17 are naiadic interseptimal intervals, and 170/169 is larger than 221/220 by a 13-limit unnoticeable comma, 2200/2197 (petrma).
It is close to one step of 118edo and is tempered as such in the 118th-octave oganesson temperament, along with 169/168, from which it differs by 28561/28560.