Template:Infobox interval

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]\displaystyle{ \leq 2^{32} }[/math], and you might happen to not encounter any problems when those are [math]\displaystyle{ \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:

• Category:Rational intervals and Category:Irrational intervals;
• Category:2-limit, Category:3-limit, ...;
• Category:Unnoticeable commas, Category:Small commas, Category:Medium commas, Category:Large commas;
• Category:Superparticular;
• Category:Harmonics, Category:Octave-reduced harmonics, Category:Subharmonics, Category:Octave-reduced subharmonics;
• Category:Pages with internal sound examples;
• Category:Todo:add interval ratio, Category:Todo:add interval name, Category:Todo:add color name, Category:Todo:remove explicit ket notation, Category:Todo:remove explicit cents, Category:Todo:initialise Infobox Interval, Category:Todo:replace sup and sub with LaTeX, Category:Todo:remove manual line breaks.

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]\displaystyle{ (0; 3.5] \to }[/math] unnoticeable, [math]\displaystyle{ (3.5; 30] \to }[/math] small, [math]\displaystyle{ (30; 100] \to }[/math] medium, [math]\displaystyle{ (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]\displaystyle{ \sqrt{n\cdot d} }[/math] weights, [math]\displaystyle{ 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

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

• Template:Infobox ET
• xen-calc – the according page of that tool gets linked automatically for rational intervals