Xenharmonic series - Revision history

BudjarnLambeth: {{Navbox scale gallery}}

2025-09-28T03:06:32Z

← Older revision		Revision as of 03:06, 28 September 2025
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	* [[:Category:Xenharmonic series]]: Some more types may be documented there.		* [[:Category:Xenharmonic series]]: Some more types may be documented there.

			{{Navbox scale gallery}}
	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

BudjarnLambeth: See also

2024-11-17T12:28:06Z

BudjarnLambeth: Make links make more intuitive sense

2024-11-17T12:26:49Z

Make links make more intuitive sense

← Older revision		Revision as of 12:26, 17 November 2024
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	* [[Prime harmonic series]]: <math>f(n) = p_n</math>, where <math>p</math> is prime		* [[Prime harmonic series]]: <math>f(n) = p_n</math>, where <math>p</math> is prime
	* [[Subharmonic series]]: <math>f(n) = \frac{1}{n}</math>		* [[Subharmonic series]]: <math>f(n) = \frac{1}{n}</math>
	* [[Subparticular~~\|Subparticular series~~]]: <math>f(n) = \frac{n}{n+1}</math>		* [[Subparticular]] series: <math>f(n) = \frac{n}{n+1}</math>
	* [[Superparticular~~\|Superparticular series~~]]: <math>f(n) = \frac{n+1}{n}</math>		* [[Superparticular]] series: <math>f(n) = \frac{n+1}{n}</math>
	* [[Triangulharmonic series]]: <math>f(n) = \frac{n^2 + n}{2}</math>		* [[Triangulharmonic series]]: <math>f(n) = \frac{n^2 + n}{2}</math>
	* [[US\|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational		* [[US\|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational

Cmloegcmluin at 01:36, 12 September 2024

2024-09-12T01:36:24Z

BudjarnLambeth: Added isoharmonic series as suggested by Mike in the discussion page

2023-04-26T05:14:17Z

Added isoharmonic series as suggested by Mike in the discussion page

← Older revision		Revision as of 05:14, 26 April 2023
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	* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math>		* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math>
	* [[Edharmonic series]]: <math>f(n) = a^{H(n)}</math>		* [[Edharmonic series]]: <math>f(n) = a^{H(n)}</math>
			* [[Isoharmonic chord\|Isoharmonic series]]
	* [[Logharmonic series]]: <math>f(n) = \log_b{n}</math>		* [[Logharmonic series]]: <math>f(n) = \log_b{n}</math>
	* [[Matharmonic series]]: <math>f(n) = H(n)</math>		* [[Matharmonic series]]: <math>f(n) = H(n)</math>

Fredg999 category edits: Removing from Category:Overview using Cat-a-lot

2023-03-06T22:14:11Z

Removing from Category:Overview using Cat-a-lot

← Older revision		Revision as of 22:14, 6 March 2023
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	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	~~[[Category:Overview]]~~

Cmloegcmluin: fix formatting

2022-05-17T23:58:35Z

fix formatting

← Older revision		Revision as of 23:58, 17 May 2022
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	* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math>		* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math>
	* [[Edharmonic series]]: <math>f(n) = a^{H(n)}</math>		* [[Edharmonic series]]: <math>f(n) = a^{H(n)}</math>
	* [[Logharmonic series]]: <math>f(n) = log_b{n}</math>		* [[Logharmonic series]]: <math>f(n) = \log_b{n}</math>
	* [[Matharmonic series]]: <math>f(n) = H(n)</math>		* [[Matharmonic series]]: <math>f(n) = H(n)</math>
	* [[Metallic harmonic series]]: <math>f(n) = μ_n</math>		* [[Metallic harmonic series]]: <math>f(n) = μ_n</math>

Fredg999: Added a few more examples, fixed full name of OS, markup, sorted list in alphabetical order, categories

2021-08-29T03:24:45Z

Added a few more examples, fixed full name of OS, markup, sorted list in alphabetical order, categories

← Older revision		Revision as of 03:24, 29 August 2021
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	~~Here~~'~~s a place to gather~~ xenharmonic variations on the [[harmonic series]].		This is a list of '''xenharmonic series''', i.e. xenharmonic variations on the [[harmonic series]].

