170/169

Interval information

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 (log2 nd)	14.8103
Weil height (log2 max(n, d))	14.8188
Wilson height (sopfr(nd))	50
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~2.11309 bits
Comma size	small
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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.

See also

• Small comma
• List of superparticular intervals