Xenharmonic 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).

• Ambitonal sequences: [math]f(n) = p^n[/math], where [math]p[/math] is rational
• Arithmetic frequency sequences: [math]f(n) = 1 + cn[/math], where [math]c[/math] is irrational
• Arithmetic length sequences: [math]f(n) = \frac{1}{1 + cn}[/math], where [math]c[/math] is irrational
• Arithmetic pitch sequences: [math]f(n) = p^n[/math], where [math]p[/math] is irrational
• Dumb Fibonacci series: [math]f(n) = f(n-1) + f(n-2)[/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]
• Matharmonic series: [math]f(n) = H(n)[/math]
• Metallic harmonic series: [math]f(n) = μ_n[/math]
• Oddharmonic series: [math]f(n) = 2n-1[/math]
• 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], where [math]p[/math] is prime
• 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]
• Utonal sequences: [math]f(n) = \frac{1}{1 + cn}[/math], where [math]c[/math] is rational