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| <includeonly>{{#invoke:Infobox Interval|infobox_interval | | <includeonly>{{#invoke:Infobox Interval|infobox_interval |
| |Ratio={{{1|{{{Ratio|{{PAGENAME}}}}}}}} | | | Ratio={{{1|{{{Ratio|{{PAGENAME}}}}}}}} |
| |Ket={{{Ket|{{{Monzo|}}}}}} | | | Ket={{{Ket|{{{Monzo|}}}}}} |
| |Cents={{{Cents|}}} | | | Cents={{{Cents|}}} |
| |Comma={{{Comma|}}} | | | Comma={{{Comma|}}} |
| |Name={{{Name|}}} | | | Name={{{Name|}}} |
| |Color name={{{Color name|}}} | | | Color name={{{Color name|}}} |
| |FJS name={{{FJS name|}}} | | | FJS name={{{FJS name|}}} |
| |Sound={{{Sound|}}} | | | Sound={{{Sound|}}} |
| |Calc={{{Calc|}}}}}</includeonly><noinclude> | | | 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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| == Usage ==
| | {{doc}} |
| There are three different ways to use this template:
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| * 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>.
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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.
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| * Large ratios: <code><nowiki>{{Infobox Interval|Ket=-2 0 0 1}}</nowiki></code>, <code><nowiki>{{Infobox Interval|Monzo=-2 0 0 1}}</nowiki></code>.
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| ** In this form, '''Ratio''' (unless you specify it explicitly, in which case it will be printed as is) and most norms are omitted.
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| ** When use this form? Whenever numerator or denominator are too large.
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| * Irrational intervals: <code><nowiki>{{Infobox Interval|Ratio=\pi|Cents=1981.795}}</nowiki></code>.
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| ** In this form, '''Factorization''', '''Subgroup''', '''Monzo''' (unless you specify it explicitly), '''FJS name''', norms are omitted.
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| ** When use this form? Whenever the interval is irrational.
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| The template will add the page to the categories when appropriate:
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| * [[:Category: Rational intervals]] and [[:Category: Irrational intervals]];
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| * [[:Category: 2-limit intervals]], [[:Category: 3-limit intervals]], …;
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| * [[:Category: Unnoticeable commas]], [[:Category: Small commas]], [[:Category: Medium commas]], [[:Category: Large commas]];
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| * [[:Category: Superparticular ratios]];
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| * [[:Category: Harmonics]], [[:Category: Octave-reduced harmonics]], [[:Category: Subharmonics]], [[:Category: Octave-reduced subharmonics]];
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| * [[:Category: Pages with internal sound examples]];
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| * [[: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 interval]], [[:Category: Todo:replace sup and sub with LaTeX]], [[:Category: Todo:remove manual line breaks]].
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| The template supports the following parameters:
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| {| class="wikitable"
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| ! Entry
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| ! Parameter
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| ! Meaning, usage notes.
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| |-
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| | Ratio
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| | 1, Ratio
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| | 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>).
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| |-
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| | Factorization
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| | Prime factorization of the ratio. Derived either from '''Ratio''' or '''Monzo''' or omitted for irrational intervals.
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| |-
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| | [[Monzo]]
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| | Ket, Monzo
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| | 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.
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| |-
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| | [[Smonzos and svals|Subgroup monzo]]
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| | Shown instead of '''Factorization''' and '''Monzo''' when there is a sequence of 4 or more zeros in ket notation. Derived either from '''Ratio''' or '''Monzo''' or omitted for irrational intervals.
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| |-
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| | [[Cent]]s
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| | Cents
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| | Size in [[cent]]s. Either derived from '''Ratio''' or '''Monzo''' or specified for irrational intervals.
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| | Name
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| | Name
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| | Name(s) of the interval. Pages with missing values go into [[:Category:Todo:add interval name]]. You should not put any <nowiki><br/></nowiki> tags between names here; it will be done automatically.
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| |-
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| | [[Kite's color notation|Color name]]
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| | Color name
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| | 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.
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| |-
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| | [[Functional Just System|FJS name]]
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| | FJS name
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| | [[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>.
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| | Special properties
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| | 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]].
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| |-
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| | [[Tenney height]]
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| | Derived from '''Ratio''' or '''Monzo''' or omitted.
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| |-
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| | [[Weil height]]
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| | Derived from '''Ratio''' or omitted.
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| |-
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| | [[Wilson height]]
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| | Derived from '''Ratio''', or omitted.
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| |-
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| | [[Harmonic entropy]]
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| | 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'''.
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| |-
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| | [[Comma|Comma size]]
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| | Comma
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| | 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.
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| |-
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| | [[Square superparticular|S-expression]]s
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| | For a rational '''Comma''', a search for S-expressions of specific forms is done.
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| |-
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| | Sound
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| | Sound
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| | Soundfile, if one exists. Only name of the file is required (no prefix "File:" and of course without brackets). Default: omitted.
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| |-
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| | [[Xen-calc]]
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| | Calc
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| | 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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| |}
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| == Examples ==
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| {{#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}}
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| Usage example for a small ratio ([[7/4]]):
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| <pre>
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| {{Infobox Interval
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| | Name = harmonic seventh
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| | Color name = z7, zo 7th
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| | Sound = jid_7_4_pluck_adu_dr220.mp3
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| }}
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| </pre>
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| Usage example for a large ratio ([[septimal ruthenia]]), which is also considered to be a comma:
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| <pre>
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| {{Infobox Interval
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| | Monzo = -263 88 0 44
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| | Name = septimal ruthenia, septiruthenia
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| | Comma = yes
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| }}
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| </pre>
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| Usage example for an irrational interval ([[sqrt(25/24)]]):
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| <pre>
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| {{Infobox Interval
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| | Ratio = \sqrt{25/24}
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| | Monzo = -3/2 -1/2 1
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| | Cents = 35.336213
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| | Name = square root of 25/24
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| | Calc = sqrt(25/24)
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| }}
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| </pre>
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| == Boilerplate ==
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| '''Empty template''' for copy & paste (to avoid copying wrong values from interval pages):
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| <pre>
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| {{Infobox Interval
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| | Name =
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| | Color name =
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| | Sound =
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| }}
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| </pre>
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| == See also ==
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| * [[Module: Infobox Interval]]
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| * [[Template: Infobox ET]]
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| * [[xen-calc]] – the according page of that tool gets linked automatically for rational intervals
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| [[Category:Templates]]
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| <!-- interwiki -->
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| [[de:Vorlage:Infobox Intervall]]
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| </noinclude> | | </noinclude> |