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| By a ''family of scales'' is meant a certain set of scales, finite or infinite, generated according to a regular and exactly specified method. Examples of scale families include:
| | A ''family of scales'' is a certain set of scales, finite or infinite, generated according to a regular and exactly specified method. Examples of scale families are [[EDO]]<nowiki/>s, [https://en.xen.wiki/w/Equal-step_tuning equal-step tunings], [[MOSScales|MOS]], and [[Fokker blocks]]. Below are some further scale families. |
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| === Just intonation scales === | | ===[[Fokker block]]s=== |
| * [[Just intonation|Just intonation scales]]
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| **[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]]
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| **[[Chord cubes]]
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| **[[Combination product sets]]
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| ***[[Dekany|Dekanies]]
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| ***[[Eikosany|Eikosanies]]
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| ***[[Hexany|Hexanies]]
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| ***[[Pentadekany|Pentadekanies]]
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| ***[[Pentany|Pentanies]]
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| **[[Crystal balls]]
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| **[[Highschool scales]]
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| **[[Homothetic just intonation|Homothetic JI scales]]
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| **[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]]
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| ***Modes of the [[oddharmonic series]]
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| ***Modes of the [[prime harmonic series]]
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| ***[[Primodality|Primodal scales]]
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| ***[[Neji|NEJI scales]]
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| ***Modes of the [[triangulharmonic series]]
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| **[[Tritriadic scale|Tritriadic scales]]
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| **[[Tonality diamond|Tonality diamonds]]
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| ***[[Breed diamonds]]
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| ***[[Diaconv scales]]
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| === Tempered scales === | | ===[[Euler-Fokker genus|Euler-Fokker genera]]=== |
| *[[Temperament|Temperaments]]
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| **[[Clippers]]
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| **[[Dwarves]]
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| ***[[Especially tempered dwarves]]
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| ***[[Marvelous dwarves]]
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| **[[Elves]]
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| **[[List of essentially tempered scales|Essentially tempered scales]]
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| **[[Hobbits]]
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| ***[[MOS scale|Moment of symmetry scales]]
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| ****[[MOS Cradle|MOS cradles]]
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| **[[Lesfip scales]]
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| **[[Regular temperament|Regular temperaments]]
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| ***[[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]]
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| ****Equal divisions
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| *****[[EDO|Equal divisions of the octave (EDOs or ED2s)]]
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| *****[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]]
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| *****[[Ed4|Equal divisions of the fourth harmonic (ED4s)]]
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| *****[[Ed5|Equal divisions of the fifth harmonic (ED5s)]]
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| *****[[Ed6|Equal divisions of the sixth harmonic (ED6s)]]
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| *****[[Ed7|Equal divisions of the seventh harmonic (ED7s)]]
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| *****[[Ed8|Equal divisions of the eighth harmonic (ED8s)]]
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| *****[[Ed9|Equal divisions of the ninth harmonic (ED9s)]]
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| *****[[Ed10|Equal divisions of the tenth harmonic (ED10s)]]
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| *****[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]]
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| *****...
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| *****[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]]
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| *****[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]]
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| *****[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]]
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| *****[[Ed5/4|Equal divisions of the major third (ED5/4s)]]
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| *****...
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| *****[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]]
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| **** Equal multiplications
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| ***** [[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]]
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| ***** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]]
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| *** [[Rank-2 temperament|Rank-2 temperaments]] ([[Map of rank-2 temperaments|map]])
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| ****[[Map of linear temperaments|Linear temperaments]]
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| ****[[Linear temperament|Moment of symmetry scales]]
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| *****[[MOS Cradle|MOS cradles]]
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| ****Families defined by a 2.3 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| ****Families defined by a 2.3.5 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| ****Clans defined by a 2.3.7 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| ****Clans defined by a 2.3.11 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| ****Clans defined by a 2.3.13 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| ****Clans defined by a 2.5.7 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| ****Clans defined by a 3.5.7 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| ****Temperament groups defined by a 2.3.5.7 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| *** [[Rank-3 temperament|Rank-3 temperaments]]
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| **** Families defined by a 2.3.5 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| **** Families defined by a 2.3.7 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| **** Families defined by a 2.3.5.7 comma
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| ***** ''see [[Tour of regular temperaments]]''
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| **** Temperament groups defined by an 11-limit comma
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| ***** ''see [[Tour of regular temperaments]]''
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| *** [[Rank-4 temperament|Rank-4 temperaments]]
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| **** [[Keenanismic temperaments]]
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| **** [[Werckismic temperaments]]
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| **** [[Swetismic temperaments]]
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| **** [[Lehmerismic temperaments]]
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| **** [[Kalismic temperaments]]
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| ** [[Well temperament|Well temperaments]]
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| *** [[Kartvelian scales]]
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| === Fokker blocks === | | ===[[Cartesian scale]]s=== |
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| * [[Fokker block|Fokker blocks]]
| | ===[[Tonality diamond]]s=== |
| **[[Linear temperament|Moment of symmetry scales]]
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| ***[[MOS Cradle|MOS cradles]]
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| **[[Gallery of wakalixes|Wakalixes]]
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| ***r-wakalixes
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| ****Triple wakalixes
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| ****Quadruple wakalixes
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| ****Pentuple wakalixes
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| ****...
