Xenharmonic series: Difference between revisions
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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 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 | * [[Subparticular]] series: <math>f(n) = \frac{n}{n+1}</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 | ||
== See also == | |||
* [[: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]] | ||
Latest revision as of 03:06, 28 September 2025
This is a list of xenharmonic series, i.e. xenharmonic variations on the harmonic series, [math]\displaystyle{ f(n) = n }[/math], where [math]\displaystyle{ n }[/math] is an integer (as it is in all formulas below).
- 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]
- Isoharmonic series: [math]\displaystyle{ f(n) = c + n }[/math] where [math]\displaystyle{ c }[/math] is rational
- 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], where [math]\displaystyle{ p }[/math] is prime
- 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
See also
- Category:Xenharmonic series: Some more types may be documented there.
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