# Acoustic pi

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 Expression $\pi$ Size in cents 1981.7954¢ Name acoustic pi Harmonic entropy(Shannon, $\sqrt{nd}$) ~4.23555 bits
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The acoustic pi, the transcendental number equal to the ratio of a circle's circumference to the diameter, is about 3.14159, a rather minor thirteenth of 1981.795 cents. It is unclear what psychoacoustic significance this interval might have.

Intervals that are close to it are 3/1, 22/7, and 355/113.

## Equal divisions

Using 3.14159…/1 as an interval of equivalence (known as the "pitave") results in some interesting nonoctave tunings.

Selected edπ–edo correspondence
N Description
2edπ A stack of two minor sevenths, represents a problem of squaring the circle
3edπ A stack of three compressed fifths, vaguely equivalent to 2edo
4edπ Close to equal multiplication of 4/3
5edπ Close to equal multiplication of 5/4, 3edo
6edπ Close to equal multiplication of 6/5, 4edo
20edπ Close to 12edo.
30edπ Close to 18edo, but sets fractional temperaments to 4:5:6 triad.
38edπ Very close to 23edo
71edπ Very close to 43edo
109edπ Extremely close to 66edo

## Temperaments of interest

Engineer's temperament, tempering out π/3, the engineer's comma.

20edπ can be used to set 3:4:5 triad with a fractional-octave temperament just as 12edo does with the 4:5:6 triad.