	* [[~~Powharmonic series~~]]: <~~span~~><math>f(n) = n^p</math></~~span~~>		* [[AS\|Ambitonal sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is rational
	* [[Edharmonic series]]: ~~<span>~~<math>f(n) = a^{H(n)}</math~~></span~~>		* [[AFS\|Arithmetic frequency sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is irrational
	* [[Logharmonic series]]: ~~<span>~~<math>f(n) = log_b{n}</math~~></span~~>		* [[ALS\|Arithmetic length sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is irrational
	* [[Matharmonic series]]: ~~<span>~~<math>f(n) = H(n)</math~~></span~~>		* [[APS\|Arithmetic pitch sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is irrational
	* [[Metallic harmonic series]]: ~~<span>~~<math>f(n) = μ_n</math~~></span~~>		* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math>
	* [[~~Superparticular~~ series]]: ~~<span>~~<math>f(n) = ~~\frac{n+~~1~~}{n}~~</math~~></span~~>		* [[Edharmonic series]]: <math>f(n) = a^{H(n)}</math>
	* [[~~Subparticular series~~]]: ~~<span>~~<math>f(n) = ~~\frac{n}{n~~+1}</math></~~span~~>		* [[Logharmonic series]]: <math>f(n) = log_b{n}</math>
	* [[~~Oddharmonic~~ series]]: ~~<span>~~<math>f(n) = ~~2n-1~~</math~~></span~~>		* [[Matharmonic series]]: <math>f(n) = H(n)</math>
	* [[Prime harmonic series]]: ~~<span>~~<math>f(n) = p_n</math></~~span~~>		* [[Metallic harmonic series]]: <math>f(n) = μ_n</math>
	* [[~~Triangulharmonic~~ series]]: ~~<span>~~<math>f(n) = \frac{~~n^2 +~~ n}{2}</math~~></span~~>		* [[Oddharmonic series]]: <math>f(n) = 2n-1</math>
	* [[~~Dumb Fibonacci\|Dumb Fibonacci~~ series]]: ~~<span>~~<math>f(n) = f(n-1~~) + f(~~n~~-2)~~</math~~></span~~>		* [[OS\|Otonal sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is rational
	* [[~~OS\|Overtone Sequences~~]]: ~~<span>~~<math>f(n) = 1 + cn</math>~~</span>, where c is rational~~		* [[Powharmonic series]]: <math>f(n) = n^p</math>
	* [[~~AFS~~\|~~Arithmetic Frequency Sequences~~]]: ~~<span>~~<math>f(n) = 1 + cn</math></~~span~~>~~, where c~~ is ~~irrational~~		* [[Prime harmonic series]]: <math>f(n) = p_n</math>
			* [[Subharmonic series]]: <math>f(n) = \frac{1}{n}</math>
			* [[Subparticular series]]: <math>f(n) = \frac{n}{n+1}</math>
			* [[Superparticular series]]: <math>f(n) = \frac{n+1}{n}</math>
			* [[Triangulharmonic series]]: <math>f(n) = \frac{n^2 + n}{2}</math>
			* [[US\|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational

			[[Category:Harmonic series‏‎]]
			[[Category:Lists of scales]]
	[[Category:Overview]]		[[Category:Overview]]
	~~[[Category:Overtone]]~~
	~~[[Category:Overtone‏‎ series]]~~
	~~[[Category:Otonality]]~~
	~~[[Category:Harmonic]]~~
	~~[[Category:Harmonic series‏‎]]~~

Fredg999: Added link to Harmonic series

2021-08-29T02:36:44Z

Added link to Harmonic series

← Older revision		Revision as of 02:36, 29 August 2021
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	Here's a place to gather xenharmonic variations on the harmonic series.		Here's a place to gather xenharmonic variations on the [[harmonic series]].

