Template:Harmonics in equal/doc - Revision history

Squib: /* Advanced */-typo

2026-03-06T04:32:31Z

Advanced: -typo

← Older revision		Revision as of 04:32, 6 March 2026
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	: Denominator of the interval that is divided equally. Can be used without parameter name. Default is 1.		: Denominator of the interval that is divided equally. Can be used without parameter name. Default is 1.

	; </code>columns</code>		; <code>columns</code>
	: Number of intervals to include. Default is 11.		: Number of intervals to include. Default is 11.

Ganaram inukshuk at 06:30, 31 October 2025

2025-10-31T06:30:43Z

← Older revision		Revision as of 06:30, 31 October 2025
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	{{Dochead~~}}{{lua~~}}		{{Dochead}}
	This template generates a table with the approximations of harmonics for a given [[equal tuning]].		This template generates a table with the approximations of harmonics for a given [[equal tuning]].

FloraC at 11:40, 17 August 2025

2025-08-17T11:40:05Z

← Older revision		Revision as of 11:40, 17 August 2025
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	{{~~dochead~~}}{{lua}}		{{Dochead}}{{lua}}
	This template generates a table with the approximations of harmonics for a given [[equal tuning]].		This template generates a table with the approximations of harmonics for a given [[equal tuning]].

	=== Usage ===		=== Usage ===
	==== Simple ====		==== Simple ====
	For divisions of the octave ([[~~EDO~~]]s), you can use one unnamed argument:		For divisions of the octave ([[edo]]s), you can use one unnamed argument:

	<code><nowiki>{{Harmonics in equal\|<~~EDO~~ number>}}</nowiki></code>		<code><nowiki>{{Harmonics in equal\|<edo number>}}</nowiki></code>

	For other divisions, you can use two or three unnamed arguments:		For other divisions, you can use two or three unnamed arguments:
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	; </code>columns</code>		; </code>columns</code>
	: Number of intervals to include. Default is 10.		: Number of intervals to include. Default is 11.

	; <code>start</code>		; <code>start</code>
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	{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2}}		{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2}}
	{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2\|prec=5\|title=Same with prec=5}}		{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2\|prec=5\|title=Same with prec=5}}

			=== See also ===
			* [[Template: Harmonics in cet]]

ArrowHead294 at 03:09, 16 February 2025

2025-02-16T03:09:22Z

← Older revision		Revision as of 03:09, 16 February 2025
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	{{dochead}}{{~~modlink~~}}		{{dochead}}{{lua}}
	This template generates a table with the approximations of harmonics for a given [[equal tuning]].		This template generates a table with the approximations of harmonics for a given [[equal tuning]].

ArrowHead294 at 14:56, 31 January 2025

2025-01-31T14:56:20Z

← Older revision		Revision as of 14:56, 31 January 2025
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	{{dochead}}		{{dochead}}{{modlink}}
	This template generates a table with the approximations of harmonics for a given [[equal tuning]].		This template generates a table with the approximations of harmonics for a given [[equal tuning]].

Line 89:		Line 89:
	{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2}}		{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2}}
	{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2\|prec=5\|title=Same with prec=5}}		{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2\|prec=5\|title=Same with prec=5}}

	~~=== See also ===~~
	* {{modlink}}

ArrowHead294 at 00:43, 26 January 2025

2025-01-26T00:43:29Z

← Older revision		Revision as of 00:43, 26 January 2025
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	{{dochead}}		{{dochead}}
	This template generates a table for ~~prime approximations in~~ [[equal tuning]]s.		This template generates a table with the approximations of harmonics for a given [[equal tuning]].

