Template:Infobox ET: Difference between revisions

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<div style="
<includeonly>{{#invoke:Infobox_ET|infobox_ET|tuning={{{1|{{PAGENAME}}}}}|Consistency={{{Consistency|}}}|Distinct consistency={{{Distinct consistency|}}}}}</includeonly><noinclude>
border: 1px solid #999;
margin: 0;
margin-left: 1em;
margin-bottom: 0.5em;
padding: 0.5em;
background-color: #f0f0f0;
min-width: 15em;
float: right;
">
{| width="100%" style="border-collapse: collapse;"
|+ '''{{PAGENAME}}'''
|-
{{#if: {{{Prime factorization|}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Prime factorization
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Prime factorization|}}} '''
}}
|-
{{#if: {{{Step size|}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Step size
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Step size|}}}'''
}}
|-
{{#if: {{{Fifth|{{{P5|}}}}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Fifth
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Fifth|{{{Fifth type|{{{P5|}}}}}}}}}'''
}}
|-
{{#if: {{{Semitones|}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Semitones (A1:m2)
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Semitones|}}}'''
}}
|-
{{#if: {{{Sharp fifth|{{{Sharp P5|}}}}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Sharp fifth
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Sharp fifth|{{{Sharp P5|}}}}}}'''
}}
|-
{{#if: {{{Flat fifth|{{{Flat P5|}}}}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Flat fifth
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Flat fifth|{{{Flat P5|}}}}}}'''
}}
|-
{{#if: {{{Major 2nd|{{{M2|}}}}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Major 2nd
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Major 2nd|{{{M2|}}}}}}'''
}}
|-
{{#if: {{{Minor 2nd|{{{m2|}}}}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Minor 2nd
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Minor 2nd|{{{m2|}}}}}}'''
}}
|-
{{#if: {{{Augmented 1sn|{{{A1|}}}}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Augmented 1sn
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Augmented 1sn|{{{A1|}}}}}}'''
}}
|-
{{#if: {{{Consistency|{{{Diamond consistency|}}}}}} |
  {{!}} style="text-align:right; padding-right: 0.25em" {{!}} Consistency limit
  {{!}} style="background-color: white; padding-left: 0.25em" {{!}} '''{{{Consistency|{{{Diamond consistency|}}}}}}'''
}}
|}
</div><noinclude>


The template '''Infobox ET''' was built to help presenting basic information about [[EDO]]s in a unified form, to make them obvious by glance. Also the formatting of the wiki text itself is easier to read and improve when it is obviously structured by this template.
The template '''Infobox ET''' was built to help presenting basic information about [[equal tuning]]s in a unified form, to make them obvious by glance. Also the formatting of the wiki text itself is easier to read and improve when it is obviously structured by this template.


The templates supports the following parameters:
The template automatically fills in the following information (certain entries may be supplied with precomputed information using the keys in the Override column):


