Template:ZPI/doc: Difference between revisions

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

This template generates a table for a particular edo's [[zeta peak index]].

=== Parameters ===

All parameters are required.

; <code>{{{~~<nowiki />~~steps}}}</code>

; <code><nowiki>{{{steps}}}</nowiki></code>

: 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 {{w|Z function|Riemann–Siegel ''Z'' function}}, ~~<math>Z\left(\frac{2\pi}{\ln 2}x\right)</math>. For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.~~

: 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 {{w|Z function|Riemann–Siegel ''Z'' function}},

; <code>{{{~~<nowiki />~~step size}}}</code>

$$ Z\left( \frac{2\pi}{\ln 2} \, x \right) $$

: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.

; <code><nowiki>{{{step size}}}</nowiki></code>

: The step size in [[cent]]s, which is 1200 divided by the aformentioned zeta-optimised step count.

; <code>{{{~~<nowiki />~~tempered height}}}</code>

For the height of the zeta peak, you can use <code>tempered height</code> and <code>pure height</code> or just <code>height</code>.

; <code><nowiki>{{{tempered height}}}</nowiki></code>

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

: Must be used in conjunction with <code>pure height</code>, do not use with <code>height</code>.

; <code>{{{~~<nowiki />~~pure height}}}</code>

; <code><nowiki>{{{pure height}}}</nowiki></code>

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

: Must be used in conjunction with <code>tempered height</code>, do not use with <code>height</code>.

; <code>{{{<nowiki />~~integral}}}~~</code>

; <code><nowiki>{{{height}}}</nowiki></code>

: 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~~.

: The absolute value of ''Z'' evaluated at a ZPI that does not correspond strongly to an edo. Do not use with <code>tempered height</code> or <code>pure height</code>.

; <code>{{{<nowiki />~~gap}}}~~</code>

; <code><nowiki>{{{integral}}}</nowiki></code>

: 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.

; <code><nowiki>{{{gap}}}</nowiki></code>

~~; <code>{{{edo}}}</code>~~

; <code><nowiki>{{{edo}}}</nowiki></code> (optional)

: This parameter is optional. Pass in the edo that the ZPI represents if the page's title does not contain it.

; <code>octave</code>

; <code><nowiki>{{{octave}}}</nowiki></code>

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

; <code>consistent</code>

; <code><nowiki>{{{consistent}}}</nowiki></code>

: The ZPI's [[consistency]] limit.

; <code>distinct</code>

; <code><nowiki>{{{distinct}}}</nowiki></code>

: The ZPI's ''distinct'' consistency limit.

=== Example (12edo) ===

Here is the complete zeta peak index table for [[12edo]] as it appears on the page:

Here is the complete zeta peak index table for [[12edo]] [[12edo #Zeta peak index|as it appears on the page]]:

<pre>

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Line 72:

| integral = 1.269599

| gap = 15.899282

~~| edo = 12edo~~

| octave = 1197.68616940005

| consistent = 10

| distinct = 6

}}

@@ Line 1: / Line 1: @@
-{{dochead}}
+{{Dochead}}{{substitute|no}}
-This template generates a table for a particular EDO's [[zeta peak index]].
+This template generates a table for a particular edo's [[zeta peak index]].
 === Parameters ===
 All parameters are required.
-; <code>{{{<nowiki />steps}}}</code>
+; <code><nowiki>{{{steps}}}</nowiki></code>
-: 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 {{w|Z function|Riemann–Siegel ''Z'' function}}, <math>Z\left(\frac{2\pi}{\ln 2}x\right)</math>. For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.
+: 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 {{w|Z function|Riemann–Siegel ''Z'' function}},
-; <code>{{{<nowiki />step size}}}</code>
+$$ Z\left( \frac{2\pi}{\ln 2} \, x \right) $$
+: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.
+; <code><nowiki>{{{step size}}}</nowiki></code>
 : The step size in [[cent]]s, which is 1200 divided by the aformentioned zeta-optimised step count.
-; <code>{{{<nowiki />tempered height}}}</code>
+For the height of the zeta peak, you can use <code>tempered height</code> and <code>pure height</code> or just <code>height</code>.
+; <code><nowiki>{{{tempered height}}}</nowiki></code>
 : The absolute value of ''Z'' evaluated at the zeta-optimised step count. For [[12edo]], this value is 5.193290 when evaluated at 12.0231830072926.
+: Must be used in conjunction with <code>pure height</code>, do not use with <code>height</code>.
-; <code>{{{<nowiki />pure height}}}</code>
+; <code><nowiki>{{{pure height}}}</nowiki></code>
 : The absolute value of ''Z'' evaluated at the exact integer. For [[12edo]], this value is 5.084467 when evaluated at exactly 12.
+: Must be used in conjunction with <code>tempered height</code>, do not use with <code>height</code>.
-; <code>{{{<nowiki />integral}}}</code>
+; <code><nowiki>{{{height}}}</nowiki></code>
-: 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.
+: The absolute value of ''Z'' evaluated at a ZPI that does not correspond strongly to an edo. Do not use with <code>tempered height</code> or <code>pure height</code>.
-; <code>{{{<nowiki />gap}}}</code>
+; <code><nowiki>{{{integral}}}</nowiki></code>
+: 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.
+; <code><nowiki>{{{gap}}}</nowiki></code>
-; <code>{{{edo}}}</code>
+; <code><nowiki>{{{edo}}}</nowiki></code> (optional)
+: This parameter is optional. Pass in the edo that the ZPI represents if the page's title does not contain it.
-; <code>octave</code>
+; <code><nowiki>{{{octave}}}</nowiki></code>
 : The zeta-optimised octave size. For 12edo, this is 1197.68616940005.
-; <code>consistent</code>
+; <code><nowiki>{{{consistent}}}</nowiki></code>
 : The ZPI's [[consistency]] limit.
-; <code>distinct</code>
+; <code><nowiki>{{{distinct}}}</nowiki></code>
 : The ZPI's ''distinct'' consistency limit.
 === Example (12edo) ===
-Here is the complete zeta peak index table for [[12edo]] as it appears on the page:
+Here is the complete zeta peak index table for [[12edo]] [[12edo #Zeta peak index|as it appears on the page]]:
 <pre>
@@ Line 61: / Line 72: @@
 | integral = 1.269599
 | gap = 15.899282
-| edo = 12edo
 | octave = 1197.68616940005
 | consistent = 10
 | distinct = 6
 }}