|
|
| (29 intermediate revisions by one other user not shown) |
| Line 1: |
Line 1: |
| 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. |
|
| |
|
| === Just intonation scales === | | ===[[Fokker block]]s=== |
| * [[Just intonation|Just intonation scales]]
| |
| **[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]]
| |
| **[[Chord cubes]]
| |
| **[[Combination product sets]]
| |
| ***[[Dekany|Dekanies]]
| |
| ***[[Eikosany|Eikosanies]]
| |
| ***[[Hexany|Hexanies]]
| |
| ***[[Pentadekany|Pentadekanies]]
| |
| **[[Crystal balls]]
| |
| **[[Highschool scales]]
| |
| **[[Homothetic just intonation|Homothetic JI scales]]
| |
| **[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]]
| |
| ***Modes of the [[oddharmonic series]]
| |
| ***Modes of the [[prime harmonic series]]
| |
| ***[[Primodality|Primodal scales]]
| |
| ***[[Neji|NEJI scales]]
| |
| ***Modes of the [[triangulharmonic series]]
| |
| **[[Tritriadic scale|Tritriadic scales]]
| |
| **[[Tonality diamond|Tonality diamonds]]
| |
| ***[[Breed diamonds]]
| |
| ***[[Diaconv scales]]
| |
|
| |
|
| === Tempered scales === | | ===[[Euler-Fokker genus|Euler-Fokker genera]]=== |
| *[[Temperament|Temperaments]]
| |
| **[[Clippers]]
| |
| **[[Dwarves]]
| |
| ***[[Especially tempered dwarves]]
| |
| ***[[Marvelous dwarves]]
| |
| **[[Elves]]
| |
| **[[List of essentially tempered scales|Essentially tempered scales]]
| |
| **[[Hobbits]]
| |
| ***[[MOS scale|Moment of symmetry scales]]
| |
| ****[[MOS Cradle|MOS cradles]]
| |
| **[[Lesfip scales]]
| |
| **[[Regular temperament|Regular temperaments]]
| |
| ***[[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]]
| |
| ****Equal divisions
| |
| *****[[EDO|Equal divisions of the octave (EDOs or ED2s)]]
| |
| *****[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]]
| |
| *****[[Ed4|Equal divisions of the fourth harmonic (ED4s)]]
| |
| *****[[Ed5|Equal divisions of the fifth harmonic (ED5s)]]
| |
| *****[[Ed6|Equal divisions of the sixth harmonic (ED6s)]]
| |
| *****[[Ed7|Equal divisions of the seventh harmonic (ED7s)]]
| |
| *****[[Ed8|Equal divisions of the eighth harmonic (ED8s)]]
| |
| *****[[Ed9|Equal divisions of the ninth harmonic (ED9s)]]
| |
| *****[[Ed10|Equal divisions of the tenth harmonic (ED10s)]]
| |
| *****[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]]
| |
| *****[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]]
| |
| *****[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]]
| |
| *****[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]]
| |
| *****[[Ed5/4|Equal divisions of the major third (ED5/4s)]]
| |
| ***** [[The Riemann zeta function and tuning|Zeta-stretched equal divisions]]
| |
| **** Equal multiplications
| |
| ***** [[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]]
| |
| ***** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]]
| |
| *** [[Rank-2 temperament|Rank-2 temperaments]]
| |
| ****[[Map of linear temperaments|Linear temperaments]]
| |
| ****[[Linear temperament|Moment of symmetry scales]]
| |
| *****[[MOS Cradle|MOS cradles]]
| |
| ****Families defined by a 2.3 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| ****Families defined by a 2.3.5 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| ****Clans defined by a 2.3.7 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| ****Clans defined by a 2.3.11 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| ****Clans defined by a 2.3.13 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| ****Clans defined by a 2.5.7 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| ****Clans defined by a 3.5.7 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| ****Temperament groups defined by a 2.3.5.7 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| *** [[Rank-3 temperament|Rank-3 temperaments]]
| |
| **** Families defined by a 2.3.5 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| **** Families defined by a 2.3.7 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| **** Families defined by a 2.3.5.7 comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| **** Temperament groups defined by an 11-limit comma
| |
| ***** See [[Tour of regular temperaments]]
| |
| *** [[Rank-4 temperament|Rank-4 temperaments]]
| |
| **** [[Keenanismic temperaments]]
| |
