Zetave: Difference between revisions
Created page with "{{Infobox interval|ratio=e^{\tau}|cents=10877.6643|Ratio=e^{2\pi}|Cents=10877.6643|Name=zetave}} The '''zetave''', e^tau or ~535.49/1 is the interval which is equally divided..." |
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{{Infobox interval|ratio=e^{\tau}|cents=10877.6643|Ratio=e^{ | {{Mathematical interest}}{{Infobox interval|ratio=e^{\tau}|cents=10877.6643|Ratio=e^{\tau}|Cents=10877.6643|Name=zetave}} | ||
The '''zetave''', e | The '''zetave''', e<sup>𝜏</sup> 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 tuning|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<sup>i𝜏</sup> = 1. | |||