3969/3968

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 height (log2 nd)	23.9088
Weil height (log2 max(n, d))	23.9091
Wilson height (sopfr(nd))	71
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The superparticular interval 3969/3968, the yunzee comma, is an unnoticeable comma in the 2.3.7.31 subgroup, of about 0.43624 cents. It is also a metasuperparticular, being the difference between between 63/62 and 64/63.

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. Curiously, 3969/3968 turns out to be 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).

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