Families of scales: Difference between revisions
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*[[Harmonotonic tuning|Harmonotonic tunings]] | *[[Harmonotonic tuning|Harmonotonic tunings]] | ||
**[[Arithmetic tuning|Arithmetic tunings]] | **[[Arithmetic tuning|Arithmetic tunings]] | ||
***[[Equal-step tuning|Equal-step tunings]] | ***Equal frequency step tunings | ||
****[[EDO|Equal divisions of the octave (EDOs)]] | ****[[Overtone scales|Overtone scales (AFDOs)]] | ||
**** [[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | *****[[Primodality|Primodal scales]] | ||
**** [[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | *****[[Neji|NEJI scales]] | ||
**** [[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | ****[[Xenharmonic series]] | ||
**** [[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | ***Equal pitch step tunings | ||
**** [[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | ****[[Equal-step tuning|Equal-step tunings]] | ||
**** [[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | *****[[EDO|Equal divisions of the octave (EDOs)]] | ||
**** [[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | *****[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]] | ||
**** [[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | *****[[Ed4|Equal divisions of the fourth harmonic (ED4s)]] | ||
**** [[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | *****[[Ed5|Equal divisions of the fifth harmonic (ED5s)]] | ||
**** [[Ed3/2|Equal divisions of the perfect fifth (ED3/2s)]] | *****[[Ed6|Equal divisions of the sixth harmonic (ED6s)]] | ||
**** [[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | *****[[Ed7|Equal divisions of the seventh harmonic (ED7s)]] | ||
**** [[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | *****[[Ed8|Equal divisions of the eighth harmonic (ED8s)]] | ||
**** [[Ed5/4|Equal divisions of the major third (ED5/4s)]] | *****[[Ed9|Equal divisions of the ninth harmonic (ED9s)]] | ||
*** | *****[[Ed10|Equal divisions of the tenth harmonic (ED10s)]] | ||
*****[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]] | |||
*****[[Ed3/2|Equal divisions of the perfect fifth (ED3/2s)]] | |||
*****[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]] | |||
*****[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]] | |||
*****[[Ed5/4|Equal divisions of the major third (ED5/4s)]] | |||
***Equal length step tunings | |||
=== Miscellaneous structures === | === Miscellaneous structures === | ||
Revision as of 11:02, 15 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
Temperament
- 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)
- Rank-2 temperaments / Linear temperaments
- Rank-3 temperaments
- Rank-4 temperaments
- Rank-1 temperaments / Equal-step tunings
Harmonotonicity
- Harmonotonic tunings
- Arithmetic tunings
- Equal frequency step tunings
- 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
- Arithmetic tunings