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~~]]: <~~span~~><math>f(n) = n^p</math></~~span~~>

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

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

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

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

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

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

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

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

* [[Dumb Fibonacci|Dumb Fibonacci series]]: <math>f(n) = f(n-1) + f(n-2)</math>

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

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

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

* [[Isoharmonic series]]: <math>f(n) = c + n</math> where <math>c</math> is rational

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

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

* [[Prime harmonic series]]: ~~~~<math>f(n) = p_n</math></~~span~~>

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

* [[~~Triangulharmonic~~ series]]: <~~span~~><math>f(n) = \frac{~~n^2 +~~ n}{2}</math~~></span~~>

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

* [[~~Dumb Fibonacci|Dumb Fibonacci series~~]]: ~~~~<math>f(n) = f(n-1~~) + f(~~n~~-2)~~</math~~></span~~>

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

* [[~~OS|Overtone Sequences~~]]: ~~~~<math>f(n) = 1 + cn</math>~~, where c is rational~~

* [[OS|Otonal sequences]]: <math>f(n) = 1 + cn</math>, where <math>c</math> is rational

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

* [[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

~~[[Category:Overview]]~~

== See also ==

[[~~Category~~:~~Overtone]]~~

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

[[Category:~~Overtone‏‎~~ series]]

~~[[Category:Otonality]]~~

~~[[Category:Harmonic]]~~

[[Category:Harmonic series‏‎]]

[[Category:Lists of scales]]

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