User:Plumtree/Infobox Interval

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The template Infobox Interval was built to help presenting basic information about intervals 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

There are three different ways to use this template:

  • Small ratios: {{Infobox Interval}} (the ratio is inferred from page name), {{Infobox Interval|7/4}}, {{Infobox Interval|Ratio=7/4}}.
    • When use this form? In most cases - whenever both numerator and denominator of the ratio are small enough to fit within Lua numbers as integers. You should not encounter any problems when those are [math]\leq 2^{32}[/math], and you might happen to not encounter any problems when those are [math]\leq 2^{53}[/math]. With larger numbers, you are almost guaranteed to get inaccurate results.
  • Large ratios: {{Infobox Interval|Ket=-2 0 0 1}}, {{Infobox Interval|Monzo=-2 0 0 1}}.
    • In this form, Ratio (unless you specify it explicitly, in which case it will be printed as is) and most norms are omitted.
    • When use this form? Whenever numerator or denominator are too large.
  • Irrational intervals: {{Infobox Interval|Ratio=\pi|Cents=1981.795}}.
    • In this form, Factorization, Subgroup, Monzo (unless you specify it explicitly), FJS name, norms are omitted.
    • When use this form? Whenever the interval is irrational.

The template will add the page to the categories when appropriate:

The template supports the following parameters:

Entry Parameter Meaning, usage notes.
Ratio 1, Ratio Frequency ratio of the interval. Specified explicitly, derived from page name or omitted. For irrational intervals, a LaTeX expression describing the interval (without <math>).
Factorization Prime factorization of the ratio. Derived either from Ratio or Monzo or omitted for irrational intervals.
Monzo Ket, Monzo Coefficients of the Monzo notation, separated by whitespaces. Derived from Ratio or specified or omitted for irrational intervals. If you specify one for an irrational interval, Template:Monzo with the provided argument will be printed.
Subgroup monzo Shown instead of Factorization and Monzo when there is a sequence of 4+ zeros in ket notation. Derived either from Ratio or Monzo or omitted for irrational intervals.
Cents Cents Size in cents. Either derived from Ratio or Monzo or specified for irrational intervals.
Comma size Comma Pass a non-empty string (for example, yes or 1) to enable this entry. For specific values of Cents, an interval is considered a comma. [math](0; 3.5] \to[/math] unnoticeable, [math](3.5; 30] \to[/math] small, [math](30; 100] \to[/math] medium, [math](100; +∞) \to[/math] large. If the interval is rational and is an integer power of another rational number, the entry is omitted.
S-expressions For a rational Comma, a search for S-expressions of specific forms is done.
Name Name Name(s) of the interval. Pages with missing values go into Category:Todo:add interval name. You should not put any <br/> tags between names here; it will be done automatically.
Color name Color name Color name after Kite's color notation in the form: written form, spoken form. For color names see also Gallery of just intervals. Pages with missing values go into Category:Todo:add color name. Default: omitted.
FJS name FJS name Functional Just System name. Provided, derived from Ratio or Monzo or omitted for irrational intervals. Use LaTeX syntax to provide custom names: P5^{11}_{5}.
Special properties Currently implemented: superparticular and square superparticular for small ratios, harmonics and subharmonics, including reduced ones, whether a ratio is reduced.
Tenney height Derived from Ratio or Monzo or omitted.
Weil height Derived from Ratio or omitted.
Benedetti height Derived from Ratio, if the result is small, or omitted.
Harmonic entropy Harmonic entropy approximation (Shannon, [math]\sqrt{n\cdot d}[/math] weights, [math]200\text{-integer limit}\cap\{x\mid\left|\left|x\right|\right|\leq 100\}[/math]). Derived from Ratio, Monzo or Cents.
Sound Sound Soundfile, if one exists. Only name of the file is required (no prefix "File:" and of course without brackets). Default: omitted.
Xen-calc Calc A link to xen-calc. Provided or derived from Ratio or Monzo or omitted. When provided (you should do that only for irrational intervals recognised by xen-calc, such as sqrt(25/24)), Calc is interpreted as the query, not the full link. It is urlencoded automatically.

Examples

Interval information
Ratio 7/4
Factorization 2-2 × 7
Monzo [-2 0 0 1⟩
Size in cents 968.82591¢
Name harmonic seventh
Color name z7, zo 7th
FJS name [math]\text{m7}^{7}[/math]
Special properties reduced
Tenney height (log2 nd) 4.80735
Weil height (log2 max(n, d)) 5.61471
Wilson height (sopfr (nd)) 11
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math]) 		~4.499 bits

[sound info]
open this interval in xen-calc

Usage example for a small ratio (7/4): 

{{Infobox Interval
| Name = harmonic seventh
| Color name = z7, zo 7th
| Sound = jid_7_4_pluck_adu_dr220.mp3
}}

Usage example for a large ratio (septimal ruthenia), which is also considered to be a comma: 

{{Infobox Interval
| Monzo = -263 88 0 44
| Name = septimal ruthenia, septiruthenia
| Comma = yes
}}

Usage example for an irrational interval (sqrt(25/24)): 

{{Infobox Interval
| Ratio = \sqrt{25/24}
| Monzo = -3/2 -1/2 1
| Cents = 35.336213
| Name = square root of 25/24
| Calc = sqrt(25/24)
}}

Boilerplate

Empty template for copy & paste (to avoid copying wrong values from interval pages): 

{{Infobox Interval
| Name = 
| Color name = 
| Sound = 
}}

See also

[[Category:Templates]]

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