Template:ZPI: Difference between revisions
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! colspan="3" | Tuning | ! colspan="3" | Tuning | ||
! colspan="{{#if: {{{tempered height|}}}{{{pure height|}}}|4|3}}" | Strength | ! colspan="{{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|4|3}}" | Strength | ||
! colspan={{#if: {{{edo|}}}|"3" {{!}} Closest edo|"2" {{!}} Octave (cents)}} | ! colspan={{safesubst:#if: {{{edo|}}}|"3" {{!}} Closest edo|"2" {{!}} Octave (cents)}} | ||
! colspan="2" | Integer limit | ! colspan="2" | Integer limit | ||
|- | |- | ||
! {{#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" {{!}}|}}}} ZPI | ||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Steps per octave | ! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Steps per octave | ||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Step size ([[cent]]s) | ! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Step size ([[cent]]s) | ||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|colspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Height | ! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|colspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Height | ||
! {{#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" {{!}}|}}}} Integral | ||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Gap | ! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Gap | ||
{{#if: {{{edo|}}} | {{safesubst:#if: {{{edo|}}} | ||
| ! rowspan{{=}}"2" {{!}} Edo | | ! rowspan{{=}}"2" {{!}} Edo | ||
! colspan{{=}}"2" {{!}} Octave (cents) | ! colspan{{=}}"2" {{!}} Octave (cents) | ||
|}}{{#if: {{{tempered height|}}}{{{pure height|}}}|{{#if: {{{edo|}}}|| | |}}{{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|{{safesubst:#if: {{{edo|}}}|| | ||
! rowspan{{=}}"2" {{!}} Size}}}} | ! rowspan{{=}}"2" {{!}} Size}}}} | ||
{{#if: {{{tempered height|}}}{{{pure height|}}}|{{#if: {{{edo|}}}|| | {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|{{safesubst:#if: {{{edo|}}}|| | ||
! rowspan{{=}}"2" {{!}} Stretch}}}} | ! rowspan{{=}}"2" {{!}} Stretch}}}} | ||
! {{#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" {{!}}|}}}} Consistent | ||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Distinct | ! {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{safesubst:#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Distinct | ||
|- | |- | ||
{{#if: {{{edo|}}} | {{safesubst:#if: {{{edo|}}} | ||
| ! Size | | ! Size | ||
! Stretch | ! Stretch | ||
|}} | |}} | ||
{{#if: {{{tempered height|}}}{{{pure height|}}} | {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}} | ||
| ! Tempered | | ! Tempered | ||
! Pure | ! Pure | ||
|}} | |}} | ||
|- | |- | ||
| {{#if: {{{zpi|}}}|[[{{#regex: {{{zpi}}}|/\d+/}}zpi]]|}} | | {{safesubst:#if: {{{zpi|}}}|[[{{safesubst:#regex: {{{zpi}}}|/\d+/}}zpi]]|}} | ||
| {{{steps}}} | | {{{steps}}} | ||
| {{{step size}}} | | {{{step size}}} | ||
{{#if: {{{tempered height|}}}{{{pure height|}}} | {{safesubst:#if: {{{tempered height|}}}{{{pure height|}}} | ||
| {{!}} {{{tempered height}}} | | {{!}} {{{tempered height}}} | ||
{{!}} {{{pure height}}} | {{!}} {{{pure height}}} | ||
| Line 41: | Line 41: | ||
| {{{integral}}} | | {{{integral}}} | ||
| {{{gap}}} | | {{{gap}}} | ||
{{#if: {{{edo|}}}|{{!}} {{{edo}}}|}} | {{safesubst:#if: {{{edo|}}}|{{!}} {{{edo}}}|}} | ||
| {{{octave}}} | | {{{octave}}} | ||
| {{#replace: {{#expr: {{{octave}}} - 1200}}|-|−}} | | {{safesubst:#replace: {{safesubst:#expr: {{{octave}}} - 1200}}|-|−}} | ||
| {{{consistent}}} | | {{{consistent}}} | ||
| {{{distinct}}} | | {{{distinct}}} | ||
Revision as of 14:55, 3 April 2025
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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 withheight.
{{{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 withheight.
{{{height}}}- The absolute value of Z evaluated at a ZPI that does not correspond strongly to an edo. Do not use with
tempered heightorpure 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 octave | Step size (cents) | Height | Integral | Gap | Size | Stretch | Consistent | Distinct | |
| Tempered | Pure | |||||||||
| [[{{safesubst:#regex: 34|/\d+/}}zpi]] | 12.0231830072926 | 99.8071807833375 | 5.193290 | 5.084467 | 1.269599 | 15.899282 | 1197.68616940005 | −2.3138305999501 | 10 | 6 |