Template:ZPI: Difference between revisions
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ArrowHead294 (talk | contribs) 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="4" | Strength | ! colspan="{{#if: {{{tempered height|}}}{{{pure height|}}}|4|3}}" | Strength | ||
! colspan=" | ! colspan={{#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 | |||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Steps<br>per 8ve | |||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Step size<br>([[cent]]s) | |||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|colspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Height | |||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Integral | |||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Gap | |||
{{#if: {{{edo|}}} | |||
| ! rowspan{{=}}"2" {{!}} Edo | |||
! colspan{{=}}"2" {{!}} Octave (cents) | |||
|}}{{#if: {{{tempered height|}}}{{{pure height|}}}|{{#if: {{{edo|}}}|| | |||
! rowspan{{=}}"2" {{!}} Size}}}} | |||
{{#if: {{{tempered height|}}}{{{pure height|}}}|{{#if: {{{edo|}}}|| | |||
! rowspan{{=}}"2" {{!}} Stretch}}}} | |||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Consistent | |||
! {{#if: {{{tempered height|}}}{{{pure height|}}}|rowspan{{=}}"2" {{!}}|{{#if: {{{edo|}}}|rowspan{{=}}"2" {{!}}|}}}} Distinct | |||
|- | |- | ||
{{#if: {{{edo|}}} | |||
! | | ! Size | ||
! | ! Stretch | ||
|}} | |||
{{#if: {{{tempered height|}}}{{{pure height|}}} | |||
| ! Tempered | |||
! Pure | |||
! | |}} | ||
! | |||
|- | |- | ||
| {{#if: {{{zpi|}}}|[[{{#rmatch: {{{zpi}}}|/(\d+)/|\1}}zpi]]|}} | |||
| {{#expr: {{{steps}}} round 6 }} | |||
| | | {{#expr: {{{step size}}} round 6 }} | ||
| [[{{{zpi}}}zpi]] | {{#if: {{{tempered height|}}}{{{pure height|}}} | ||
| {{{steps}}} | | {{!}} {{#expr: {{{tempered height}}} round 6 }} | ||
| {{{step size}}} | {{!}} {{#expr: {{{pure height}}} round 6 }} | ||
| {{{ | | {{!}} {{#expr: {{{height}}} round 6 }} | ||
| {{{ | }} | ||
| {{{integral}}} | | {{#expr: {{{integral}}} round 6 }} | ||
| {{{gap}}} | | {{#expr: {{{gap}}} round 6 }} | ||
| {{{edo|{{ | {{#if: {{{edo|}}}|{{!}} {{{edo}}}|}} | ||
| {{{octave}}} | | {{#expr: {{{octave}}} round 6}} | ||
| {{#replace: {{#expr: {{{octave}}} - 1200 round 6}}|-|−}} | |||
| {{{consistent}}} | | {{{consistent}}} | ||
| {{{distinct}}} | | {{{distinct}}} | ||
Latest revision as of 19:36, 20 May 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 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 |