|
|
| (3 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]]
| |
| **[[Crystal balls]]
| |
| **[[Highschool scales]]
| |
| **[[Homothetic just intonation|Homothetic JI scales]]
| |
| **[[Tritriadic scale|Tritriadic scales]]
| |
| **[[Tonality diamond|Tonality diamonds]]
| |
| ***[[Breed diamonds]]
| |
| ***[[Diaconv scales]]
| |
| **[[Combination product sets]]
| |
| ***[[Dekany|Dekanies]]
| |
| ***[[Eikosany|Eikosanies]]
| |
| ***[[Hexany|Hexanies]]
| |
| ***[[Pentadekany|Pentadekanies]]
| |
| ***[[Pentany|Pentanies]]
| |
| **[[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]]
| |
|
| |
|
| === Tempered scales === | | ===[[Euler-Fokker genus|Euler-Fokker genera]]=== |
| *[[Temperament|Temperaments]]
| |
| **[[Clippers]]
| |
| **[[Elves]]
| |
| **[[List of essentially tempered scales|Essentially tempered scales]]
| |
| **[[Lesfip scales]]
| |
| **[[Well temperament|Well temperaments]]
| |
| ***[[Kartvelian scales]]
| |
| **[[Dwarves]]
| |
| ***[[Especially tempered dwarves]]
| |
| ***[[Marvelous dwarves]]
| |
| **[[Hobbits]]
| |
| ***[[MOS scale|Moment of symmetry scales]]
| |
| ****[[MOS Cradle|MOS cradles]]
| |
| **[[Regular temperament|Regular temperaments]]
| |
| ***[[Rank-4 temperament|Rank-4 temperaments]]
| |
| ****[[Keenanismic temperaments]]
| |
| ****[[Werckismic temperaments]]
| |
| ****[[Swetismic temperaments]]
| |
| ****[[Lehmerismic temperaments]]
| |
| ****[[Kalismic 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-2 temperament|Rank-2 temperaments]] ([[Map of rank-2 temperaments|map]])
| |
| ****[[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]]''
| |
| *** [[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]]
| |
| ****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 divisions
| |
| *****[[EDO|Equal divisions of the octave (EDOs or ED2s)]]
| |
| *****[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]]
| |
| *****[[Edonoi|Edonois]]
| |
| ******[[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)]]
| |
| ******[[:Category:Edonoi|...]]
| |
| ******[[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)]]
| |
| ******[[:Category:Edonoi|...]]
| |
| ******[[Ed5/2|Equal divisions of 5/2 (EDXs or ED5/2s)]]
| |
| ******[[Ed7/2|Equal divisions of 7/2 (ED7/2s)]]
| |
| ******[[:Category:Edonoi|...]]
| |
| ******[[Ed7/3|Equal divisions of 7/3 (ED7/3s)]]
| |
| ******[[Ed8/3|Equal divisions of 8/3 (ED8/3s)]]
| |
| ******[[Ed10/3|Equal divisions of 10/3 (ED10/3s)]]
| |
| ******[[:Category:Edonoi|...]]
| |
| ******[[Ed9/4|Equal divisions of 9/4 (EDIXs or ED9/4s)]]
| |
| ******[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]]
| |
| ******[[Edφ|Equal divisions of Phi (Edφs)]]
| |
| ******[[CET|''n''-cent equal tunings (''n''-cETs)]]
| |
|
| |
|
| === Fokker blocks === | | ===[[Cartesian scale]]s=== |
|
| |
|
| * [[Fokker block|Fokker blocks]]
| | ===[[Tonality diamond]]s=== |
| **[[Linear temperament|Moment of symmetry scales]]
| |
| ***[[MOS Cradle|MOS cradles]]
| |
| **[[Gallery of wakalixes|Superwakalixes]]
| |
| **[[Gallery of wakalixes|Wakalixes]]
| |
| ***r-wakalixes
| |
| ****Triple wakalixes
| |
| ****Quadruple wakalixes
| |
| ****Pentuple wakalixes
| |
| ****...
