Families of scales: Difference between revisions
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** [[Polymicrotonality|Polysystemic scales / Polymicrotonal scales]] | ** [[Polymicrotonality|Polysystemic scales / Polymicrotonal scales]] | ||
=== | === Periodic scales === | ||
*[[Harmonotonic tuning|Harmonotonic / step-monotonic tunings]] | * [[Periodic scale|Periodic scales]] | ||
**[[Arithmetic tuning|Arithmetic tunings]] | **[[Generator-offset property|Generator-offset scales]] | ||
***Equal frequency step tunings | **[[Harmonotonic tuning|Harmonotonic / step-monotonic tunings]] | ||
****[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]] | ***[[Arithmetic tuning|Arithmetic tunings]] | ||
*****Modes of the [[oddharmonic series]] | ****Equal frequency step tunings | ||
*****Modes of the [[prime harmonic series]] | *****[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]] | ||
*****[[Primodality|Primodal scales]] | ******Modes of the [[oddharmonic series]] | ||
*****[[Neji|NEJI scales]] | ******Modes of the [[prime harmonic series]] | ||
*****Modes of the [[triangulharmonic series]] | ******[[Primodality|Primodal scales]] | ||
***Equal pitch step tunings | ******[[Neji|NEJI scales]] | ||
****[[Equal-step tuning|Equal-step tunings]] | ******Modes of the [[triangulharmonic series]] | ||
*****Equal divisions | ****Equal pitch step tunings | ||
******[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | *****[[Equal-step tuning|Equal-step tunings]] | ||
******[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ******Equal divisions | ||
******[[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | *******[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | ||
******[[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | *******[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ||
******[[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | *******[[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ||
******[[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | *******[[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | ||
******[[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | *******[[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | ||
******[[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | *******[[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | ||
******[[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | *******[[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | ||
******[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | *******[[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | ||
******... | *******[[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | ||
******[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]] | *******[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | ||
******[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | *******... | ||
******[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | *******[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]] | ||
******[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | *******[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | ||
******... | *******[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | ||
******[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]] | *******[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | ||
***** Equal multiplications | *******... | ||
****** [[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | *******[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]] | ||
****** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]] | ****** Equal multiplications | ||
***Equal length step tunings | *******[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | ||
*******[[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]] | |||
****Equal length step tunings | |||
*****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | |||
***Non-arithmetic harmonotonic tunings | |||
****[[Powharmonic series]] | |||
****[[Logharmonic series]] | |||
****[[Powharmonic series|Subpowharmonic series]] | |||
****[[Logharmonic series|Sublogharmonic series]] | |||
***[[Xenharmonic series]] | |||
****[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | |||
****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ||
* | ****[[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]] | ||
***[[ | ****[[Powharmonic series]] | ||
***[[ | ****Modes of the [[prime harmonic series]] | ||
***[[ | ****[[Logharmonic series]] | ||
***[[Logharmonic | ****Modes of the [[metallic harmonic series]] | ||
**[[ | ****Modes of the [[oddharmonic series]] | ||
*** | ****[[Powharmonic series|Subpowharmonic series]] | ||
* | ****[[Logharmonic series|Sublogharmonic series]] | ||
* | ****Modes of the [[triangulharmonic series]] | ||
***[[Powharmonic series| | **[[Maximal harmony epimorphic scales]] | ||
* | **[[SN scale|Step-nested scales]] | ||
***[[Logharmonic series| | ***[[Linear temperament|Moment of symmetry scales]] | ||
***Modes of the [[ | ****[[MOS Cradle|MOS cradles]] | ||
** | |||
***[[ | |||
*** | |||
=== Miscellaneous scale structures === | === Miscellaneous scale structures === | ||
*[[Cartesian scale|Cartesian scales]] | *[[Cartesian scale|Cartesian scales]] | ||
*[[Euler-Fokker genus|Euler-Fokker genera]] | *[[Euler-Fokker genus|Euler-Fokker genera]] | ||
*[[Omniconsonant scale|Omniconsonant scales]] | *[[Omniconsonant scale|Omniconsonant scales]] | ||
*[[Yantras]] | *[[Yantras]] | ||