Template:ZPI/doc

This template generates a table for a particular EDO's zeta peak index.

Parameters

All parameters are required.

{{{steps}}}

The zeta-optimised number of steps per octave, corresponding to the location of a particular EDO's nearest local maximum or minimum according to the Riemann–Siegel Z function, [math]\displaystyle{ Z\left(\frac{2\pi}{\ln 2}x\right) }[/math]. For example, 12edo's local zeta-optimised step count is 12.0231830072926.

{{{step size}}}

The step size in cents, which is 1200 divided by the aformentioned zeta-optimised step count.

{{{tempered height}}}

The absolute value of Z evaluated at the zeta-optimised step count. For 12edo, this value is 5.193290 when evaluated at 12.0231830072926.

{{{pure height}}}

The absolute value of Z evaluated at the exact integer. For 12edo, this value is 5.084467 when evaluated at exactly 12.

{{{integral}}}

The absolute value of the integral between the two roots (zeroes) of Z closest to the given EDO. For 12edo, this value is 1.269599.

{{{gap}}}

{{{edo}}}

octave

The zeta-optimised octave size. For 12edo, this is 1197.68616940005.

consistent

The ZPI's consistency limit.

distinct

The ZPI's distinct consistency limit.