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.
[[Category:Infoboxes]]
The templates supports the following parameters:
{| class="wikitable"
! width="15%" | Parameter
! width="85%" | Meaning, usage notes
|-
| 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. (<code>P5 := round(log2(3/2)*edo)</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.
|-
| 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.
|-
| <s>Minor 2nd</s>
| <s>Size of the minor second (m2) in edosteps and cents as generated by the fifth. (<code>m2 := 3*P8 - 5*P5</code>)</s>
|-
| <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
| The odd limit diamond to which the edo is consistent.
|}
Usage example for [[24edo]]:
<nowiki>{{Infobox ET
| 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>
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Empty (Step size is self-filling) template for copy & paste (to avoid copying wrong values from edo pages:
The Infobox ET template 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.
Usage
The template should be placed at the beginning of an equal tuning page.
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 and 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 equal temperaments in the family.
Prime factorization
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 of the equal temperament in cents (6 significant digits). (step size = 1200/X)
Octave
The closest approximation of 2/1, the octave (P8), in edosteps and in cents. Hidden for edos. (P8 := round(X/log2(Y)))
Twelfth
The closest approximation of 3/1, the twelfth (P12), in edosteps and in cents. Hidden for edos and edts. (P12 := round(X/log3(Y)))
Fifth
The closest approximation of 3/2, the perfect fifth (P5), in edosteps and in cents. Shown only for edos. (P5 := P12 - P8))
Semitones
Size of the augmented unison (A1) and minor second (m2) in edosteps and cents as generated by the fifth. Shown only for edos. The A1 is the sharpness of the edo. (A1 := 7 * P12 - 11 * P8; m2 := 8 * P8 - 5 * P12)
Dual sharp fifth
For dual-fifths edos (fifth error > 1/3 edostep), the closest sharp approximation of 3/2, in edosteps and in cents.
Dual flat fifth
For dual-fifths edos (fifth error > 1/3 edostep), the closest flat approximation of 3/2, in edosteps and in cents.
Dual 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 tuning 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 Yℤ ⋅ a⁄b; a, b ≤ n, 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 tuning is distinctly consistent. This template will stop trying to compute this if the value is at least 43.
Special properties
Zeta
If the size is highly composite, an additional entry states the fact. See Highly composite equal division. If the size is within integer sequences associated with zeta peaks, zeta integrals or zeta gaps, an additional entry states the fact. See The Riemann zeta function and tuning. Zeta information is hidden by default, pass the value of yes to display it (if any zeta category applies). Zeta-related categories are included regardless of the zeta display parameter.
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