Template:ZPI/doc - Revision history

ArrowHead294 at 19:36, 20 May 2025

2025-05-20T19:36:44Z

← Older revision		Revision as of 19:36, 20 May 2025
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	{{Dochead}}		{{Dochead}}{{substitute\|no}}
	This template generates a table for a particular edo's [[zeta peak index]].		This template generates a table for a particular edo's [[zeta peak index]].

FloraC: Cleanup

2025-04-21T10:47:54Z

Cleanup

← Older revision		Revision as of 10:47, 21 April 2025
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	{{~~dochead~~}}		{{Dochead}}
	This template generates a table for a particular ~~EDO~~'s [[zeta peak index]].		This template generates a table for a particular edo's [[zeta peak index]].

	=== Parameters ===		=== Parameters ===
	All parameters are required.		All parameters are required.

	; <code>{{{~~<nowiki />~~steps}}}</code>		; <code><nowiki>{{{steps}}}</nowiki></code>
	: The zeta-optimised number of steps per octave, corresponding to the location of a particular ~~EDO~~'s nearest local maximum or minimum according to the {{w\|Z function\|Riemann–Siegel ''Z'' function}}, ~~<math>~~Z\left(\frac{2\pi}{\ln 2}\,x\right)~~</math>.~~		: The zeta-optimised number of steps per octave, corresponding to the location of a particular edo's nearest local maximum or minimum according to the {{w\|Z function\|Riemann–Siegel ''Z'' function}},

			$$ Z\left( \frac{2\pi}{\ln 2} \, x \right) $$

	: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.		: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.

	; <code>{{{~~<nowiki />~~step size}}}</code>		; <code><nowiki>{{{step size}}}</nowiki></code>
	: The step size in [[cent]]s, which is 1200 divided by the aformentioned zeta-optimised step count.		: The step size in [[cent]]s, which is 1200 divided by the aformentioned zeta-optimised step count.

	For the height of the zeta peak, you can use <code>tempered~~ ~~height</code> and <code>pure~~ ~~height</code> or just <code>height</code>.		For the height of the zeta peak, you can use <code>tempered height</code> and <code>pure height</code> or just <code>height</code>.

	; <code>{{{~~<nowiki />~~tempered height}}}</code>		; <code><nowiki>{{{tempered height}}}</nowiki></code>
	: The absolute value of ''Z'' evaluated at the zeta-optimised step count. For [[12edo]], this value is 5.193290 when evaluated at 12.0231830072926.		: The absolute value of ''Z'' evaluated at the zeta-optimised step count. For [[12edo]], this value is 5.193290 when evaluated at 12.0231830072926.
	: Must be used in conjunction with <code>pure~~ ~~height</code>, do not use with <code>height</code>.		: Must be used in conjunction with <code>pure height</code>, do not use with <code>height</code>.

	; <code>{{{~~<nowiki />~~pure height}}}</code>		; <code><nowiki>{{{pure height}}}</nowiki></code>
	: The absolute value of ''Z'' evaluated at the exact integer. For [[12edo]], this value is 5.084467 when evaluated at exactly 12.		: The absolute value of ''Z'' evaluated at the exact integer. For [[12edo]], this value is 5.084467 when evaluated at exactly 12.
	: Must be used in conjunction with <code>tempered~~ ~~height</code>, do not use with <code>height</code>.		: Must be used in conjunction with <code>tempered height</code>, do not use with <code>height</code>.

	; <code>{{{~~<nowiki />~~height}}}</code>		; <code><nowiki>{{{height}}}</nowiki></code>
	: The absolute value of ''Z'' evaluated at a ZPI that does not correspond strongly to an ~~EDO~~. Do not use with <code>tempered~~ ~~height</code> or <code>pure~~ ~~height</code>.		: The absolute value of ''Z'' evaluated at a ZPI that does not correspond strongly to an edo. Do not use with <code>tempered height</code> or <code>pure height</code>.

	; <code>{{{~~<nowiki />~~integral}}}</code>		; <code><nowiki>{{{integral}}}</nowiki></code>
	: The absolute value of the integral between the two roots (zeroes) of ''Z'' closest to the given ~~EDO~~. For 12edo, this value is 1.269599.		: The absolute value of the integral between the two roots (zeroes) of ''Z'' closest to the given edo. For 12edo, this value is 1.269599.

