3969/3968

The superparticular interval 3969/3968, the yunzee comma, is an unnoticeable comma in the 2.3.7.31 subgroup, of about 0.43624 cents.

Interval information

Ratio	3969/3968
Subgroup monzo	2.3.7.31 [-7 4 2 -1⟩
Size in cents	0.4362439¢
Name	yunzee comma
Color name	large thiwuzozo 2nd (L31uzz2)
FJS name	[math]\displaystyle{ \text{m2}^{49}_{31} }[/math]
Special properties	square superparticular, reduced
Tenney norm (log2 nd)	23.9088
Weil norm (log2 max(n, d))	23.9091
Wilson norm (sopfr(nd))	71
Open this interval in xen-calc

The 2.3.7.31 subgroup is notable for being the basis of the first tunings used in La Monte Young's The Well-Tuned Piano, before it was changed to eliminate 31-based intervals. Interestingly, 3969/3968 is the difference between several complex intervals in the later tuning and simpler 31-based intervals, such as 189/128 and 31/21, 567/512 and 31/28, 1323/1024 and 31/24, etc. Thus it is named for the stressed syllables in both Young's surname and that of his wife, Marian Zazeela (who provided the light art for WTP performances). 3969/3968 is also the difference between 63/62 and 64/63.

Tempering it out within its subgroup leads to the very accurate (but still possibly sacrilegious) rank-3 yunzee temperament.