Families of scales: Difference between revisions
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*****[[MOS Cradle|MOS cradles]] | *****[[MOS Cradle|MOS cradles]] | ||
****Families defined by a 2.3 comma | ****Families defined by a 2.3 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
****Families defined by a 2.3.5 comma | ****Families defined by a 2.3.5 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
****Clans defined by a 2.3.7 comma | ****Clans defined by a 2.3.7 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
****Clans defined by a 2.3.11 comma | ****Clans defined by a 2.3.11 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
****Clans defined by a 2.3.13 comma | ****Clans defined by a 2.3.13 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
****Clans defined by a 2.5.7 comma | ****Clans defined by a 2.5.7 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
****Clans defined by a 3.5.7 comma | ****Clans defined by a 3.5.7 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
****Temperament groups defined by a 2.3.5.7 comma | ****Temperament groups defined by a 2.3.5.7 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
*** [[Rank-3 temperament|Rank-3 temperaments]] | *** [[Rank-3 temperament|Rank-3 temperaments]] | ||
**** Families defined by a 2.3.5 comma | **** Families defined by a 2.3.5 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
**** Families defined by a 2.3.7 comma | **** Families defined by a 2.3.7 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
**** Families defined by a 2.3.5.7 comma | **** Families defined by a 2.3.5.7 comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
**** Temperament groups defined by an 11-limit comma | **** Temperament groups defined by an 11-limit comma | ||
***** | ***** ''see [[Tour of regular temperaments]]'' | ||
*** [[Rank-4 temperament|Rank-4 temperaments]] | *** [[Rank-4 temperament|Rank-4 temperaments]] | ||
**** [[Keenanismic temperaments]] | **** [[Keenanismic temperaments]] | ||
Revision as of 01:14, 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
- Combination product sets
- 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
Tempered scales
- Temperaments
- Clippers
- Dwarves
- Elves
- Essentially tempered scales
- Hobbits
- 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
- Equal divisions
- 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-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-4 temperaments
- Rank-1 temperaments / Equal-step tunings
- Well temperaments
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
- Overtone scales (modes of the harmonic series) / AFDOs
- 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
- Equal divisions
- Equal-step tunings
- Equal length step tunings
- Equal frequency step tunings
- 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
- Arithmetic tunings
Miscellaneous scale structures
- Cartesian scales
- Euler-Fokker genera
- Fokker blocks
- Generator-offset scales
- Maximal harmony epimorphic scales
- Omniconsonant scales
- Step-nested scales
- Yantras