	* [[Powharmonic series]]: <span><math>f(n) = n^p</math></span>		* [[Powharmonic series]]: <span><math>f(n) = n^p</math></span>

Cmloegcmluin at 22:05, 22 March 2021

2021-03-22T22:05:45Z

← Older revision		Revision as of 22:05, 22 March 2021
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	* [[Triangulharmonic series]]: <span><math>f(n) = \frac{n^2 + n}{2}</math></span>		* [[Triangulharmonic series]]: <span><math>f(n) = \frac{n^2 + n}{2}</math></span>
	* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <span><math>f(n) = f(n-1) + f(n-2)</math></span>		* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <span><math>f(n) = f(n-1) + f(n-2)</math></span>
			* [[OS\|Overtone Sequences]]: <span><math>f(n) = 1 + cn</math></span>, where c is rational
			* [[AFS\|Arithmetic Frequency Sequences]]: <span><math>f(n) = 1 + cn</math></span>, where c is irrational

	[[Category:Overview]]		[[Category:Overview]]
			[[Category:Overtone]]
	~~See also~~: [[~~Arithmetic tunings~~]].		[[Category:Overtone‏‎ series]]
			[[Category:Otonality]]
			[[Category:Harmonic]]
			[[Category:Harmonic series‏‎]]

← Older revision		Revision as of 12:28, 17 November 2024
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	* [[Triangulharmonic series]]: <math>f(n) = \frac{n^2 + n}{2}</math>		* [[Triangulharmonic series]]: <math>f(n) = \frac{n^2 + n}{2}</math>
	* [[US\|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational		* [[US\|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational

			== See also ==
			* [[:Category:Xenharmonic series]]: Some more types may be documented there.

	[[Category:Harmonic series‏‎]]		[[Category:Harmonic series‏‎]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

← Older revision		Revision as of 01:36, 12 September 2024
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	This is a list of '''xenharmonic series''', i.e. xenharmonic variations on the [[harmonic series]].		This is a list of '''xenharmonic series''', i.e. xenharmonic variations on the [[harmonic series]], <math>f(n) = n</math>, where <math>n</math> is an integer (as it is in all formulas below).

	* [[AS\|Ambitonal sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is rational		* [[AS\|Ambitonal sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is rational
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	* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math>		* [[Dumb Fibonacci\|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math>
	* [[Edharmonic series]]: <math>f(n) = a^{H(n)}</math>		* [[Edharmonic series]]: <math>f(n) = a^{H(n)}</math>
	* [[~~Isoharmonic chord\|~~Isoharmonic series]]		* [[Isoharmonic series]]: <math>f(n) = c + n</math> where <math>c</math> is rational
	* [[Logharmonic series]]: <math>f(n) = \log_b{n}</math>		* [[Logharmonic series]]: <math>f(n) = \log_b{n}</math>
	* [[Matharmonic series]]: <math>f(n) = H(n)</math>		* [[Matharmonic series]]: <math>f(n) = H(n)</math>
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	* [[OS\|Otonal sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is rational		* [[OS\|Otonal sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is rational
	* [[Powharmonic series]]: <math>f(n) = n^p</math>		* [[Powharmonic series]]: <math>f(n) = n^p</math>
	* [[Prime harmonic series]]: <math>f(n) = p_n</math>		* [[Prime harmonic series]]: <math>f(n) = p_n</math>, where <math>p</math> is prime
	* [[Subharmonic series]]: <math>f(n) = \frac{1}{n}</math>		* [[Subharmonic series]]: <math>f(n) = \frac{1}{n}</math>
	* [[Subparticular series]]: <math>f(n) = \frac{n}{n+1}</math>		* [[Subparticular\|Subparticular series]]: <math>f(n) = \frac{n}{n+1}</math>
	* [[Superparticular series]]: <math>f(n) = \frac{n+1}{n}</math>		* [[Superparticular\|Superparticular series]]: <math>f(n) = \frac{n+1}{n}</math>
	* [[Triangulharmonic series]]: <math>f(n) = \frac{n^2 + n}{2}</math>		* [[Triangulharmonic series]]: <math>f(n) = \frac{n^2 + n}{2}</math>
	* [[US\|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational		* [[US\|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational