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
  • Combination product sets
    • Dekanies
    • Eikosanies
    • Hexanies
    • Pentadekanies
    • Pentanies
  • Crystal balls
  • Highschool scales
  • Homothetic JI scales
  • 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
  • Tritriadic scales
  • Tonality diamonds
    • Breed diamonds
    • Diaconv scales

Tempered scales

• Temperaments
  • Clippers
  • Dwarves
    • Especially tempered dwarves
    • Marvelous dwarves
  • Elves
  • Essentially tempered scales
  • Hobbits
    • Moment of symmetry scales
      • MOS cradles
  • Lesfip scales
  • Regular temperaments
    • Rank-1 temperaments / Equal-step tunings
      • Equal divisions
        • 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 (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)
        • Zeta-stretched equal divisions
      • Equal multiplications
        • Ambitonal sequences (AS) / Equal multiplications of a rational interval
        • Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval
    • 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-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 temperaments
      • Keenanismic temperaments
      • Werckismic temperaments
      • Swetismic temperaments
      • Lehmerismic temperaments
      • Kalismic temperaments
  • Well temperaments

Metascales

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

Harmonotonic scales

• Harmonotonic / step-monotonic tunings
  • Arithmetic tunings
    • 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
      • Equal-step tunings
        • Equal divisions
          • 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 (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)
          • Zeta-stretched equal divisions
        • Equal multiplications
          • Ambitonal sequences (AS) / Equal multiplications of a rational interval
          • Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval
    • Equal length step tunings
      • Aliquot scales (modes of the subharmonic series) / EDLs
  • Non-arithmetic harmonotonic tunings
    • Powharmonic series
    • Logharmonic series
    • Subpowharmonic series
    • Sublogharmonic series
  • 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

Miscellaneous scale structures

• Cartesian scales
• Euler-Fokker genera
• Fokker blocks
  • Wakalixes
• Generator-offset scales
• Maximal harmony epimorphic scales
• Omniconsonant scales
• Step-nested scales
  • Moment of symmetry scales
    • MOS cradles
• Yantras

See also

• Approaches to musical tuning
• Historical temperaments