Families of scales

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 scales

• Just intonation scales
  • Aliquot scales (modes of the subharmonic series) / EDLs
  • Chord cubes
  • Crystal balls
  • Highschool scales
  • Homothetic JI scales
  • Tritriadic scales
  • Tonality diamonds
    • Breed diamonds
    • Diaconv scales
  • Combination product sets
    • Dekanies
    • Eikosanies
    • Hexanies
    • Pentadekanies
    • Pentanies
  • Overtone scales (modes of the harmonic series) / AFDOs
    • Modes of the oddharmonic series
    • Modes of the prime harmonic series
    • Primodal scales
    • NEJI scales
    • Modes of the triangulharmonic series

Tempered scales

• Temperaments
  • Clippers
  • Elves
  • Essentially tempered scales
  • Lesfip scales
  • Well temperaments
    • Kartvelian scales
  • Dwarves
    • Especially tempered dwarves
    • Marvelous dwarves
  • Hobbits
    • Moment of symmetry scales
      • MOS cradles
  • Regular temperaments
    • Rank-4 temperaments
      • Keenanismic temperaments
      • Werckismic temperaments
      • Swetismic temperaments
      • Lehmerismic temperaments
      • Kalismic temperaments
    • 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 temperaments (map)
      • Linear temperaments
      • Moment of symmetry scales
        • 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-1 temperaments / Equal-step tunings
      • Equal multiplications
        • Ambitonal sequences (AS) / Equal multiplications of a rational interval
        • Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval
      • Equal divisions
        • Equal divisions of the octave (EDOs or ED2s)
        • Zeta-stretched equal divisions
        • Edonois
          • 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 (EDFs or 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)
          • ...
          • Equal divisions of 5/2 (EDXs or ED5/2s)
          • Equal divisions of 7/2 (ED7/2s)
          • ...
          • Equal divisions of 7/3 (ED7/3s)
          • Equal divisions of 8/3 (ED8/3s)
          • Equal divisions of 10/3 (ED10/3s)
          • ...
          • Equal divisions of 11/5 (ED11/5s)
          • Equal divisions of Phi (Edφs)
          • Cent ETs (cETs)

Fokker blocks

• Fokker blocks
  • Moment of symmetry scales
    • MOS cradles
  • Superwakalixes
  • Wakalixes
    • r-wakalixes
      • Triple wakalixes
      • Quadruple wakalixes
      • Pentuple wakalixes
      • ...

Metascales

• Metascales
  • Compound scales
  • Scale products and scale powers
  • MOS cradles
  • MOS muddles
  • Polysystemic scales / Polymicrotonal scales

Periodic scales

• Periodic scales
  • Generator-offset scales
  • Maximal harmony epimorphic scales
  • Step-nested scales
    • Moment of symmetry scales
      • MOS cradles
  • Harmonotonic / step-monotonic tunings
    • Xenharmonic series
      • Ambitonal sequences (AS) / Equal multiplications of a rational interval
      • Aliquot scales (modes of the subharmonic series) / EDLs
      • 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
      • Subpowharmonic series
      • Sublogharmonic series
      • Modes of the triangulharmonic series
    • Non-arithmetic harmonotonic tunings
      • Powharmonic series
      • Logharmonic series
      • Subpowharmonic series
      • Sublogharmonic series
    • Arithmetic tunings
      • Equal length step tunings
        • Aliquot scales (modes of the subharmonic series) / EDLs
      • Equal frequency step tunings
        • Overtone scales (modes of the harmonic series) / AFDOs
          • Modes of the oddharmonic series
          • Modes of the prime harmonic series
          • Primodal scales
          • NEJI scales
          • Modes of the triangulharmonic series
      • Equal pitch step tunings
        • Rank-1 temperaments / Equal-step tunings
          • Equal multiplications
            • Ambitonal sequences (AS) / Equal multiplications of a rational interval
            • Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval
          • Equal divisions
            • Equal divisions of the octave (EDOs or ED2s)
            • Zeta-stretched equal divisions
            • Edonois
              • 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 (EDFs or 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)
              • ...
              • Equal divisions of 5/2 (EDXs or ED5/2s)
              • Equal divisions of 7/2 (ED7/2s)
              • ...
              • Equal divisions of 7/3 (ED7/3s)
              • Equal divisions of 8/3 (ED8/3s)
              • Equal divisions of 10/3 (ED10/3s)
              • ...
              • Equal divisions of 11/5 (ED11/5s)
              • Equal divisions of Phi (Edφs)

Miscellaneous scale structures

• Cartesian scales
• Euler-Fokker genera
• Omniconsonant scales
• Yantras

See also

• Approaches to musical tuning
• Historical temperaments
• Scale properties simplified