	=== Usage ===		=== Usage ===

FloraC: Undo revision 156729 by ArrowHead294 (talk). Readability

2024-09-28T08:30:39Z

Undo revision 156729 by ArrowHead294 (talk). Readability

← Older revision		Revision as of 08:30, 28 September 2024
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	For divisions of the octave ([[EDO]]s), you can use one unnamed argument:		For divisions of the octave ([[EDO]]s), you can use one unnamed argument:

	<code>{{Harmonics in equal~~<nowiki />~~\|<EDO number>}}</code>		<code><nowiki>{{Harmonics in equal\|<EDO number>}}</nowiki></code>

	For other divisions, you can use two or three unnamed arguments:		For other divisions, you can use two or three unnamed arguments:

	<code>{{Harmonics in equal~~<nowiki />~~\|<steps>\|<numerator>\|<denominator>}}</code>		<code><nowiki>{{Harmonics in equal\|<steps>\|<numerator>\|<denominator>}}</nowiki></code>

	By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed. Edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.		By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed. Edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.
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	For edos it is sufficient to only input the number of steps:		For edos it is sufficient to only input the number of steps:

	<code>{{Harmonics in equal~~<nowiki />~~\|31}}</code>		<code><nowiki>{{Harmonics in equal\|31}}</nowiki></code>
	{{{{ROOTPAGENAME}}\|31}}		{{{{ROOTPAGENAME}}\|31}}

	For tritave or other integer divisions, two arguments is enough:		For tritave or other integer divisions, two arguments is enough:</nowiki>

	<code>{{Harmonics in equal~~<nowiki />~~\|13\|3}}</code>		<code><nowiki>{{Harmonics in equal\|13\|3}}</nowiki></code>
	{{{{ROOTPAGENAME}}\|13\|3}}		{{{{ROOTPAGENAME}}\|13\|3}}

	In the most general case, we can input the number of steps, numerator and denominator.		In the most general case, we can input the number of steps, numerator and denominator.

	<code>{{Harmonics in equal~~<nowiki />~~\|15\|7\|3}}</code>		<code><nowiki>{{Harmonics in equal\|15\|7\|3}}</nowiki></code>
	{{{{ROOTPAGENAME}}\|15\|7\|3}}		{{{{ROOTPAGENAME}}\|15\|7\|3}}

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	Sometimes you want to see more or skip some lower columns and have to adjust the title:		Sometimes you want to see more or skip some lower columns and have to adjust the title:

	<code>{{Harmonics in equal~~<nowiki />~~\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}</code>		<code><nowiki>{{Harmonics in equal\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}</nowiki></code>
	{{{{ROOTPAGENAME}}\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}		{{{{ROOTPAGENAME}}\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}

ArrowHead294 at 00:49, 28 September 2024

2024-09-28T00:49:02Z

← Older revision		Revision as of 00:49, 28 September 2024
Line 6:		Line 6:
	For divisions of the octave ([[EDO]]s), you can use one unnamed argument:		For divisions of the octave ([[EDO]]s), you can use one unnamed argument:

	<code~~><nowiki~~>{{Harmonics in equal\|<EDO number>}}~~</nowiki>~~</code>		<code>{{Harmonics in equal<nowiki />\|<EDO number>}}</code>

	For other divisions, you can use two or three unnamed arguments:		For other divisions, you can use two or three unnamed arguments:

	<code~~><nowiki~~>{{Harmonics in equal\|<steps>\|<numerator>\|<denominator>}}~~</nowiki>~~</code>		<code>{{Harmonics in equal<nowiki />\|<steps>\|<numerator>\|<denominator>}}</code>

	By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed. Edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.		By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed. Edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.
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	For edos it is sufficient to only input the number of steps:		For edos it is sufficient to only input the number of steps:

	<code~~><nowiki~~>{{Harmonics in equal\|31}}~~</nowiki>~~</code>		<code>{{Harmonics in equal<nowiki />\|31}}</code>
	{{{{ROOTPAGENAME}}\|31}}		{{{{ROOTPAGENAME}}\|31}}

	For tritave or other integer divisions, two arguments is enough:~~</nowiki>~~		For tritave or other integer divisions, two arguments is enough:

	<code~~><nowiki~~>{{Harmonics in equal\|13\|3}}~~</nowiki>~~</code>		<code>{{Harmonics in equal<nowiki />\|13\|3}}</code>
	{{{{ROOTPAGENAME}}\|13\|3}}		{{{{ROOTPAGENAME}}\|13\|3}}

	In the most general case, we can input the number of steps, numerator and denominator.		In the most general case, we can input the number of steps, numerator and denominator.

