User:Fredg999/Template:Infobox ET: Difference between revisions

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<includeonly>{{#invoke:Infobox_ET|infobox_ET|tuning={{{1|{{PAGENAME}}}}}|Consistency={{{Consistency|}}}|Distinct consistency={{{Distinct consistency|}}}}}</includeonly><noinclude>{{todo|inline=1|comment=Work in progress! The original version is [[Template:Infobox ET]].}}
#REDIRECT [[Template:Infobox ET]]
 
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 template automatically fills in the following information (certain entries may be supplied with precomputed information using the keys in the Override column):
 
{| class="wikitable"
! width="15%" | Entry
! 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 letter 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 of the equal temperament (e.g. 12 = 2<sup>2</sup> × 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. (<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
|
| 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
|
| 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. (<code>M2 := P5_flat + P5_sharp - P8</code>)
|-
| 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>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 ==
{{#invoke:Infobox_ET|infobox_ET|tuning=12edo}}
 
For a regular ET page:
<pre>
{{User:Fredg999/Template:Infobox ET}}
</pre>
Specifying a specific ET from unrelated page:
<pre>
{{User:Fredg999/Template:Infobox ET|7ed5/4}}
</pre>
Supplying precomputed consistency limits when those are too large to recompute on each page update:
<pre>
{{User:Fredg999/Template:Infobox ET|5407372813edo|Consistency=155|Distinct consistency=155}}
</pre>
 
== See also ==
* [[Template:Infobox ET]]
 
<!-- [[Category:Templates]] -->
</noinclude>

Latest revision as of 03:00, 5 October 2022

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