Families of scales: Difference between revisions
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=== Just intonation scales === | === Just intonation scales === | ||
* [[Just intonation|Just intonation scales]] | * [[Just intonation|Just intonation scales]] | ||
**[[ | **[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ||
**[[Chord cubes]] | **[[Chord cubes]] | ||
**[[Combination product sets]] | **[[Combination product sets]] | ||
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**[[Highschool scales]] | **[[Highschool scales]] | ||
**[[Homothetic just intonation|Homothetic JI scales]] | **[[Homothetic just intonation|Homothetic JI scales]] | ||
**[[Overtone scale|Overtone scales]] / [[AFDO|AFDOs]] | **[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]] | ||
***Modes of the [[oddharmonic series]] | |||
***Modes of the [[prime harmonic series]] | ***Modes of the [[prime harmonic series]] | ||
***[[Primodality|Primodal scales]] | ***[[Primodality|Primodal scales]] | ||
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**[[Hobbits]] | **[[Hobbits]] | ||
***[[MOS scale|Moment of symmetry scales]] | ***[[MOS scale|Moment of symmetry scales]] | ||
****[[MOS Cradle|MOS cradles]] | |||
**[[Lesfip scales]] | **[[Lesfip scales]] | ||
**[[Regular temperament|Regular temperaments]] | **[[Regular temperament|Regular temperaments]] | ||
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****[[Linear temperament|Linear temperaments]] | ****[[Linear temperament|Linear temperaments]] | ||
****[[Linear temperament|Moment of symmetry scales]] | ****[[Linear temperament|Moment of symmetry scales]] | ||
*****[[MOS Cradle|MOS cradles]] | |||
*** [[Rank-3 temperament|Rank-3 temperaments]] | *** [[Rank-3 temperament|Rank-3 temperaments]] | ||
*** [[Rank-4 temperament|Rank-4 temperaments]] | *** [[Rank-4 temperament|Rank-4 temperaments]] | ||
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**[[Arithmetic tuning|Arithmetic tunings]] | **[[Arithmetic tuning|Arithmetic tunings]] | ||
***Equal frequency step tunings | ***Equal frequency step tunings | ||
****[[Overtone scale|Overtone scales]] / [[AFDO|AFDOs]] | ****[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]] | ||
*****Modes of the [[oddharmonic series]] | |||
*****Modes of the [[prime harmonic series]] | *****Modes of the [[prime harmonic series]] | ||
*****[[Primodality|Primodal scales]] | *****[[Primodality|Primodal scales]] | ||
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*****[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | *****[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | ||
***Equal length step tunings | ***Equal length step tunings | ||
****[[ | ****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ||
**Non-arithmetic harmonotonic tunings | **Non-arithmetic harmonotonic tunings | ||
***[[Powharmonic series]] | ***[[Powharmonic series]] | ||
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***[[Logharmonic series|Sublogharmonic series]] | ***[[Logharmonic series|Sublogharmonic series]] | ||
**[[Xenharmonic series]] | **[[Xenharmonic series]] | ||
***[[ | ***[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ||
***[[Xenharmonic series|Powharmonic series]] | ***[[Xenharmonic series|Powharmonic series]] | ||
***Modes of the [[prime harmonic series]] | ***Modes of the [[prime harmonic series]] | ||
***[[Xenharmonic series|Logharmonic series]] | ***[[Xenharmonic series|Logharmonic series]] | ||
***Modes of the [[metallic harmonic series]] | ***Modes of the [[metallic harmonic series]] | ||
***Modes of the [[oddharmonic series]] | |||
***[[Xenharmonic series|Subpowharmonic series]] | ***[[Xenharmonic series|Subpowharmonic series]] | ||
***[[Xenharmonic series|Sublogharmonic series]] | ***[[Xenharmonic series|Sublogharmonic series]] | ||
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*[[SN scale|Step-nested scales]] | *[[SN scale|Step-nested scales]] | ||
**[[Linear temperament|Moment of symmetry scales]] | **[[Linear temperament|Moment of symmetry scales]] | ||
***[[MOS Cradle|MOS cradles]] | |||
*[[Yantras]] | *[[Yantras]] | ||
Revision as of 00:20, 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
Temperaments
- Temperaments
- Clippers
- Dwarves
- Elves
- Essentially tempered scales
- Hobbits
- 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)
- Zeta-stretched equal-step tunings
- Rank-2 temperaments
- Rank-3 temperaments
- Rank-4 temperaments
- Rank-1 temperaments / Equal-step tunings
- Well temperaments
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 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-step tunings
- Equal length step tunings
- Equal frequency step tunings
- Non-arithmetic harmonotonic tunings
- Xenharmonic series
- Aliquot scales (modes of the subharmonic series) / EDLs
- 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