	<code~~><nowiki~~>{{Harmonics in equal\|15\|7\|3}}~~</nowiki>~~</code>		<code>{{Harmonics in equal<nowiki />\|15\|7\|3}}</code>
	{{{{ROOTPAGENAME}}\|15\|7\|3}}		{{{{ROOTPAGENAME}}\|15\|7\|3}}

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	Sometimes you want to see more or skip some lower columns and have to adjust the title:		Sometimes you want to see more or skip some lower columns and have to adjust the title:

	<code~~><nowiki~~>{{Harmonics in equal\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}~~</nowiki>~~</code>		<code>{{Harmonics in equal<nowiki />\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}</code>
	{{{{ROOTPAGENAME}}\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}		{{{{ROOTPAGENAME}}\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}

ArrowHead294: Per Ganaram inukshuk

2024-09-14T20:08:15Z

Per Ganaram inukshuk

← Older revision		Revision as of 20:08, 14 September 2024
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	For divisions of the octave ([[EDO]]s), you can use one unnamed argument:		For divisions of the octave ([[EDO]]s), you can use one unnamed argument:

	<code>{{~~((}}~~Harmonics in equal~~{{!}}{{^(}}~~EDO number~~{{)^}}{{))~~}}</code>		<code><nowiki>{{Harmonics in equal\|<EDO number>}}</nowiki></code>

	For other divisions, you can use two or three unnamed arguments:		For other divisions, you can use two or three unnamed arguments:

	<code>{{~~((}}~~Harmonics in equal~~{{!}}{{^(}}~~steps~~{{)^}}{{!}}{{^(}}~~numerator~~{{)^}}{{!}}{{^(}}~~denominator~~{{)^}}{{))~~}}</code>		<code><nowiki>{{Harmonics in equal\|<steps>\|<numerator>\|<denominator>}}</nowiki></code>

	By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed. Edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.		By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed. Edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.
Line 62:		Line 62:
	For edos it is sufficient to only input the number of steps:		For edos it is sufficient to only input the number of steps:

	<code>{{~~((}}~~Harmonics in equal~~{{!}}~~31~~{{))~~}}</code>		<code><nowiki>{{Harmonics in equal\|31}}</nowiki></code>
	{{{{ROOTPAGENAME}}\|31}}		{{{{ROOTPAGENAME}}\|31}}

	For tritave or other integer divisions, two arguments is enough:		For tritave or other integer divisions, two arguments is enough:</nowiki>
	<code>{{~~((}}~~Harmonics in equal~~{{!}}~~13~~{{!}}~~3~~{{))~~}}</code>
			<code><nowiki>{{Harmonics in equal\|13\|3}}</nowiki></code>
	{{{{ROOTPAGENAME}}\|13\|3}}		{{{{ROOTPAGENAME}}\|13\|3}}

	In the most general case, we can input the number of steps, numerator and denominator.		In the most general case, we can input the number of steps, numerator and denominator.
	<code>{{~~((}}~~Harmonics in equal~~{{!}}~~15~~{{!}}~~7~~{{!}}~~3~~{{))~~}}</code>
			<code><nowiki>{{Harmonics in equal\|15\|7\|3}}</nowiki></code>
	{{{{ROOTPAGENAME}}\|15\|7\|3}}		{{{{ROOTPAGENAME}}\|15\|7\|3}}

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	Sometimes you want to see more or skip some lower columns and have to adjust the title:		Sometimes you want to see more or skip some lower columns and have to adjust the title:

