3969/3968
| Ratio | 3969/3968 |
| Subgroup monzo | 2.3.7.31 [-7 4 2 -1⟩ |
| Size in cents | 0.43624394¢ |
| Name | yunzee comma |
| Color name | L31uzz2, lathiwuzozo 2nd, Lathiwuzozo comma |
| FJS name | [math]\text{m2}^{7,7}_{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 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20087 bits |
| Comma size | unnoticeable |
| S-expression | S63 |
| open this interval in xen-calc | |
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.