Template:ZPI: Difference between revisions

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Allow 6 decimal places at max to reduce the width of the table
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m Removed substitution directories; this isn't supposed to be substituted and they were only for testing
 
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|-
|-
! colspan="3" | Tuning
! colspan="3" | Tuning
! colspan="{{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|4|3}}" | Strength
! colspan="{{#if: {{{tempered height|}}}{{{pure height|}}}|4|3}}" | Strength
! colspan={{safesubst:#if: {{{edo|}}}|"3" {{!}} Closest edo|"2" {{!}} Octave (cents)}}
! colspan={{#if: {{{edo|}}}|"3" {{!}} Closest edo|"2" {{!}} Octave (cents)}}
! colspan="2" | Integer limit
! colspan="2" | Integer limit
|-
|-
! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} ZPI
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} ZPI
! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Steps<br>per 8ve
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Steps<br>per 8ve
! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Step size<br>([[cent]]s)
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Step size<br>([[cent]]s)
! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|colspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Height
! {{#if: {{{tempered height|}}}{{{pure height|}}}|colspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Height
! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Integral
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Integral
! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Gap
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Gap
{{safesubst:#if: {{{edo|}}}
{{#if: {{{edo|}}}
| ! rowspan{{=}}"2" {{!}} Edo
| ! rowspan{{=}}"2" {{!}} Edo
! colspan{{=}}"2" {{!}} Octave (cents)
! colspan{{=}}"2" {{!}} Octave (cents)
|}}{{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|{{safesubst:#if: {{{edo|}}}||  
|}}{{#if: {{{tempered height|}}}{{{pure height|}}}|{{#if: {{{edo|}}}||  
! rowspan{{=}}"2" {{!}} Size}}}}
! rowspan{{=}}"2" {{!}} Size}}}}
{{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|{{safesubst:#if: {{{edo|}}}||  
{{#if: {{{tempered height|}}}{{{pure height|}}}|{{#if: {{{edo|}}}||  
! rowspan{{=}}"2" {{!}} Stretch}}}}
! rowspan{{=}}"2" {{!}} Stretch}}}}
! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Consistent
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Consistent
! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Distinct
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Distinct
|-
|-
{{safesubst:#if: {{{edo|}}}
{{#if: {{{edo|}}}
| ! Size
| ! Size
! Stretch
! Stretch
|}}
|}}
{{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}
{{#if: {{{tempered height|}}}{{{pure height|}}}
| ! Tempered
| ! Tempered
! Pure
! Pure
|}}
|}}
|-
|-
| {{safesubst:#if: {{{zpi|}}}|[[{{safesubst:#rmatch: {{{zpi}}}|/(\d+)/|\1}}zpi]]|}}
| {{#if: {{{zpi|}}}|[[{{#rmatch: {{{zpi}}}|/(\d+)/|\1}}zpi]]|}}
| {{#expr: {{{steps}}} round 6 }}
| {{#expr: {{{steps}}} round 6 }}
| {{#expr: {{{step size}}} round 6 }}
| {{#expr: {{{step size}}} round 6 }}
{{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}
{{#if: {{{tempered height|}}}{{{pure height|}}}
| {{!}} {{#expr: {{{tempered height}}} round 6 }}
| {{!}} {{#expr: {{{tempered height}}} round 6 }}
{{!}} {{#expr: {{{pure height}}} round 6 }}
{{!}} {{#expr: {{{pure height}}} round 6 }}
Line 41: Line 41:
| {{#expr: {{{integral}}} round 6 }}
| {{#expr: {{{integral}}} round 6 }}
| {{#expr: {{{gap}}} round 6 }}
| {{#expr: {{{gap}}} round 6 }}
{{safesubst:#if: {{{edo|}}}|{{!}} {{{edo}}}|}}
{{#if: {{{edo|}}}|{{!}} {{{edo}}}|}}
| {{#expr: {{{octave}}} round 6}}
| {{#expr: {{{octave}}} round 6}}
| {{safesubst:#replace: {{safesubst:#expr: {{{octave}}} - 1200 round 6}}|-|−}}
| {{#replace: {{#expr: {{{octave}}} - 1200 round 6}}|-|−}}
| {{{consistent}}}
| {{{consistent}}}
| {{{distinct}}}
| {{{distinct}}}

Latest revision as of 19:36, 20 May 2025

Template documentation[view] [edit] [history] [purge]
This template should not be substituted.

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,

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

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.

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

{{{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.
Must be used in conjunction with pure height, do not use with height.
{{{pure height}}}
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 tempered height, do not use with height.
{{{height}}}
The absolute value of Z evaluated at a ZPI that does not correspond strongly to an edo. Do not use with tempered height or pure height.
{{{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}}} (optional)
This parameter is optional. Pass in the edo that the ZPI represents if the page's title does not contain it.
{{{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.

Example (12edo)

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

{{ZPI
| zpi = 34
| steps = 12.0231830072926
| step size = 99.8071807833375
| tempered height = 5.193290
| pure height = 5.084467
| integral = 1.269599
| gap = 15.899282
| octave = 1197.68616940005
| consistent = 10
| distinct = 6
}}
Tuning Strength Octave (cents) Integer limit
ZPI Steps
per 8ve 		Step size
(cents) 		Height Integral Gap Size Stretch Consistent Distinct
Tempered Pure
34zpi 12.023183 99.807181 5.19329 5.084467 1.269599 15.899282 1197.686169 −2.313831 10 6
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