| |
|
| |
|
| === Metascales === | | ===[[Breed diamonds]]=== |
| * [[Metascales]]
| |
| **[[Compound scale|Compound scales]]
| |
| ** [[Scale products and scale powers]]
| |
| ** [[MOS Cradle|MOS cradles]]
| |
| ** [[Muddle|MOS muddles]]
| |
| ** [[Polymicrotonality|Polysystemic scales / Polymicrotonal scales]]
| |
|
| |
|
| === Periodic scales === | | ===[[Diaconv scales]]=== |
| * [[Periodic scale|Periodic scales]]
| |
| **[[Generator-offset property|Generator-offset scales]]
| |
| **[[Maximal harmony epimorphic scales]]
| |
| **[[SN scale|Step-nested scales]]
| |
| ***[[Linear temperament|Moment of symmetry scales]]
| |
| ****[[MOS Cradle|MOS cradles]]
| |
| **[[Harmonotonic tuning|Harmonotonic / step-monotonic tunings]]
| |
| ***[[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]]
| |
| ****[[Powharmonic series]]
| |
| ****Modes of the [[prime harmonic series]]
| |
| ****[[Logharmonic series]]
| |
| ****Modes of the [[metallic harmonic series]]
| |
| ****Modes of the [[oddharmonic series]]
| |
| ****[[Powharmonic series|Subpowharmonic series]]
| |
| ****[[Logharmonic series|Sublogharmonic series]]
| |
| ****Modes of the [[triangulharmonic series]]
| |
| ***Non-arithmetic harmonotonic tunings
| |
| ****[[Powharmonic series]]
| |
| ****[[Logharmonic series]]
| |
| ****[[Powharmonic series|Subpowharmonic series]]
| |
| ****[[Logharmonic series|Sublogharmonic series]]
| |
| ***[[Arithmetic tuning|Arithmetic tunings]]
| |
| ****Equal length step tunings
| |
| *****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]]
| |
| ****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|Rank-1 temperaments / Equal-step tunings]]
| |
| ******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 divisions
| |
| *******[[EDO|Equal divisions of the octave (EDOs or ED2s)]]
| |
| *******[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]]
| |
| *******[[Edonoi|Edonois]]
| |
| ********[[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)]]
| |
| ********[[:Category:Edonoi|...]]
| |
| ********[[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)]]
| |
| ********[[:Category:Edonoi|...]]
| |
| ********[[Ed5/2|Equal divisions of 5/2 (EDXs or ED5/2s)]]
| |
| ********[[Ed7/2|Equal divisions of 7/2 (ED7/2s)]]
| |
| ********[[:Category:Edonoi|...]]
| |
| ********[[Ed7/3|Equal divisions of 7/3 (ED7/3s)]]
| |
| ********[[Ed8/3|Equal divisions of 8/3 (ED8/3s)]]
| |
| ********[[Ed10/3|Equal divisions of 10/3 (ED10/3s)]]
| |
| ********[[:Category:Edonoi|...]]
| |
| ********[[Ed9/4|Equal divisions of 9/4 (EDIXs or ED9/4s)]]
| |
| ********[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]]
| |
| ********[[Edφ|Equal divisions of Phi (Edφs)]]
| |
| ********[[CET|Cent equal temperaments (cETs)]]
| |
|
| |
|
| === Miscellaneous scale structures === | | ===[[Scale products and scale powers]]=== |
| *[[Cartesian scale|Cartesian scales]]
| |
| *[[Euler-Fokker genus|Euler-Fokker genera]]
| |
| *[[Omniconsonant scale|Omniconsonant scales]]
| |
| *[[Yantras]]
| |
|
| |
|
| === See also === | | ===[[Combination product sets]]=== |
|
| |
|
| * [[List of approaches to musical tuning]]
| | ===[[Dwarves]]=== |
| * [[Historical temperaments]]
| | |
| * [[ScaleIndex]]
| | ===[[Marvelous dwarves]]=== |
| * [[Scale properties simplified]]
| | |
| | ===[[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]]
| |
| [[Category:Lists of temperaments]]
| |