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| **[[Wakalix|Superwakalixes]]
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| === Metascales === | | ===[[Breed diamonds]]=== |
| * [[Metascales]]
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| **[[Compound scale|Compound scales]]
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| ** [[Scale products and scale powers]]
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| ** [[MOS Cradle|MOS cradles]]
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| ** [[Muddle|MOS muddles]]
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| ** [[Polymicrotonality|Polysystemic scales / Polymicrotonal scales]]
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| === Harmonotonic scales === | | ===[[Diaconv scales]]=== |
| *[[Harmonotonic tuning|Harmonotonic / step-monotonic tunings]]
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| **[[Arithmetic tuning|Arithmetic tunings]]
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| ***Equal frequency step tunings
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| ****[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]]
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| *****Modes of the [[oddharmonic series]]
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| *****Modes of the [[prime harmonic series]]
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| *****[[Primodality|Primodal scales]]
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| *****[[Neji|NEJI scales]]
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| *****Modes of the [[triangulharmonic series]]
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| ***Equal pitch step tunings
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| ****[[Equal-step tuning|Equal-step tunings]]
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| *****Equal divisions
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| ******[[EDO|Equal divisions of the octave (EDOs or ED2s)]]
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| ******[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]]
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| ******[[Ed4|Equal divisions of the fourth harmonic (ED4s)]]
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| ******[[Ed5|Equal divisions of the fifth harmonic (ED5s)]]
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| ******[[Ed6|Equal divisions of the sixth harmonic (ED6s)]]
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| ******[[Ed7|Equal divisions of the seventh harmonic (ED7s)]]
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| ******[[Ed8|Equal divisions of the eighth harmonic (ED8s)]]
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| ******[[Ed9|Equal divisions of the ninth harmonic (ED9s)]]
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| ******[[Ed10|Equal divisions of the tenth harmonic (ED10s)]]
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| ******[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]]
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| ******...
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| ******[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]]
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| ******[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]]
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| ******[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]]
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| ******[[Ed5/4|Equal divisions of the major third (ED5/4s)]]
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| ******...
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| ******[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]]
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| ***** Equal multiplications
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| ****** [[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]]
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| ****** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]]
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| ***Equal length step tunings
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| ****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]]
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| **Non-arithmetic harmonotonic tunings
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| ***[[Powharmonic series]]
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| ***[[Logharmonic series]]
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| ***[[Powharmonic series|Subpowharmonic series]]
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| ***[[Logharmonic series|Sublogharmonic series]]
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| **[[Xenharmonic series]]
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| ***[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]]
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| ***[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]]
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| *** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]]
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| ***[[Powharmonic series|Powharmonic series]]
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| ***Modes of the [[prime harmonic series]]
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| ***[[Logharmonic series|Logharmonic series]]
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| ***Modes of the [[metallic harmonic series]]
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| ***Modes of the [[oddharmonic series]]
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| ***[[Powharmonic series|Subpowharmonic series]]
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| ***[[Logharmonic series|Sublogharmonic series]]
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| ***Modes of the [[triangulharmonic series]]
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| === Miscellaneous scale structures === | | ===[[Scale products and scale powers]]=== |
| *[[Cartesian scale|Cartesian scales]]
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| *[[Euler-Fokker genus|Euler-Fokker genera]]
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| *[[Generator-offset property|Generator-offset scales]]
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| *[[Maximal harmony epimorphic scales]]
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| *[[Omniconsonant scale|Omniconsonant scales]]
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| *[[SN scale|Step-nested scales]]
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| **[[Linear temperament|Moment of symmetry scales]]
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| ***[[MOS Cradle|MOS cradles]]
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| *[[Yantras]]
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| === See also === | | ===[[Combination product sets]]=== |
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| * [[List of approaches to musical tuning|Approaches to musical tuning]]
| | ===[[Dwarves]]=== |
| * [[Historical temperaments]]
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| | ===[[Marvelous dwarves]]=== |
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| | ===[[Especially tempered dwarves]]=== |
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| | ===[[Elves]]=== |
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| | ===[[Hobbits]]=== |
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| | ===[[Clippers]]=== |
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| | ===[[Maximal harmony epimorphic scales]]=== |
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| | ===[[Lesfip scales]]=== |
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| | ===[[Highschool scales]]=== |
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| | ===[[Crystal balls]]=== |
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| | ===[[Chord cubes]]=== |
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| | ===[[List of essentially tempered scales|Essentially tempered scales]]=== |
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| | ===[[Yantras]]=== |
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| | ===[[Overtone scales]]=== |
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| | {{todo|inline=1|rework|review heading structure|improve layout|improve synopsis}} |
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| [[Category:Scales by family| ]] <!-- main article --> | | [[Category:Scales by family| ]] <!-- main article --> |
| [[Category:Lists of scales]] | | [[Category:Lists of scales]] |
| [[category:todo:expand]]
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| [[Category:Lists of temperaments]]
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