Xenharmonic series: Difference between revisions

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~~Here~~'~~s a place to gather~~ 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).

[[~~Powharmonic~~ series|Powharmonic series]]: <~~span~~><math>f(n) = n^p</math></~~span~~>

* [[AS|Ambitonal sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is rational

* [[AFS|Arithmetic frequency sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is irrational

* [[ALS|Arithmetic length sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is irrational

* [[APS|Arithmetic pitch sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is irrational

* [[Dumb Fibonacci|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>

* [[OS|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>

* [[US|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational

[[~~Edharmonic series|Edharmonic~~ series]]: ~~<math>f(n) = a^{H(n)}</math>~~

== See also ==

* [[:Category:Xenharmonic series]]: Some more types may be documented there.

~~[[Logharmonic series|Logharmonic series]]: <math>f(n) = log_b~~{n}~~</math>~~

[[Category:Harmonic series‏‎]]

[[~~Matharmonic series|Matharmonic series]]~~: ~~<math>f(n) = H(n)</math>~~

[[Category:Lists of scales]]

~~[[Metallic harmonic series|Metallic harmonic series]]: <math>f(n) = μ_n</math>~~

~~[[Superparticular series|Superparticular series~~]]~~: <math>f(n) = \frac{n+1}{n}</math>~~

[[~~Subparticular series|Subparticular series]]~~: ~~<math>f(n) = \frac{n}{n+1}</math>~~

~~[[Oddharmonic series|Oddharmonic series~~]]~~: <math>f(n) = 2n-1</math>~~

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-Here's a place to gather 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).
-[[Powharmonic series|Powharmonic series]]: <span><math>f(n) = n^p</math></span>
+* [[AS|Ambitonal sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is rational
+* [[AFS|Arithmetic frequency sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is irrational
+* [[ALS|Arithmetic length sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is irrational
+* [[APS|Arithmetic pitch sequences]]: <math>f(n) = p^n</math>, where <math>p</math> is irrational
+* [[Dumb Fibonacci|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>
+* [[OS|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>
+* [[US|Utonal sequences]]: <math>f(n) = \frac{1}{1 + cn}</math>, where <math>c</math> is rational
-[[Edharmonic series|Edharmonic series]]: <span><math>f(n) = a^{H(n)}</math></span>
+== See also ==
+* [[:Category:Xenharmonic series]]: Some more types may be documented there.
-[[Logharmonic series|Logharmonic series]]: <span><math>f(n) = log_b{n}</math></span>
+{{Navbox scale gallery}}
+[[Category:Harmonic series‏‎]]
-[[Matharmonic series|Matharmonic series]]: <span><math>f(n) = H(n)</math></span>
+[[Category:Lists of scales]]
-[[Metallic harmonic series|Metallic harmonic series]]: <span><math>f(n) = μ_n</math></span>
-[[Superparticular series|Superparticular series]]: <span><math>f(n) = \frac{n+1}{n}</math></span>
-[[Subparticular series|Subparticular series]]: <span><math>f(n) = \frac{n}{n+1}</math></span>
-[[Oddharmonic series|Oddharmonic series]]: <span><math>f(n) = 2n-1</math></span>