69/64

Interval information

Ratio	69/64
Subgroup monzo	2.3.23 [-6 1 1⟩
Size in cents	130.2293¢
Names	nice second, vicesimotertial supraminor second, vicesimotertial neutral second, 69th harmonic
Color name	23o2, twenty-tho 2nd
FJS name	[math]\text{A1}^{23}[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	12.1085
Weil height (log2 max(n, d))	12.217
Wilson height (sopfr(nd))	38
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.2557 bits
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69/64, the nice second, is the octave-reduced 69th harmonic. It is a 23-limit interval that is near the border between neutral and supraminor seconds (although it is defined as an augmented unison by the FJS). It is 897/896 above the more common 14/13 interval, and so qualifies as a sinaic, as well as being roughly equidistant from the well-known 17/16 minor second and the 35/32 neutral second.

Etymology

This interval was named by Jerdle in 2024. While the name "nice" resembles a combination of "neutral" and "vicesimotertial", the actual origin is rather different. It's the 69th harmonic, what else was it going to be called?