Families of scales: Difference between revisions
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**[[Regular temperament|Regular temperaments]] | **[[Regular temperament|Regular temperaments]] | ||
***[[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]] | ***[[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]] | ||
****[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | ****Equal divisions | ||
**** [[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | *****[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | ||
**** [[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | *****[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ||
**** [[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | *****[[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ||
**** [[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | *****[[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | ||
**** [[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | *****[[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | ||
**** [[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | *****[[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | ||
**** [[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | *****[[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | ||
**** [[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | *****[[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | ||
**** [[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | *****[[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | ||
**** [[Ed3/2|Equal divisions of the perfect fifth (ED3/2s)]] | *****[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | ||
**** [[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | *****[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]] | ||
**** [[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | *****[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | ||
**** [[Ed5/4|Equal divisions of the major third (ED5/4s)]] | *****[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | ||
**** [[The Riemann zeta function and tuning|Zeta-stretched equal | *****[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | ||
***** [[The Riemann zeta function and tuning|Zeta-stretched equal divisions]] | |||
**** Equal multiplications | |||
***** [[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | |||
***** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]] | |||
*** [[Rank-2 temperament|Rank-2 temperaments]] | *** [[Rank-2 temperament|Rank-2 temperaments]] | ||
****[[Linear temperament|Linear temperaments]] | ****[[Linear temperament|Linear temperaments]] | ||
| Line 80: | Line 84: | ||
***Equal pitch step tunings | ***Equal pitch step tunings | ||
****[[Equal-step tuning|Equal-step tunings]] | ****[[Equal-step tuning|Equal-step tunings]] | ||
*****[[EDO|Equal divisions of the octave (EDOs)]] | *****Equal divisions | ||
*****[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ******[[EDO|Equal divisions of the octave (EDOs or ED2s)]] | ||
*****[[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ******[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ||
*****[[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | ******[[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ||
*****[[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | ******[[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | ||
*****[[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | ******[[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | ||
*****[[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | ******[[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | ||
*****[[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | ******[[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | ||
*****[[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | ******[[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | ||
*****[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | ******[[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | ||
*****[[Ed3/2|Equal divisions of the perfect fifth (ED3/2s)]] | ******[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | ||
*****[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | ******[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]] | ||
*****[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | ******[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | ||
*****[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | ******[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | ||
******[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | |||
****** [[The Riemann zeta function and tuning|Zeta-stretched equal divisions]] | |||
***** Equal multiplications | |||
****** [[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | |||
****** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]] | |||
***Equal length step tunings | ***Equal length step tunings | ||
****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ||
| Line 102: | Line 111: | ||
***[[Logharmonic series|Sublogharmonic series]] | ***[[Logharmonic series|Sublogharmonic series]] | ||
**[[Xenharmonic series]] | **[[Xenharmonic series]] | ||
***[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]] | |||
***[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ***[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]] | ||
*** [[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]] | |||
***[[Xenharmonic series|Powharmonic series]] | ***[[Xenharmonic series|Powharmonic series]] | ||
***Modes of the [[prime harmonic series]] | ***Modes of the [[prime harmonic series]] | ||
Revision as of 00:32, 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
- Rank-3 temperaments
- Rank-4 temperaments
- Rank-1 temperaments / Equal-step tunings
- Well temperaments
Composite scales
- Composite scales
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