	; <code>{{{~~<nowiki />~~gap}}}</code>		; <code><nowiki>{{{gap}}}</nowiki></code>


	; <code>{{{~~<nowiki />~~edo}}}</code> (optional)		; <code><nowiki>{{{edo}}}</nowiki></code> (optional)
	: This parameter is optional. Pass in the ~~EDO~~ that the ZPI represents if the page's title does not contain it.		: This parameter is optional. Pass in the edo that the ZPI represents if the page's title does not contain it.

	; <code>{{{~~<nowiki />~~octave}}}</code>		; <code><nowiki>{{{octave}}}</nowiki></code>
	: The zeta-optimised octave size. For 12edo, this is 1197.68616940005.		: The zeta-optimised octave size. For 12edo, this is 1197.68616940005.

	; <code>{{{~~<nowiki />~~consistent}}}</code>		; <code><nowiki>{{{consistent}}}</nowiki></code>
	: The ZPI's [[consistency]] limit.		: The ZPI's [[consistency]] limit.

	; <code>{{{~~<nowiki />~~distinct}}}</code>		; <code><nowiki>{{{distinct}}}</nowiki></code>
	: The ZPI's ''distinct'' consistency limit.		: The ZPI's ''distinct'' consistency limit.

	=== Example (12edo) ===		=== Example (12edo) ===
	Here is the complete zeta peak index table for [[12edo]] [[12edo#~~Zeta_peak_index~~\|as it appears on the page]]:		Here is the complete zeta peak index table for [[12edo]] [[12edo #Zeta peak index\|as it appears on the page]]:

	<pre>		<pre>

ArrowHead294 at 11:24, 10 April 2025

2025-04-10T11:24:46Z

← Older revision		Revision as of 11:24, 10 April 2025
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	; <code>{{{<nowiki />steps}}}</code>		; <code>{{{<nowiki />steps}}}</code>
	: The zeta-optimised number of steps per octave, corresponding to the location of a particular EDO's nearest local maximum or minimum according to the {{w\|Z function\|Riemann–Siegel ''Z'' function}}, ''Z''({{~~frac\|2π\|~~ln(2)}}''x'').		: The zeta-optimised number of steps per octave, corresponding to the location of a particular EDO's nearest local maximum or minimum according to the {{w\|Z function\|Riemann–Siegel ''Z'' function}}, <math>Z\left(\frac{2\pi}{\ln 2}\,x\right)</math>.
	: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.		: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.

ArrowHead294 at 00:54, 31 March 2025

2025-03-31T00:54:48Z

← Older revision		Revision as of 00:54, 31 March 2025
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	\| integral = 1.269599		\| integral = 1.269599
	\| gap = 15.899282		\| gap = 15.899282
	~~\| edo = 12edo~~
	\| octave = 1197.68616940005		\| octave = 1197.68616940005
	\| consistent = 10		\| consistent = 10
	\| distinct = 6		\| distinct = 6
	}}		}}

ArrowHead294 at 00:11, 27 March 2025

2025-03-27T00:11:43Z

← Older revision		Revision as of 00:11, 27 March 2025
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	; <code>{{{<nowiki />steps}}}</code>		; <code>{{{<nowiki />steps}}}</code>
	: The zeta-optimised number of steps per octave, corresponding to the location of a particular EDO's nearest local maximum or minimum according to the {{w\|Z function\|Riemann–Siegel ''Z'' function}}, ~~<math>~~Z~~\left~~(~~\frac~~{~~2\pi}~~{\ln 2}x~~\right~~)~~</math>~~.		: The zeta-optimised number of steps per octave, corresponding to the location of a particular EDO's nearest local maximum or minimum according to the {{w\|Z function\|Riemann–Siegel ''Z'' function}}, ''Z''({{frac\|2π\|ln(2)}}''x'').
	: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.		: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.

