Families of scales: Difference between revisions
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******[[Ed10/3|Equal divisions of 10/3 (ED10/3s)]] | ******[[Ed10/3|Equal divisions of 10/3 (ED10/3s)]] | ||
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******[[Ed9/4|Equal divisions of 9/4 (EDIXs or ED9/4s)]] | |||
******[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]] | ******[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]] | ||
******[[Edφ|Equal divisions of Phi (Edφs)]] | ******[[Edφ|Equal divisions of Phi (Edφs)]] | ||
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********[[Ed9/4|Equal divisions of 9/4 (EDIXs or ED9/4s)]] | |||
********[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]] | ********[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]] | ||
********[[Edφ|Equal divisions of Phi (Edφs)]] | ********[[Edφ|Equal divisions of Phi (Edφs)]] | ||
Revision as of 03:33, 16 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 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
- Combination product sets
- 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
- Dwarves
- Hobbits
- Regular temperaments
- Rank-4 temperaments
- Rank-3 temperaments
- Families defined by a 2.3.5 comma
- Families defined by a 2.3.7 comma
- Families defined by a 2.3.5.7 comma
- Temperament groups defined by an 11-limit comma
- Rank-2 temperaments (map)
- Linear temperaments
- Moment of symmetry scales
- Families defined by a 2.3 comma
- Families defined by a 2.3.5 comma
- Clans defined by a 2.3.7 comma
- Clans defined by a 2.3.11 comma
- Clans defined by a 2.3.13 comma
- Clans defined by a 2.5.7 comma
- Clans defined by a 3.5.7 comma
- Temperament groups defined by a 2.3.5.7 comma
- Rank-1 temperaments / Equal-step tunings
- Equal multiplications
- 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 9/4 (EDIXs or ED9/4s)
- Equal divisions of 11/5 (ED11/5s)
- Equal divisions of Phi (Edφs)
- Cent equal temperaments (cETs)
Fokker blocks
- Fokker blocks
- Moment of symmetry scales
- Superwakalixes
- Wakalixes
- r-wakalixes
- Triple wakalixes
- Quadruple wakalixes
- Pentuple wakalixes
- ...
- r-wakalixes
Metascales
Periodic scales
- Periodic scales
- Generator-offset scales
- Maximal harmony epimorphic scales
- Step-nested scales
- 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
- Arithmetic tunings
- Equal length step 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
- Overtone scales (modes of the harmonic series) / AFDOs
- Equal pitch step tunings
- Rank-1 temperaments / Equal-step tunings
- Equal multiplications
- 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 9/4 (EDIXs or ED9/4s)
- Equal divisions of 11/5 (ED11/5s)
- Equal divisions of Phi (Edφs)
- Cent equal temperaments (cETs)
- Rank-1 temperaments / Equal-step tunings
- Xenharmonic series