Template:Infobox ET

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).
Octave		The closest approximation of 2/1, the octave (P8), in edosteps and in cents. Hidden for EDOs. (P8 := round(size / log2(equave)))
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)))
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)
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 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.
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. To hide zeta information, pass the value of no.

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	Highly composite

For a regular ET page:

{{Infobox ET}}

Specifying a specific ET from an unrelated page:

{{Infobox ET|7ed5/4|debug=1}}

Note: debug=1 will disable categories.

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

• Module:Infobox ET
• Template:Infobox Interval

Todo: Reach consensus on parameters, see discussion page!