	<code>{{~~((}}~~Harmonics in equal~~{{!}}~~13~~{{!}}~~3~~{{!}}~~columns{{=}}11~~{{!}}~~start{{=}}2~~{{!}}~~title{{=}}Primes in ~~{{!((}}<nowiki />~~13edt~~{{))!}}{{!}}~~intervals{{=}}prime~~{{))~~}}</code>		<code><nowiki>{{Harmonics in equal\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}</nowiki></code>
	{{{{ROOTPAGENAME}}\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}		{{{{ROOTPAGENAME}}\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}

ArrowHead294 at 14:55, 6 September 2024

2024-09-06T14:55:27Z

← Older revision		Revision as of 14:55, 6 September 2024
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	=== Usage ===		=== Usage ===
	==== Simple ====		==== Simple ====
	For divisions of the octave ([[~~edo~~]]), you can use one unnamed argument:		For divisions of the octave ([[EDO]]s), you can use one unnamed argument:

	<~~syntaxhighlight lang="text"~~>		<code>{{((}}Harmonics in equal{{!}}{{^(}}EDO number{{)^}}{{))}}</code>
	{{Harmonics in equal\|<EDO number>}}
	</~~syntaxhighlight~~>

	For other divisions, you can use two or three unnamed arguments:		For other divisions, you can use two or three unnamed arguments:

	<~~syntaxhighlight lang="text"~~>		<code>{{((}}Harmonics in equal{{!}}{{^(}}steps{{)^}}{{!}}{{^(}}numerator{{)^}}{{!}}{{^(}}denominator{{)^}}{{))}}</code>
	{{Harmonics in equal\|<steps~~>\|<~~numerator~~>\|<~~denominator>}}
	</~~syntaxhighlight~~>

	By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed. Edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.		By default, the titles for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed. Edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.
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	The template takes up to 9 arguments:		The template takes up to 9 arguments:

	<~~syntaxhighlight lang="text"~~>		<pre>
	{{Harmonics in equal		{{Harmonics in equal
	\| steps = <number of steps>		\| steps = <number of steps>
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	\| collapsed = <anything>		\| collapsed = <anything>
	}}		}}
	</~~syntaxhighlight~~>		</pre>

	; <code>steps</code>		; <code>steps</code>
	: Number of steps. This parameter can also be given without the parameter name. Default: 12.		: Number of steps. This parameter can also be given without the parameter name. Default is 12.

	; <code>num</code>		; <code>num</code>
	: Numerator of the interval that is divided equally. Can be used without parameter name. Default: 2.		: Numerator of the interval that is divided equally. Can be used without parameter name. Default is 2.

	; <code>denom</code>		; <code>denom</code>
	: Denominator of the interval that is divided equally. Can be used without parameter name. Default: 1.		: Denominator of the interval that is divided equally. Can be used without parameter name. Default is 1.

	; </code>columns</code>		; </code>columns</code>
	: Number of intervals to include. Default: 10.		: Number of intervals to include. Default is 10.

	; <code>start</code>		; <code>start</code>
	: Default is 1 (which means the prime 2), set to 2 to skip the octave.		: Default is 1 (which means the prime 2), set to 2 to skip the octave.

	; <code>prec</code>		; <code>prec</code>
	: Precision of absolute error (digits after the decimal point), default is estimated according to the step size.		: Precision of absolute error (digits after the decimal point), default is estimated according to the step size.

	; <code>title</code>		; <code>title</code>
	: Default is: "Approximations of harmonics in ''name''". By default, the names for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed.		: Default is: "Approximations of harmonics in ''name''". By default, the names for divisions of 2/1, 3/1 and 3/2 will be displayed as 'edo', 'edt' and 'edf' respectively. When the denominator is 1, it will not be displayed.

