Xenharmonic series: Difference between revisions
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This is a list of '''xenharmonic series''', i.e. xenharmonic variations on the [[harmonic series]]. | |||
* [[ | * [[AS|Ambitonal sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is rational | ||
* [[Edharmonic series]]: | * [[AFS|Arithmetic frequency sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is irrational | ||
* [[Logharmonic series]]: | * [[ALS|Arithmetic length sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is irrational | ||
* [[Matharmonic series]]: | * [[APS|Arithmetic pitch sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is irrational | ||
* [[Metallic harmonic series]]: | * [[Dumb Fibonacci|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math> | ||
* [[ | * [[Edharmonic series]]: <math>f(n) = a^{H(n)}</math> | ||
* [[ | * [[Logharmonic series]]: <math>f(n) = log_b{n}</math> | ||
* [[ | * [[Matharmonic series]]: <math>f(n) = H(n)</math> | ||
* [[Prime harmonic series]]: | * [[Metallic harmonic series]]: <math>f(n) = μ_n</math> | ||
* [[ | * [[Oddharmonic series]]: <math>f(n) = 2n-1</math> | ||
* [[ | * [[OS|Otonal sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is rational | ||
* [[ | * [[Powharmonic series]]: <math>f(n) = n^p</math> | ||
* [[ | * [[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]] | ||
Revision as of 03:24, 29 August 2021
This is a list of xenharmonic series, i.e. xenharmonic variations on the harmonic series.
- Ambitonal sequences: [math]\displaystyle{ f(n) = p^n }[/math], where [math]\displaystyle{ p }[/math] is rational
- Arithmetic frequency sequences: [math]\displaystyle{ f(n) = 1 + cn }[/math], where [math]\displaystyle{ c }[/math] is irrational
- Arithmetic length sequences: [math]\displaystyle{ f(n) = \frac{1}{1 + cn} }[/math], where [math]\displaystyle{ c }[/math] is irrational
- Arithmetic pitch sequences: [math]\displaystyle{ f(n) = p^n }[/math], where [math]\displaystyle{ p }[/math] is irrational
- Dumb Fibonacci series: [math]\displaystyle{ f(n) = f(n-1) + f(n-2) }[/math]
- Edharmonic series: [math]\displaystyle{ f(n) = a^{H(n)} }[/math]
- Logharmonic series: [math]\displaystyle{ f(n) = log_b{n} }[/math]
- Matharmonic series: [math]\displaystyle{ f(n) = H(n) }[/math]
- Metallic harmonic series: [math]\displaystyle{ f(n) = μ_n }[/math]
- Oddharmonic series: [math]\displaystyle{ f(n) = 2n-1 }[/math]
- Otonal sequences: [math]\displaystyle{ f(n) = 1 + cn }[/math], where [math]\displaystyle{ c }[/math] is rational
- Powharmonic series: [math]\displaystyle{ f(n) = n^p }[/math]
- Prime harmonic series: [math]\displaystyle{ f(n) = p_n }[/math]
- Subharmonic series: [math]\displaystyle{ f(n) = \frac{1}{n} }[/math]
- Subparticular series: [math]\displaystyle{ f(n) = \frac{n}{n+1} }[/math]
- Superparticular series: [math]\displaystyle{ f(n) = \frac{n+1}{n} }[/math]
- Triangulharmonic series: [math]\displaystyle{ f(n) = \frac{n^2 + n}{2} }[/math]
- Utonal sequences: [math]\displaystyle{ f(n) = \frac{1}{1 + cn} }[/math], where [math]\displaystyle{ c }[/math] is rational