Template:Infobox ET/doc: Difference between revisions
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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
+ where you're supposed to put this template |
Make zeta properties display opt-in, but always include zeta categories nonetheless |
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| Special properties | | Special properties | ||
| Zeta | | 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]]. | | 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 <code>yes</code> to display it (if any zeta category applies). Zeta-related categories are included regardless of the zeta display parameter. | ||
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Latest revision as of 18:43, 4 August 2025
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This template should not be substituted. |
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This template uses Lua: |
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.
|
Examples
| ← 11edo | 12edo | 13edo → |
(convergent)
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
|
Todo: discuss Reach consensus on parameters (see discussion page) |