Families of scales

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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:

Just intonation 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 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
- Well temperaments
  - Kartvelian scales

Fokker blocks

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

Metascales

Metascales

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
- 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

See also

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