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User:Plumtree/Infobox Interval: Difference between revisions

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|Ket={{{Ket|{{{Monzo|}}}}}}
|Ket={{{Ket|{{{Monzo|}}}}}}
|Cents={{{Cents|}}}
|Cents={{{Cents|}}}
|Comma={{{Comma|}}}
|Name={{{Name|}}}
|Name={{{Name|}}}
|Color name={{{Color name|}}}
|Color name={{{Color name|}}}
|FJS name={{{FJS name|}}}
|FJS name={{{FJS name|}}}
|Sound={{{Sound|}}}}}</includeonly><noinclude>
|Sound={{{Sound|}}}
|Calc={{{Calc|}}}}}</includeonly><noinclude>
The template '''Infobox Interval''' was built to help presenting basic information about [[interval]]s 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 '''Infobox Interval''' was built to help presenting basic information about [[interval]]s 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.


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There are three different ways to use this template:
There are three different ways to use this template:
* Small ratios: <code><nowiki>{{Infobox Interval}}</nowiki></code> (the ratio is inferred from page name), <code><nowiki>{{Infobox Interval|7/4}}</nowiki></code>, <code><nowiki>{{Infobox Interval|Ratio=7/4}}</nowiki></code>.
* Small ratios: <code><nowiki>{{Infobox Interval}}</nowiki></code> (the ratio is inferred from page name), <code><nowiki>{{Infobox Interval|7/4}}</nowiki></code>, <code><nowiki>{{Infobox Interval|Ratio=7/4}}</nowiki></code>.
** 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>\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.
** 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: <code><nowiki>{{Infobox Interval|Ket=-2 0 0 1}}</nowiki></code>, <code><nowiki>{{Infobox Interval|Monzo=-2 0 0 1}}</nowiki></code>.
* Large ratios: <code><nowiki>{{Infobox Interval|Ket=-2 0 0 1}}</nowiki></code>, <code><nowiki>{{Infobox Interval|Monzo=-2 0 0 1}}</nowiki></code>.
** In this form, '''Ratio''' and '''Norms''' are omitted, '''Factorization''', '''Subgroup''', '''Cents''', '''FJS name''', '''Harmonic entropy''' are computed automatically.
** 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.
** When use this form? Whenever numerator or denominator are too large.
* Irrational intervals: <code><nowiki>{{Infobox Interval|Ratio=π|Cents=1981.795}}</nowiki></code>.
* Irrational intervals: <code><nowiki>{{Infobox Interval|Ratio=\pi|Cents=1981.795}}</nowiki></code>.
** In this form, '''Factorization''', '''Subgroup''', '''Monzo''', '''FJS name''', '''Norms''', '''Harmonic entropy''' are omitted.
** 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.
** When use this form? Whenever the interval is irrational.


