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

• Just intonated scales
  • Chord cubes
  • Combination product sets
    • Dekanies
    • Eikosanies
    • Hexanies
    • Pentadekanies
  • Crystal balls
  • Highschool scales
  • Homothetic JI scales
  • Overtone scales (AFDOs)
    • Primodal scales
    • NEJI 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 frequency step tunings
      • Overtone scales (AFDOs)
        • Primodal scales
        • NEJI scales
      • Xenharmonic series
    • Equal pitch step 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)
    • Equal length step tunings

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