Families of scales: Difference between revisions

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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:               
A '''family of scales''' is a collection of scales, finite or infinite, generated according to a regular and exactly specified method.


=== Just Intonation ===
== List of scale families ==
* Just intonated scales
* [[Equal-step tuning]]s (including [[EDO]]s)
**Chord cubes
* [[Moment of symmetry]] (MOS) scales
**Combination product sets
* [[Generator-offset]] (GO) scales
***Dekanies
* [[Fokker block]]s
***Eikosanies
* [[Euler-Fokker genus|Euler-Fokker genera]]
***Hexanies
* [[Cartesian scale]]s
***Pentadekanies
* [[Tonality diamond]]s
**Crystal balls
* [[Breed diamonds]]
**Highschool scales
* [[Diaconv scales]]
**Homothetic JI scales
* [[Scale products and scale powers]]
**Overtone scales (AFDOs)
* [[Combination product set]]s
***Primodal scales
* [[Dwarves]]
**Tritriadic scales
* [[Marvelous dwarves]]
**Tonality diamonds
* [[Especially tempered dwarves]]
***Breed diamonds
* [[Elves]]
***Diaconv scales
* [[Hobbits]]
* [[Clippers]]
* [[Maximal harmony epimorphic scales]]
* [[Lesfip scales]]
* [[Highschool scales]]
* [[Crystal balls]]
* [[Chord cubes]]
* [[List of essentially tempered scales|Essentially tempered scales]]
* [[Yantras]]
* [[Overtone scales]]


=== Temperament ===
{{todo|inline=1|complete list|improve layout|comment=Maybe turn this list into a glossary with a short description below each scale family?}}
*Temperaments
**Clippers
**Dwarves
***Especially tempered dwarves
***Marvelous dwarves
**Elves
**Essentially tempered scales
**Hobbits
***Moment of symmetry scales
**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
****Moment of symmetry scales
*** Rank-3 temperaments
*** Rank-4 temperaments
 
=== Harmonotonicity ===
*Harmonotonic tunings
**Arithmetic 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)
***Overtone scales (AFDOs)
****Primodal scales
***Xenharmonic series
 
=== Miscellaneous structures ===
*Cartesian scales
*Compound scales
*Euler-Fokker genera
*Fokker blocks
**Wakalixes
*Generator-offset scales
*Maximal harmony epimorphic scales
*Omniconsonant scales
*Scale products and scale powers
*Step-nested scales
**Moment of symmetry scales
*Yantras


[[Category:Scales by family| ]] <!-- main article -->
[[Category:Scales by family| ]] <!-- main article -->
[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[category:todo:expand]]

Latest revision as of 20:17, 27 July 2026

A family of scales is a collection of scales, finite or infinite, generated according to a regular and exactly specified method.

List of scale families

Todo: complete list, improve layout

Maybe turn this list into a glossary with a short description below each scale family?

Retrieved from "https://en.xen.wiki/index.php?title=Families_of_scales&oldid=234744"