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> | ||
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The template '''Infobox ET''' was built to help presenting basic information about [[ | 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 | 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%" | | ! width="15%" | Entry | ||
! width=" | ! 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) | | | ||
| 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>) | |||
|- | |- | ||
| | | 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 | ||
| The | | 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 | == Usage examples == | ||
{{#invoke:Infobox_ET|infobox_ET|tuning=12edo}} | |||
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}} | |||
For a regular ET page: | |||
<pre> | |||
{{Infobox ET}} | |||
</pre> | |||
| | Specifying a specific ET from an unrelated page: | ||
| | <pre> | ||
| | {{Infobox ET|7ed5/4}} | ||
}}</ | </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 == | ||