Families of scales: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
mNo edit summary
No edit summary
 
(56 intermediate revisions by one other user not shown)
Line 1: Line 1:
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 certain set of scales, finite or infinite, generated according to a regular and exactly specified method. Examples of scale families are [[EDO]]<nowiki/>s, [https://en.xen.wiki/w/Equal-step_tuning equal-step tunings], [[MOSScales|MOS]], and [[Fokker blocks]]. Below are some further scale families.


=== Just Intonation ===
===[[Fokker block]]s===
* Just intonated scales
**Chord cubes
**Combination product sets
***Dekanies
***Eikosanies
***Hexanies
***Pentadekanies
**Crystal balls
**Highschool scales
**Homothetic JI scales
**Overtone scales (AFDOs)
***Primodal scales
**Tritriadic scales
**Tonality diamonds
***Breed diamonds
***Diaconv scales


=== Temperament ===
===[[Euler-Fokker genus|Euler-Fokker genera]]===
*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 ===
===[[Cartesian scale]]s===
*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 ===
===[[Tonality diamond]]s===
*Cartesian scales
 
*Compound scales
===[[Breed diamonds]]===
*Euler-Fokker genera
 
*Fokker blocks
===[[Diaconv scales]]===
**Wakalixes
 
*Generator-offset scales
===[[Scale products and scale powers]]===
*Maximal harmony epimorphic scales
 
*Omniconsonant scales
===[[Combination product sets]]===
*Scale products and scale powers
 
*Step-nested scales
===[[Dwarves]]===
**Moment of symmetry scales
 
*Yantras
===[[Marvelous dwarves]]===
 
===[[Especially tempered dwarves]]===
 
===[[Elves]]===
 
===[[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]]===
 
 
{{todo|inline=1|rework|review heading structure|improve layout|improve synopsis}}


[[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 02:28, 2 April 2025

A family of scales is a certain set of scales, finite or infinite, generated according to a regular and exactly specified method. Examples of scale families are EDOs, equal-step tunings, MOS, and Fokker blocks. Below are some further scale families.

Fokker blocks

Euler-Fokker genera

Cartesian scales

Tonality diamonds

Breed diamonds

Diaconv scales

Scale products and scale powers

Combination product sets

Dwarves

Marvelous dwarves

Especially tempered dwarves

Elves

Hobbits

Clippers

Maximal harmony epimorphic scales

Lesfip scales

Highschool scales

Crystal balls

Chord cubes

Essentially tempered scales

Yantras

Overtone scales

Todo: rework , review heading structure, improve layout, improve synopsis
Retrieved from "https://en.xen.wiki/index.php?title=Families_of_scales&oldid=189541"