ArrowHead294: /* Example (12edo) */

2025-03-26T20:35:53Z

Example (12edo)

← Older revision		Revision as of 20:35, 26 March 2025
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	=== Example (12edo) ===		=== Example (12edo) ===
	Here is the complete zeta peak index table for [[12edo]] [[12edo\|#Zeta_peak_index\|as it appears on the page]]:		Here is the complete zeta peak index table for [[12edo]] [[12edo#Zeta_peak_index\|as it appears on the page]]:

	<pre>		<pre>

ArrowHead294: /* Example (12edo) */

2025-03-26T20:35:46Z

Example (12edo)

← Older revision		Revision as of 20:35, 26 March 2025
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	=== Example (12edo) ===		=== Example (12edo) ===
	Here is the complete zeta peak index table for [[12edo]] as it appears on the page:		Here is the complete zeta peak index table for [[12edo]] [[12edo\|#Zeta_peak_index\|as it appears on the page]]:

	<pre>		<pre>

ArrowHead294 at 20:35, 26 March 2025

2025-03-26T20:35:11Z

← Older revision		Revision as of 20:35, 26 March 2025
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	; <code>{{{edo}}}</code>		; <code>{{{<nowiki />edo}}}</code> (optional)
			: This parameter is optional. Pass in the EDO that the ZPI represents if the page's title does not contain it.

	; <code>{{{<nowiki />octave}}}</code>		; <code>{{{<nowiki />octave}}}</code>

ArrowHead294 at 15:43, 20 March 2025

2025-03-20T15:43:28Z

← Older revision		Revision as of 15:43, 20 March 2025
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	; <code>{{{<nowiki />steps}}}</code>		; <code>{{{<nowiki />steps}}}</code>
	: The zeta-optimised number of steps per octave, corresponding to the location of a particular EDO's nearest local maximum or minimum according to the {{w\|Z function\|Riemann–Siegel ''Z'' function}}, <math>Z\left(\frac{2\pi}{\ln 2}x\right)</math>. For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.		: The zeta-optimised number of steps per octave, corresponding to the location of a particular EDO's nearest local maximum or minimum according to the {{w\|Z function\|Riemann–Siegel ''Z'' function}}, <math>Z\left(\frac{2\pi}{\ln 2}x\right)</math>.
			: For example, [[12edo]]'s local zeta-optimised step count is 12.0231830072926.

	; <code>{{{<nowiki />step size}}}</code>		; <code>{{{<nowiki />step size}}}</code>

ArrowHead294 at 15:43, 20 March 2025

2025-03-20T15:43:16Z

← Older revision		Revision as of 15:43, 20 March 2025
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	; <code>{{{<nowiki />step size}}}</code>		; <code>{{{<nowiki />step size}}}</code>
	: The step size in [[cent]]s, which is 1200 divided by the aformentioned zeta-optimised step count.		: The step size in [[cent]]s, which is 1200 divided by the aformentioned zeta-optimised step count.

			For the height of the zeta peak, you can use <code>tempered height</code> and <code>pure height</code> or just <code>height</code>.

	; <code>{{{<nowiki />tempered height}}}</code>		; <code>{{{<nowiki />tempered height}}}</code>
	: The absolute value of ''Z'' evaluated at the zeta-optimised step count. For [[12edo]], this value is 5.193290 when evaluated at 12.0231830072926.		: The absolute value of ''Z'' evaluated at the zeta-optimised step count. For [[12edo]], this value is 5.193290 when evaluated at 12.0231830072926.
			: Must be used in conjunction with <code>pure height</code>, do not use with <code>height</code>.

	; <code>{{{<nowiki />pure height}}}</code>		; <code>{{{<nowiki />pure height}}}</code>
	: The absolute value of ''Z'' evaluated at the exact integer. For [[12edo]], this value is 5.084467 when evaluated at exactly 12.		: The absolute value of ''Z'' evaluated at the exact integer. For [[12edo]], this value is 5.084467 when evaluated at exactly 12.
			: Must be used in conjunction with <code>tempered height</code>, do not use with <code>height</code>.

			; <code>{{{<nowiki />height}}}</code>
			: The absolute value of ''Z'' evaluated at a ZPI that does not correspond strongly to an EDO. Do not use with <code>tempered height</code> or <code>pure height</code>.

	; <code>{{{<nowiki />integral}}}</code>		; <code>{{{<nowiki />integral}}}</code>