Xenharmonic series: Difference between revisions
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Added a few more examples, fixed full name of OS, markup, sorted list in alphabetical order, categories |
Cmloegcmluin (talk | contribs) m fix formatting |
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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> | ||
Revision as of 23:58, 17 May 2022
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