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 intonation|Just intonated scales]]
* Just intonated scales
**[[Chord cubes]]
**Chord cubes
**[[Combination product sets]]
**Combination product sets
***[[Dekany|Dekanies]]
***Dekanies
***[[Eikosany|Eikosanies]]
***Eikosanies
***[[Hexany|Hexanies]]
***Hexanies
***[[Pentadekany|Pentadekanies]]
***Pentadekanies
**[[Crystal balls]]
**Crystal balls
**[[Highschool scales]]
**Highschool scales
**[[Homothetic just intonation|Homothetic JI scales]]
**Homothetic JI scales
**[[Overtone scales|Overtone scales (AFDOs)]]
**Overtone scales (AFDOs)
***[[Primodality|Primodal scales]]
***Primodal scales
**[[Tritriadic scale|Tritriadic scales]]
**Tritriadic scales
**[[Tonality diamond|Tonality diamonds]]
**Tonality diamonds
***[[Breed diamonds]]
***Breed diamonds
***[[Diaconv scales]]
***Diaconv scales


=== '''Temperament''' ===
=== Temperament ===
*[[Temperament|Temperaments]]
*Temperaments
**[[Clippers]]
**Clippers
**[[Dwarves]]
**Dwarves
***[[Especially tempered dwarves]]
***Especially tempered dwarves
***[[Marvelous dwarves]]
***Marvelous dwarves
**[[Elves]]
**Elves
**[[List of essentially tempered scales|Essentially tempered scales]]
**Essentially tempered scales
**[[Hobbits]]
**Hobbits
***[[MOS scale|Moment of symmetry scales]]
***Moment of symmetry scales
**[[Lesfip scales]]
**Lesfip scales
**[[Regular temperament|Regular temperaments]]
**Regular temperaments
*** [[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]]
*** Rank-1 temperaments / Equal-step tunings
**** [[EDO|Equal divisions of the octave (EDOs or ED2s)]]
**** Equal divisions of the octave (EDOs or ED2s)
**** [[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]]
**** Equal divisions of the third harmonic (EDTs or ED3s)
**** [[Ed4|Equal divisions of the fourth harmonic (ED4s)]]
**** Equal divisions of the fourth harmonic (ED4s)
**** [[Ed5|Equal divisions of the fifth harmonic (ED5s)]]
**** Equal divisions of the fifth harmonic (ED5s)
**** [[Ed6|Equal divisions of the sixth harmonic (ED6s)]]
**** Equal divisions of the sixth harmonic (ED6s)
**** [[Ed7|Equal divisions of the seventh harmonic (ED7s)]]
**** Equal divisions of the seventh harmonic (ED7s)
**** [[Ed8|Equal divisions of the eighth harmonic (ED8s)]]
**** Equal divisions of the eighth harmonic (ED8s)
**** [[Ed9|Equal divisions of the ninth harmonic (ED9s)]]
**** Equal divisions of the ninth harmonic (ED9s)
**** [[Ed10|Equal divisions of the tenth harmonic (ED10s)]]
**** Equal divisions of the tenth harmonic (ED10s)
**** [[Ed11|Equal divisions of the eleventh harmonic (ED11s)]]
**** Equal divisions of the eleventh harmonic (ED11s)
**** [[Ed3/2|Equal divisions of the perfect fifth (ED3/2s)]]
**** Equal divisions of the perfect fifth (ED3/2s)
**** [[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]]
**** Equal divisions of the perfect fourth (ED4/3s)
**** [[Ed5/3|Equal divisions of the major sixth (ED5/3s)]]
**** Equal divisions of the major sixth (ED5/3s)
**** [[Ed5/4|Equal divisions of the major third (ED5/4s)]]
**** Equal divisions of the major third (ED5/4s)
*** [[Rank-2 temperament|Rank-2 temperaments]] / [[Linear temperament|Linear temperaments]]
*** Rank-2 temperaments / Linear temperaments
****[[Linear temperament|Moment of symmetry scales]]
****Moment of symmetry scales
*** [[Rank-3 temperament|Rank-3 temperaments]]
*** Rank-3 temperaments
*** [[Rank-4 temperament|Rank-4 temperaments]]
*** Rank-4 temperaments


