Xenharmonic series: Difference between revisions
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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> | ||
Revision as of 02:36, 29 August 2021
Here's a place to gather xenharmonic variations on the harmonic series.
- Powharmonic series: [math]\displaystyle{ f(n) = n^p }[/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]
- Superparticular series: [math]\displaystyle{ f(n) = \frac{n+1}{n} }[/math]
- Subparticular series: [math]\displaystyle{ f(n) = \frac{n}{n+1} }[/math]
- Oddharmonic series: [math]\displaystyle{ f(n) = 2n-1 }[/math]
- Prime harmonic series: [math]\displaystyle{ f(n) = p_n }[/math]
- Triangulharmonic series: [math]\displaystyle{ f(n) = \frac{n^2 + n}{2} }[/math]
- Dumb Fibonacci series: [math]\displaystyle{ f(n) = f(n-1) + f(n-2) }[/math]
- Overtone Sequences: [math]\displaystyle{ f(n) = 1 + cn }[/math], where c is rational
- Arithmetic Frequency Sequences: [math]\displaystyle{ f(n) = 1 + cn }[/math], where c is irrational