{| class="wikitable"
{| class="wikitable"
! width="15%" | Parameter
! width="15%" | Entry
! width="85%" | Meaning, usage notes
! width="15%" | Override
! width="70%" | Meaning, usage notes
|-
| ET identifier
| 1
| An identifier of the form ''X''ed''Y'', where ''X'' is the number of steps and ''Y'' is an [[equave]]: a non-negative integer, a positive rational number or one of letters signifying a rational number (<code>f</code>= 3/2, <code>o</code>= 2, <code>t</code>= 3). If not provided, the page title is assumed to be such an identifier. If parsing is unsuccessful, [[12edo]] is chosen as a fallback.
|-
| Adjacent ETs
|
| Links to the previous and the next ETs in the family.
|-
|-
| Prime factorization  
| Prime factorization  
|
| Prime factorization of the equal temperament (e.g. 12 = 2<sup>2</sup> × 3), even if prime per se (e.g. 17 (prime)).  
| Prime factorization of the equal temperament (e.g. 12 = 2<sup>2</sup> × 3), even if prime per se (e.g. 17 (prime)).  
|-
|-
| Step size
| Step size
|
| One step (1200/edo) of the equal temperament in cents (6 significant digits).
| One step (1200/edo) of the equal temperament in cents (6 significant digits).
|-
|-
| Fifth
| Fifth
| The closest approximation of 3/2, the perfect fifth (P5), in edosteps and in cents. (<code>P5 := round(log2(3/2)*edo)</code>)
|
| The closest approximation of 3/2, the perfect fifth (P5), in edosteps and in cents. Hidden for EDFs. (<code>P5 := round(size * log2(3/2) / log2(equave))</code>)
|-
| Octave
|
| The closest approximation of 2/1, the octave (P8), in edosteps and in cents. Hidden for EDOs. (<code>P8 := round(size / log2(equave))</code>)
|-
|-
| Semitones
| Semitones
| Size of the augmented unison (A1) and minor second (m2) in edosteps and cents as generated by the fifth. <br>The A1 is the [[sharpness]] of the edo.  
|
| Size of the augmented unison (A1) and minor second (m2) in edosteps and cents as generated by the fifth. <br>The A1 is the [[sharpness]] of the edo. (<code>A1 := 7 * P5 - 4 * P8; m2 := 3 * P8 - 5 * P5</code>)
|-
|-
| Sharp fifth
| Sharp fifth
|
| For dual-fifths edos (fifth error > 1/3 edostep), the closest sharp approximation of 3/2, in edosteps and in cents.
| For dual-fifths edos (fifth error > 1/3 edostep), the closest sharp approximation of 3/2, in edosteps and in cents.
|-
|-
| Flat fifth
| Flat fifth
|
| For dual-fifths edos (fifth error > 1/3 edostep), the closest flat approximation of 3/2, in edosteps and in cents.  
| For dual-fifths edos (fifth error > 1/3 edostep), the closest flat approximation of 3/2, in edosteps and in cents.  
|-
|-
| Major 2nd
| Major 2nd
| For dual-fifths edos (fifth error > 1/3 edostep), size of the major second (M2) in edosteps and cents as generated by the sharp fifth and the flat fifth.  
|
| For dual-fifths edos (fifth error > 1/3 edostep), size of the major second (M2) in edosteps and cents as generated by the sharp fifth and the flat fifth. (<code>M2 := P5_flat + P5_sharp - P8</code>)
|-
|-
| <s>Minor 2nd</s>
| Consistency
| <s>Size of the minor second (m2) in edosteps and cents as generated by the fifth. (<code>m2 := 3*P8 - 5*P5</code>)</s>
| Consistency
|-
| The limit diamond to which the ET is [[consistent]]. This template will stop trying to compute this if the value is at least 43. The following generalization is used for arbitrary equaves: for degree '''n''', all ratios of the form <math>equave^{\mathbb{Z}} \cdot \frac{a}{b}, a, b \leq n</math>, are considered; when an increase of '''n''' does not add any new ratios, this degree is skipped.
| <s>Augmented 1sn</s>
| <s>Size of the augmented unison (A1) in edosteps and cents as generated by the fifth. This is also the sharpness/flatness of the edo. (<code>A1 := M2 - m2</code>)</s>  
|-
|-
| Consistency
| Distinct consistency
| The odd limit diamond to which the edo is consistent.  
| Distinct consistency
| The limit diamond to which the ET is distinctly [[consistent]]. This template will stop trying to compute this if the value is at least 43.
|}
|}


Usage example for [[24edo]]:
== Usage examples ==
<nowiki>{{Infobox ET
{{#invoke:Infobox_ET|infobox_ET|tuning=12edo}}
| Prime factorization = 2<sup>3</sup> × 3
| Step size = 50.0000¢
| Fifth = 14\24 (700.0¢) (→ [[12edo|7\12]])
| Semitones = 2:2 (100.0¢ : 100.0¢)
| Consistency = 5
}}</nowiki>
 
