Families of scales: Difference between revisions
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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: | 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: | ||
=== Just Intonation === | === '''Just Intonation''' === | ||
* Just intonated scales | * [[Just intonation|Just intonated scales]] | ||
**Chord cubes | **[[Chord cubes]] | ||
**Combination product sets | **[[Combination product sets]] | ||
***Dekanies | ***[[Dekany|Dekanies]] | ||
***Eikosanies | ***[[Eikosany|Eikosanies]] | ||
***Hexanies | ***[[Hexany|Hexanies]] | ||
***Pentadekanies | ***[[Pentadekany|Pentadekanies]] | ||
**Crystal balls | **[[Crystal balls]] | ||
**Highschool scales | **[[Highschool scales]] | ||
**Homothetic JI scales | **[[Homothetic just intonation|Homothetic JI scales]] | ||
**Overtone scales (AFDOs) | **[[Overtone scales|Overtone scales (AFDOs)]] | ||
***Primodal scales | ***[[Primodality|Primodal scales]] | ||
**Tritriadic scales | **[[Tritriadic scale|Tritriadic scales]] | ||
**Tonality diamonds | **[[Tonality diamond|Tonality diamonds]] | ||
***Breed diamonds | ***[[Breed diamonds]] | ||
***Diaconv scales | ***[[Diaconv scales]] | ||
=== Temperament === | === '''Temperament''' === | ||
*Temperaments | *[[Temperament|Temperaments]] | ||
**Clippers | **[[Clippers]] | ||
**Dwarves | **[[Dwarves]] | ||
***Especially tempered dwarves | ***[[Especially tempered dwarves]] | ||
***Marvelous dwarves | ***[[Marvelous dwarves]] | ||
**Elves | **[[Elves]] | ||
**Essentially tempered scales | **[[List of essentially tempered scales|Essentially tempered scales]] | ||
**Hobbits | **[[Hobbits]] | ||
***Moment of symmetry scales | ***[[MOS scale|Moment of symmetry scales]] | ||
**Lesfip scales | **[[Lesfip scales]] | ||
**Regular temperaments | **[[Regular temperament|Regular temperaments]] | ||
*** Rank-1 temperaments / Equal-step tunings | *** [[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]] | ||
**** Equal divisions of the octave (EDOs or ED2s) | **** [[EDO|Equal divisions of the octave (EDOs or ED2s)]] | ||
**** Equal divisions of the third harmonic (EDTs or ED3s) | **** [[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ||
**** Equal divisions of the fourth harmonic (ED4s) | **** [[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ||
**** Equal divisions of the fifth harmonic (ED5s) | **** [[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | ||
**** Equal divisions of the sixth harmonic (ED6s) | **** [[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | ||
**** Equal divisions of the seventh harmonic (ED7s) | **** [[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | ||
**** Equal divisions of the eighth harmonic (ED8s) | **** [[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | ||
**** Equal divisions of the ninth harmonic (ED9s) | **** [[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | ||
**** Equal divisions of the tenth harmonic (ED10s) | **** [[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | ||
**** Equal divisions of the eleventh harmonic (ED11s) | **** [[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | ||
**** Equal divisions of the perfect fifth (ED3/2s) | **** [[Ed3/2|Equal divisions of the perfect fifth (ED3/2s)]] | ||
**** Equal divisions of the perfect fourth (ED4/3s) | **** [[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | ||
**** Equal divisions of the major sixth (ED5/3s) | **** [[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | ||
**** Equal divisions of the major third (ED5/4s) | **** [[Ed5/4|Equal divisions of the major third (ED5/4s)]] | ||
*** Rank-2 temperaments / Linear temperaments | *** [[Rank-2 temperament|Rank-2 temperaments]] / [[Linear temperament|Linear temperaments]] | ||
****Moment of symmetry scales | ****[[Linear temperament|Moment of symmetry scales]] | ||
*** Rank-3 temperaments | *** [[Rank-3 temperament|Rank-3 temperaments]] | ||
*** Rank-4 temperaments | *** [[Rank-4 temperament|Rank-4 temperaments]] | ||
=== Harmonotonicity === | === '''Harmonotonicity''' === | ||
*Harmonotonic tunings | *[[Harmonotonic tuning|Harmonotonic tunings]] | ||
**Arithmetic tunings | **[[Arithmetic tuning|Arithmetic tunings]] | ||
***Equal-step tunings | ***[[Equal-step tuning|Equal-step tunings]] | ||
****Equal divisions of the octave (EDOs) | ****[[EDO|Equal divisions of the octave (EDOs)]] | ||
**** Equal divisions of the third harmonic (EDTs or ED3s) | **** [[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ||
**** Equal divisions of the fourth harmonic (ED4s) | **** [[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ||
**** Equal divisions of the fifth harmonic (ED5s) | **** [[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | ||
**** Equal divisions of the sixth harmonic (ED6s) | **** [[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | ||
**** Equal divisions of the seventh harmonic (ED7s) | **** [[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | ||
**** Equal divisions of the eighth harmonic (ED8s) | **** [[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | ||
**** Equal divisions of the ninth harmonic (ED9s) | **** [[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | ||
**** Equal divisions of the tenth harmonic (ED10s) | **** [[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | ||
**** Equal divisions of the eleventh harmonic (ED11s) | **** [[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | ||
**** Equal divisions of the perfect fifth (ED3/2s) | **** [[Ed3/2|Equal divisions of the perfect fifth (ED3/2s)]] | ||
**** Equal divisions of the perfect fourth (ED4/3s) | **** [[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | ||
**** Equal divisions of the major sixth (ED5/3s) | **** [[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | ||
**** Equal divisions of the major third (ED5/4s) | **** [[Ed5/4|Equal divisions of the major third (ED5/4s)]] | ||
***Overtone scales (AFDOs) | ***[[Overtone scales|Overtone scales (AFDOs)]] | ||
****Primodal scales | ****[[Primodality|Primodal scales]] | ||
***Xenharmonic series | ***[[Xenharmonic series]] | ||
=== Miscellaneous structures === | === '''Miscellaneous structures''' === | ||
*Cartesian scales | *[[Cartesian scale|Cartesian scales]] | ||
*Compound scales | *[[Compound scale|Compound scales]] | ||
*Euler-Fokker genera | *[[Euler-Fokker genus|Euler-Fokker genera]] | ||
*Fokker blocks | *[[Fokker block|Fokker blocks]] | ||
**Wakalixes | **[[Gallery of wakalixes|Wakalixes]] | ||
*Generator-offset scales | *[[Generator-offset property|Generator-offset scales]] | ||
*Maximal harmony epimorphic scales | *[[Maximal harmony epimorphic scales]] | ||
*Omniconsonant scales | *[[Omniconsonant scale|Omniconsonant scales]] | ||
*Scale products and scale powers | *[[Scale products and scale powers]] | ||
*Step-nested scales | *[[SN scale|Step-nested scales]] | ||
**Moment of symmetry scales | **[[Linear temperament|Moment of symmetry scales]] | ||
*Yantras | *[[Yantras]] | ||
[[Category:Scales by family| ]] <!-- main article --> | [[Category:Scales by family| ]] <!-- main article --> | ||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
[[category:todo:expand]] | [[category:todo:expand]] | ||