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User:Plumtree/Infobox Interval: Difference between revisions

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|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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** 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.
** 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 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 color 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
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| [[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]]
| [[Smonzos and svals|Subgroup monzo]]
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| [[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|Comma size]]
| Comma
| 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.
| 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.
|-
| [[Square superparticular|S-expression]]s
|
| For a rational '''Comma''', a search for S-expressions of specific forms is done.
|-
|-
| Name
| Name
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| [[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]] and [[square superparticular]] for small ratios, [[harmonic]]s and [[subharmonic]]s, whether a ratio is [[octave reduction|reduced]].
| 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.
|}
|}


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</pre>
</pre>


Usage example for a large ratio ([[Septimal ruthenia]]), which is also considered to be a comma:
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
| FJS name = P1^{7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7}
| Comma = yes
| 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>
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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"