User:Plumtree/Infobox Interval: Difference between revisions
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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''' (unless you specify it explicitly, in which case it will be printed as is) 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= | * 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. | ||
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* [[:Category:Harmonics]], [[:Category:Octave-reduced harmonics]], [[:Category:Subharmonics]], [[:Category:Octave-reduced subharmonics]]; | * [[: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: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]]. | * [[: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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| [[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 size]] | | [[Comma|Comma size]] | ||
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| [[Xen-calc]] | | [[Xen-calc]] | ||
| 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), '''Calc''' is interpreted as the query, not the full link. It is urlencoded automatically. | | 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 an irrational interval ([[ | Usage example for an irrational interval ([[sqrt(25/24)]]): | ||
<pre> | <pre> | ||
{{Infobox Interval | {{Infobox Interval | ||
| Ratio = \ | | Ratio = \sqrt{25/24} | ||
| Cents = | | Monzo = -3/2 -1/2 1 | ||
| Name = | | Cents = 35.336213 | ||
| Name = square root of 25/24 | |||
| Calc = sqrt(25/24) | |||
}} | }} | ||
</pre> | </pre> | ||