	; <code>intervals</code>		; <code>intervals</code>
	: Can be <code>prime</code> for primes, <code>odd</code> for odd harmonics and <code>integer</code> for integer harmonics. By default, edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.		: Can be <code>prime</code> for primes, <code>odd</code> for odd harmonics and <code>integer</code> for integer harmonics. By default, edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds. Everything that is not an edo gets integers.

	; <code>collapsed</code>		; <code>collapsed</code>
	: Anything here to collapse the table.		: Anything here to collapse the table.
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	For edos it is sufficient to only input the number of steps:		For edos it is sufficient to only input the number of steps:

	<~~syntaxhighlight lang="text"~~>		<code>{{((}}Harmonics in equal{{!}}31{{))}}</code>
	{{Harmonics in equal\|31}}		{{{{ROOTPAGENAME}}\|31}}
	</~~syntaxhighlight~~>
	{{~~Harmonics in equal~~\|31}}

	For tritave or other integer divisions, two arguments is enough:		For tritave or other integer divisions, two arguments is enough:
	<~~syntaxhighlight lang="text"~~>		<code>{{((}}Harmonics in equal{{!}}13{{!}}3{{))}}</code>
	{{Harmonics in equal\|13\|3}}		{{{{ROOTPAGENAME}}\|13\|3}}
	</~~syntaxhighlight~~>
	{{~~Harmonics in equal~~\|13\|3}}

	In the most general case, we can input the number of steps, numerator and denominator.		In the most general case, we can input the number of steps, numerator and denominator.
			<code>{{((}}Harmonics in equal{{!}}15{{!}}7{{!}}3{{))}}</code>
	<~~syntaxhighlight lang="text"~~>		{{{{ROOTPAGENAME}}\|15\|7\|3}}
	{{Harmonics in equal\|15\|7\|3}}
	</~~syntaxhighlight~~>
	{{~~Harmonics in equal~~\|15\|7\|3}}

	==== Advanced ====		==== Advanced ====
	Sometimes you want to see more or skip some lower columns and have to adjust the title:		Sometimes you want to see more or skip some lower columns and have to adjust the title:

	<~~syntaxhighlight lang="text"~~>		<code>{{((}}Harmonics in equal{{!}}13{{!}}3{{!}}columns{{=}}11{{!}}start{{=}}2{{!}}title{{=}}Primes in {{!((}}<nowiki />13edt{{))!}}{{!}}intervals{{=}}prime{{))}}</code>
	{{Harmonics in equal\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt~~]]\|~~intervals=prime}}		{{{{ROOTPAGENAME}}\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}
	</~~syntaxhighlight~~>
	{{~~Harmonics in equal~~\|13\|3\|columns=11\|start=2\|title=Primes in [[13edt]]\|intervals=prime}}

	For large divisions ([[313edo]] in this example) the absolute error gets very small. The default precision gets calculated automatically, but if we want to increase it even further, we can set <code>prec</code> to a higher value. This is not recommended generally.		For large divisions ([[313edo]] in this example) the absolute error gets very small. The default precision gets calculated automatically, but if we want to increase it even further, we can set <code>prec</code> to a higher value. This is not recommended generally.

	<~~syntaxhighlight lang="text">~~		<pre>
	~~{{Harmonics in equal\|313\|columns=9\|start=2}}~~
	~~{{Harmonics in equal\|313\|columns=9\|start=2\|prec=5\|title=Same with prec=5}}~~
	~~</syntaxhighlight~~>
	{{Harmonics in equal\|313\|columns=9\|start=2}}		{{Harmonics in equal\|313\|columns=9\|start=2}}
	{{Harmonics in equal\|313\|columns=9\|start=2\|prec=5\|title=Same with prec=5}}		{{Harmonics in equal\|313\|columns=9\|start=2\|prec=5\|title=Same with prec=5}}
			</pre>
			{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2}}
			{{{{ROOTPAGENAME}}\|313\|columns=9\|start=2\|prec=5\|title=Same with prec=5}}

	=== See also ===		=== See also ===
	* {{modlink}}		* {{modlink}}