Xenharmonic series

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.