| **** [[Werckismic temperaments]]
| |
| **** [[Swetismic temperaments]]
| |
| **** [[Lehmerismic temperaments]]
| |
| **** [[Kalismic temperaments]]
| |
| ** [[Well temperament|Well temperaments]]
| |
|
| |
|
| === Metascales === | | ===[[Cartesian scale]]s=== |
| * [[Metascales]]
| |
| **[[Compound scale|Compound scales]]
| |
| ** [[Scale products and scale powers]]
| |
| ** [[MOS Cradle|MOS cradles]]
| |
| ** [[Muddle|MOS muddles]]
| |
| ** [[Polymicrotonality|Polysystemic scales / Polymicrotonal scales]]
| |
|
| |
|
| === Harmonotonic scales === | | ===[[Tonality diamond]]s=== |
| *[[Harmonotonic tuning|Harmonotonic / step-monotonic tunings]]
| |
| **[[Arithmetic tuning|Arithmetic tunings]]
| |
| ***Equal frequency step tunings
| |
| ****[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]]
| |
| *****Modes of the [[oddharmonic series]]
| |
| *****Modes of the [[prime harmonic series]]
| |
| *****[[Primodality|Primodal scales]]
| |
| *****[[Neji|NEJI scales]]
| |
| *****Modes of the [[triangulharmonic series]]
| |
| ***Equal pitch step tunings
| |
| ****[[Equal-step tuning|Equal-step tunings]]
| |
| *****Equal divisions
| |
| ******[[EDO|Equal divisions of the octave (EDOs or ED2s)]]
| |
| ******[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]]
| |
| ******[[Ed4|Equal divisions of the fourth harmonic (ED4s)]]
| |
| ******[[Ed5|Equal divisions of the fifth harmonic (ED5s)]]
| |
| ******[[Ed6|Equal divisions of the sixth harmonic (ED6s)]]
| |
| ******[[Ed7|Equal divisions of the seventh harmonic (ED7s)]]
| |
| ******[[Ed8|Equal divisions of the eighth harmonic (ED8s)]]
| |
| ******[[Ed9|Equal divisions of the ninth harmonic (ED9s)]]
| |
| ******[[Ed10|Equal divisions of the tenth harmonic (ED10s)]]
| |
| ******[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]]
| |
| ******[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]]
| |
| ******[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]]
| |
| ******[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]]
| |
| ******[[Ed5/4|Equal divisions of the major third (ED5/4s)]]
| |
| ****** [[The Riemann zeta function and tuning|Zeta-stretched equal divisions]]
| |
| ***** Equal multiplications
| |
| ****** [[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]]
| |
| *** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]]
| |
| ***[[Xenharmonic series|Powharmonic series]]
| |
| ***Modes of the [[prime harmonic series]]
| |
| ***[[Xenharmonic series|Logharmonic series]]
| |
| ***Modes of the [[metallic harmonic series]]
| |
| ***Modes of the [[oddharmonic series]]
| |
| ***[[Xenharmonic series|Subpowharmonic series]]
| |
| ***[[Xenharmonic series|Sublogharmonic series]]
| |
| ***Modes of the [[triangulharmonic series]]
| |
|
| |
|
| === Miscellaneous scale structures === | | ===[[Breed diamonds]]=== |
| *[[Cartesian scale|Cartesian scales]]
| | |
| *[[Euler-Fokker genus|Euler-Fokker genera]]
| | ===[[Diaconv scales]]=== |
| *[[Fokker block|Fokker blocks]]
| | |
| **[[Gallery of wakalixes|Wakalixes]]
| | ===[[Scale products and scale powers]]=== |
| *[[Generator-offset property|Generator-offset scales]]
| | |
| *[[Maximal harmony epimorphic scales]]
| | ===[[Combination product sets]]=== |
| *[[Omniconsonant scale|Omniconsonant scales]]
| | |
| *[[SN scale|Step-nested scales]]
| | ===[[Dwarves]]=== |
| **[[Linear temperament|Moment of symmetry scales]]
| | |
| ***[[MOS Cradle|MOS cradles]]
| | ===[[Marvelous dwarves]]=== |
| *[[Yantras]]
| | |
| | ===[[Especially tempered dwarves]]=== |
| | |
| | ===[[Elves]]=== |
| | |
| | ===[[Hobbits]]=== |
| | |
| | ===[[Clippers]]=== |
| | |
| | ===[[Maximal harmony epimorphic scales]]=== |
| | |
| | ===[[Lesfip scales]]=== |
| | |
| | ===[[Highschool scales]]=== |
| | |
| | ===[[Crystal balls]]=== |
| | |
| | ===[[Chord cubes]]=== |
| | |
| | ===[[List of essentially tempered scales|Essentially tempered scales]]=== |
| | |
| | ===[[Yantras]]=== |
| | |
| | ===[[Overtone scales]]=== |
| | |
| | |
| | {{todo|inline=1|rework|review heading structure|improve layout|improve synopsis}} |
|
| |
|
| [[Category:Scales by family| ]] <!-- main article --> | | [[Category:Scales by family| ]] <!-- main article --> |
| [[Category:Lists of scales]] | | [[Category:Lists of scales]] |
| [[category:todo:expand]]
| |