The template will add the page to the categories when appropriate:
The template will add the page to the categories when appropriate:
* [[:Category:Rational intervals]] and [[:Category:Irrational intervals]];
* [[: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: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:Pages with internal sound examples]];
* [[:Category:Todo:add interval name]].
* [[: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:
The template supports the following parameters:
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| Ratio
| Ratio
| 1, Ratio
| 1, Ratio
| Frequency [[ratio]] of the interval. Specified explicitly, derived from page name or omitted.
| Frequency [[ratio]] of the interval. Specified explicitly, derived from page name or omitted. For irrational intervals, a LaTeX expression describing the interval (without <nowiki><math></nowiki>).
|-
|-
| Factorization
| Factorization
|
|
| Prime factorization of the ratio. Derived either from '''Ratio''' or '''Monzo''' or omitted for irrational intervals.
| Prime factorization of the ratio. Derived either from '''Ratio''' or '''Monzo''' or omitted for irrational intervals.
|-
| [[Just intonation subgroup|Subgroup]]
|
| JI subgroup generated by factors of the ratio. Derived either from '''Ratio''' or '''Monzo''' or omitted for irrational intervals.
|-
|-
| [[Monzo]]
| [[Monzo]]
| Ket, Monzo
| Ket, Monzo
| Coefficients of the [[Monzo]] notation, separated by whitespaces. Derived from '''Ratio''' or specified or omitted for irrational intervals.
| 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.
|-
| [[Smonzos and svals|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.
|-
|-
| [[Cent]]s
| [[Cent]]s
| Cents
| Cents
| Size in [[cent]]s. Either derived from '''Ratio''' or '''Monzo''' or specified.
| Size in [[cent]]s. Either derived from '''Ratio''' or '''Monzo''' or specified for irrational intervals.
|-
| [[Comma|Comma size]]
| Comma
| Pass a non-empty string (for example, <code>yes</code> or <code>1</code>) 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.
|-
|-
| [[Comma]]
| [[Square superparticular|S-expression]]s
|
|
| 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; 250] \to</math> large. If the interval is rational and is an integer power of another rational number, the entry is omitted.
| For a rational '''Comma''', a search for S-expressions of specific forms is done.
|-
|-
| Name
| Name
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| [[Kite's color notation|Color name]]
| [[Kite's color notation|Color name]]
| Color name
| Color name
| Color name after [[Kite's color notation]] in the form: <code>written form, spoken form</code>. For color names see also [[Gallery of just intervals]]. Default: omitted.
| Color name after [[Kite's color notation]] in the form: <code>written form, spoken form</code>. For color names see also [[Gallery of just intervals]]. Pages with missing values go into [[:Category:Todo:add color name]]. Default: omitted.
|-
|-
| [[Functional Just System|FJS name]]
| [[Functional Just System|FJS name]]
| 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.
| [[Functional Just System]] name. Provided, derived from '''Ratio''' or '''Monzo''' or omitted for irrational intervals. Use LaTeX syntax to provide custom names: <code>P5^{11}_{5}</code>.
|-
|-
| Special properties
| Special properties
|
|
| Currently implemented: [[Superparticular interval|superparticular]] for small ratios.
| Currently implemented: [[Superparticular interval|superparticular]] and [[square superparticular]] for small ratios, [[harmonic]]s and [[subharmonic]]s, including reduced ones, whether a ratio is [[octave reduction|reduced]].
|-
| [[Tenney height]]
|
| Derived from '''Ratio''' or '''Monzo''' or omitted.
|-
|-
| Norms
| [[Weil height]]
|
|
| [[Tenney height]], [[Weil height]], [[Benedetti height]]. Derived from '''Ratio''' or omitted.
| Derived from '''Ratio''' or omitted.
|-
| [[Benedetti height]]
|
| Derived from '''Ratio''', if the result is small, or omitted.
|-
|-
| [[Harmonic entropy]]
| [[Harmonic entropy]]
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|-
|-
| [[Xen-calc]]
| [[Xen-calc]]
|
| Calc
| A link to xen-calc. Appears when '''Ratio''' is shown.
| 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 <code>sqrt(25/24)</code>), '''Calc''' is interpreted as the query, not the full link. It is urlencoded automatically.
|}
|}


== Examples ==
== Examples ==
{{#invoke:Infobox Interval|infobox_interval|Ratio=7/4|Name=harmonic seventh|Color name=z7, zo 7th|Sound=jid_7_4_pluck_adu_dr220.mp3|debug=1}}
{{#invoke:Infobox Interval|infobox_interval|Ratio=7/4|Name=harmonic seventh|Color name=z7, zo 7th|Sound=jid_7_4_pluck_adu_dr220.mp3|debug=hide}}
Usage example for a small ratio ([[7/4]]):
Usage example for a small ratio ([[7/4]]):
<pre>
<pre>
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</pre>
</pre>


Usage example for a large ratio ([[Septimal ruthenia]]):
Usage example for a large ratio ([[septimal ruthenia]]), which is also considered to be a comma:
<pre>
<pre>
{{Infobox Interval
{{Infobox Interval
| Monzo = -263 88 0 44
| Monzo = -263 88 0 44
| Name = septimal ruthenia, septiruthenia
| Name = septimal ruthenia, septiruthenia
| Comma = yes
}}
}}
</pre>
</pre>


Usage example for an irrational interval ([[Pitave]]):
Usage example for an irrational interval ([[sqrt(25/24)]]):
<pre>
<pre>
{{Infobox Interval
{{Infobox Interval
| Ratio = π
| Ratio = \sqrt{25/24}
| Cents = 1981.795
| Monzo = -3/2 -1/2 1
| Name = pitave
| Cents = 35.336213
| Name = square root of 25/24
| Calc = sqrt(25/24)
}}
}}
</pre>
</pre>


== Boilerplates ==
== Boilerplate ==
'''Empty template''' for copy &amp; paste (to avoid copying wrong values from interval pages):
'''Empty template''' for copy &amp; paste (to avoid copying wrong values from interval pages):
<pre>
<pre>
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== See also ==
== See also ==
* [[Template:Infobox ET]]
* [[Template:Infobox ET]]
* [[xen-calc]] – the according page of that tool gets linked automatically if the <code>Ratio</code> parameter is filled in
* [[xen-calc]] – the according page of that tool gets linked automatically for rational intervals


<nowiki>[[Category:Templates]]</nowiki>
<nowiki>[[Category:Templates]]</nowiki>
</noinclude>
</noinclude>
Retrieved from "https://en.xen.wiki/w/User:Plumtree/Infobox_Interval"