----


Empty (Step size is self-filling) template for copy &amp; paste (to avoid copying wrong values from edo pages:
For a regular ET page:
<nowiki>{{Infobox ET
<pre>
| Prime factorization =
{{Infobox ET}}
| Step size = {{subst:#number_format:{{subst:#expr:1200/{{subst:#regex:{{subst:PAGENAME}}|/(\d+)-?EDO/i|\1}}}}|5}}
</pre>
| Fifth =
Specifying a specific ET from an unrelated page:
| Semitones =
<pre>
| Consistency =  
{{Infobox ET|7ed5/4}}
}}</nowiki>
</pre>
Supplying precomputed consistency limits when those are too large to be recomputed on each page update:
<pre>
{{Infobox ET|5407372813edo|Consistency=155|Distinct consistency=155}}
</pre>


== See also ==
== See also ==

Revision as of 12:13, 4 October 2022


The template Infobox ET was built to help presenting basic information about equal tunings in a unified form, to make them obvious by glance. Also the formatting of the wiki text itself is easier to read and improve when it is obviously structured by this template.

The template automatically fills in the following information (certain entries may be supplied with precomputed information using the keys in the Override column):

Entry Override Meaning, usage notes
ET identifier 1 An identifier of the form XedY, where X is the number of steps and Y is an equave: a non-negative integer, a positive rational number or one of letters signifying a rational number (f= 3/2, o= 2, t= 3). If not provided, the page title is assumed to be such an identifier. If parsing is unsuccessful, 12edo is chosen as a fallback.
Adjacent ETs Links to the previous and the next ETs in the family.
Prime factorization Prime factorization of the equal temperament (e.g. 12 = 22 × 3), even if prime per se (e.g. 17 (prime)).
Step size One step (1200/edo) of the equal temperament in cents (6 significant digits).
Fifth The closest approximation of 3/2, the perfect fifth (P5), in edosteps and in cents. Hidden for EDFs. (P5 := round(size * log2(3/2) / log2(equave)))
Octave The closest approximation of 2/1, the octave (P8), in edosteps and in cents. Hidden for EDOs. (P8 := round(size / log2(equave)))
Semitones Size of the augmented unison (A1) and minor second (m2) in edosteps and cents as generated by the fifth.
The A1 is the sharpness of the edo. (A1 := 7 * P5 - 4 * P8; m2 := 3 * P8 - 5 * P5)
Sharp fifth For dual-fifths edos (fifth error > 1/3 edostep), the closest sharp approximation of 3/2, in edosteps and in cents.
Flat fifth For dual-fifths edos (fifth error > 1/3 edostep), the closest flat approximation of 3/2, in edosteps and in cents.
Major 2nd For dual-fifths edos (fifth error > 1/3 edostep), size of the major second (M2) in edosteps and cents as generated by the sharp fifth and the flat fifth. (M2 := P5_flat + P5_sharp - P8)
Consistency Consistency The limit diamond to which the ET is consistent. This template will stop trying to compute this if the value is at least 43. The following generalization is used for arbitrary equaves: for degree n, all ratios of the form [math]\displaystyle{ equave^{\mathbb{Z}} \cdot \frac{a}{b}, a, b \leq n }[/math], are considered; when an increase of n does not add any new ratios, this degree is skipped.
Distinct consistency Distinct consistency The limit diamond to which the ET is distinctly consistent. This template will stop trying to compute this if the value is at least 43.

Usage examples

← 11edo 12edo 13edo →
Prime factorization 22 × 3
Step size 100 ¢ (by definition) 
Fifth 7\12 (700 ¢)
(convergent)
Semitones (A1:m2) 1:1 (100 ¢ : 100 ¢)
Consistency limit 9
Distinct consistency limit 5
Special properties

For a regular ET page: 

{{Infobox ET}}

Specifying a specific ET from an unrelated page: 

{{Infobox ET|7ed5/4}}

Supplying precomputed consistency limits when those are too large to be recomputed on each page update: 

{{Infobox ET|5407372813edo|Consistency=155|Distinct consistency=155}}

See also

Todo:

Reach consensus on parameters, see discussion page!

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