=== '''Harmonotonicity''' ===
=== Harmonotonicity ===
*[[Harmonotonic tuning|Harmonotonic tunings]]
*Harmonotonic tunings
**[[Arithmetic tuning|Arithmetic tunings]]
**Arithmetic tunings
***[[Equal-step tuning|Equal-step tunings]]
***Equal-step tunings
****[[EDO|Equal divisions of the octave (EDOs)]]
****Equal divisions of the octave (EDOs)
**** [[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]]
**** Equal divisions of the third harmonic (EDTs or ED3s)
**** [[Ed4|Equal divisions of the fourth harmonic (ED4s)]]
**** Equal divisions of the fourth harmonic (ED4s)
**** [[Ed5|Equal divisions of the fifth harmonic (ED5s)]]
**** Equal divisions of the fifth harmonic (ED5s)
**** [[Ed6|Equal divisions of the sixth harmonic (ED6s)]]
**** Equal divisions of the sixth harmonic (ED6s)
**** [[Ed7|Equal divisions of the seventh harmonic (ED7s)]]
**** Equal divisions of the seventh harmonic (ED7s)
**** [[Ed8|Equal divisions of the eighth harmonic (ED8s)]]
**** Equal divisions of the eighth harmonic (ED8s)
**** [[Ed9|Equal divisions of the ninth harmonic (ED9s)]]
**** Equal divisions of the ninth harmonic (ED9s)
**** [[Ed10|Equal divisions of the tenth harmonic (ED10s)]]
**** Equal divisions of the tenth harmonic (ED10s)
**** [[Ed11|Equal divisions of the eleventh harmonic (ED11s)]]
**** Equal divisions of the eleventh harmonic (ED11s)
**** [[Ed3/2|Equal divisions of the perfect fifth (ED3/2s)]]
**** Equal divisions of the perfect fifth (ED3/2s)
**** [[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]]
**** Equal divisions of the perfect fourth (ED4/3s)
**** [[Ed5/3|Equal divisions of the major sixth (ED5/3s)]]
**** Equal divisions of the major sixth (ED5/3s)
**** [[Ed5/4|Equal divisions of the major third (ED5/4s)]]
**** Equal divisions of the major third (ED5/4s)
***[[Overtone scales|Overtone scales (AFDOs)]]
***Overtone scales (AFDOs)
****[[Primodality|Primodal scales]]
****Primodal scales
***[[Xenharmonic series]]
***Xenharmonic series


=== '''Miscellaneous structures''' ===
=== Miscellaneous structures ===
*[[Cartesian scale|Cartesian scales]]
*Cartesian scales
*[[Compound scale|Compound scales]]
*Compound scales
*[[Euler-Fokker genus|Euler-Fokker genera]]
*Euler-Fokker genera
*[[Fokker block|Fokker blocks]]
*Fokker blocks
**[[Gallery of wakalixes|Wakalixes]]
**Wakalixes
*[[Generator-offset property|Generator-offset scales]]
*Generator-offset scales
*[[Maximal harmony epimorphic scales]]
*Maximal harmony epimorphic scales
*[[Omniconsonant scale|Omniconsonant scales]]
*Omniconsonant scales
*[[Scale products and scale powers]]
*Scale products and scale powers
*[[SN scale|Step-nested scales]]
*Step-nested scales
**[[Linear temperament|Moment of symmetry scales]]
**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]]

Revision as of 10:52, 15 April 2023

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 intonated scales
    • Chord cubes
    • Combination product sets
      • Dekanies
      • Eikosanies
      • Hexanies
      • Pentadekanies
    • Crystal balls
    • Highschool scales
    • Homothetic JI scales
    • Overtone scales (AFDOs)
      • Primodal scales
    • Tritriadic scales
    • Tonality diamonds
      • Breed diamonds
      • Diaconv scales

Temperament

  • Temperaments
    • Clippers
    • Dwarves
      • Especially tempered dwarves
      • Marvelous dwarves
    • Elves
    • Essentially tempered scales
    • Hobbits
      • Moment of symmetry scales
    • Lesfip scales
    • Regular temperaments
      • Rank-1 temperaments / Equal-step tunings
        • Equal divisions of the octave (EDOs or ED2s)
        • Equal divisions of the third harmonic (EDTs or ED3s)
        • Equal divisions of the fourth harmonic (ED4s)
        • Equal divisions of the fifth harmonic (ED5s)
        • Equal divisions of the sixth harmonic (ED6s)
        • Equal divisions of the seventh harmonic (ED7s)
        • Equal divisions of the eighth harmonic (ED8s)
        • Equal divisions of the ninth harmonic (ED9s)
        • Equal divisions of the tenth harmonic (ED10s)
        • Equal divisions of the eleventh harmonic (ED11s)
        • Equal divisions of the perfect fifth (ED3/2s)
        • Equal divisions of the perfect fourth (ED4/3s)
        • Equal divisions of the major sixth (ED5/3s)
        • Equal divisions of the major third (ED5/4s)
      • Rank-2 temperaments / Linear temperaments
        • Moment of symmetry scales
      • Rank-3 temperaments
      • Rank-4 temperaments

Harmonotonicity

  • Harmonotonic tunings
    • Arithmetic tunings
      • Equal-step tunings
        • Equal divisions of the octave (EDOs)
        • Equal divisions of the third harmonic (EDTs or ED3s)
        • Equal divisions of the fourth harmonic (ED4s)
        • Equal divisions of the fifth harmonic (ED5s)
        • Equal divisions of the sixth harmonic (ED6s)
        • Equal divisions of the seventh harmonic (ED7s)
        • Equal divisions of the eighth harmonic (ED8s)
        • Equal divisions of the ninth harmonic (ED9s)
        • Equal divisions of the tenth harmonic (ED10s)
        • Equal divisions of the eleventh harmonic (ED11s)
        • Equal divisions of the perfect fifth (ED3/2s)
        • Equal divisions of the perfect fourth (ED4/3s)
        • Equal divisions of the major sixth (ED5/3s)
        • Equal divisions of the major third (ED5/4s)
      • Overtone scales (AFDOs)
        • Primodal scales
      • Xenharmonic series

Miscellaneous structures

  • Cartesian scales
  • Compound scales
  • Euler-Fokker genera
  • Fokker blocks
    • Wakalixes
  • Generator-offset scales
  • Maximal harmony epimorphic scales
  • Omniconsonant scales
  • Scale products and scale powers
  • Step-nested scales
    • Moment of symmetry scales
  • Yantras
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