User:Plumtree/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}}.
  • In this form, Factorization, Subgroup, Monzo, Cents, FJS name, Norms, Harmonic entropy are computed automatically.
  • 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 and Norms are omitted, Factorization, Subgroup, Cents, FJS name, Harmonic entropy are computed automatically.
  • When use this form? Whenever numerator or denominator are too large.
• Irrational intervals: {{Infobox Interval|Ratio=π|Cents=1981.795}}.
  • In this form, Factorization, Subgroup, Monzo, FJS name, Norms, Harmonic entropy 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:Unnoticeable commas, Category:Small commas, Category:Medium commas, Category:Large commas;
• Category:Pages with internal sound examples;
• Category:Todo:add interval name.

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.
Factorization		Prime factorization of the ratio. Derived either from Ratio or Monzo or omitted for irrational intervals.
Subgroup		JI subgroup generated by factors 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.
Cents	Cents	Size in cents. Either derived from Ratio or Monzo or specified.
Comma		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; 250] \to }[/math] large. If the interval is rational and is an integer power of another rational number, the entry is omitted.
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. Default: omitted.
FJS name	FJS name	Functional Just System name. Provided, derived from Ratio or Monzo or omitted for irrational intervals. At the moment, when computed automatically, results may be incorrect in rare cases.
Special properties		Currently implemented: superparticular for small ratios.
Norms		Tenney height, Weil height, Benedetti height. Derived from Ratio 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		A link to xen-calc. Appears when Ratio is shown.

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):

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

Usage example for an irrational interval (Pitave):

{{Infobox Interval
| Ratio = π
| Cents = 1981.795
| Name = pitave
}}

Boilerplates

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 if the Ratio parameter is filled in

[[Category:Templates]]