Zetave

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Interval information

Expression	[math]\displaystyle{ e^{\tau} }[/math]
Size in cents	10877.66¢
Name	zetave

The zetave, e^𝜏 or ~535.49/1 is the interval which is equally divided when the zeta function is not scaled so that Im(s) corresponds to edos. In other words, imaginary values on the Riemann zeta function correspond to equal divisions of the zetave (EDZ). 12edo is about 108.776643404edz. The appearance of the zetave in the zeta function's usage in tuning suggests that it has some sort of natural relation to equal-step tunings.

Trivia

• The zetave, as a ratio, can be expressed as an i-th root of 1; this is, in fact, a statement of Euler's identity that e^i𝜏 = 1.