Xenharmonic Wiki

6edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
Yourmusic Productions (talk | contribs)
autopatrolled
891 edits
Expand on properties of edo, and show how it crushes the distinction between the 3-limit & 13-limit by mapping 3/2 and 13/8 to the same step.
Fredg999 (talk | contribs)
autopatrolled, Interface administrators, Sysops
6,129 edits
Reorganized lead and Music sections, added Intervals section, uniformized "edo" spelling
Line 5: Line 5:
| ja = 6平均律
| ja = 6平均律
}}
}}
'''6-EDO''' divides the 1200-[[cent]] octave into 6 equal parts, making its smallest interval exactly 200¢, or the sixth root of 2. It's known as the "whole tone" scale. As a subset of 12-edo, it can be notated on a five-line staff with standard notation. It is the first edo that is not a [[The_Riemann_zeta_function_and_tuning#Zeta_EDO_lists|zeta peak]], has lower [[Consistency_levels_of_small_EDOs|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for it's size at creating traditional tonal music, with 5 & 7 both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12 tone instrument.
'''6 equal divisions of the octave''' ('''6edo''') is the [[tuning system]] derived by dividing the [[octave]] into 6 equal steps of 200 [[cent]]s each, or the sixth root of 2. It is also known as the "whole tone" scale. As a subset of [[12edo]], it can be notated on a five-line staff with standard notation. It is the first edo that is not a [[The_Riemann_zeta_function_and_tuning#Zeta_EDO_lists|zeta peak]], has lower [[Consistency_levels_of_small_EDOs|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for it's size at creating traditional tonal music, with 5 & 7 both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12 tone instrument.
 
== Theory ==
 
{{primes in edo|6|columns=6|prec=2}}
{{primes in edo|6|columns=6|prec=2}}


Related EDOs:
While 6edo does not well approximate the 3rd harmonic, it does contain a good approximation of the 9th harmonic. Therefore, 6edo can be treated as a 2.5.7.9 subgroup temperament.
* Subset: [[2edo]], [[3edo]]
 
Related edos:
* Subsets: [[2edo]], [[3edo]]
* Supersets: [[12edo]], [[18edo]], [[24edo]]...
* Supersets: [[12edo]], [[18edo]], [[24edo]]...
* Neighbours: [[5edo]], [[7edo]]
* Neighbours: [[5edo]], [[7edo]]
== Intervals ==
{| class="wikitable right-1 right-2"
! Steps
! Cents
! colspan="3" | Interval
! Approximate JI Ratios*
|-
| 0
| 0
| unison
| P1
| D
| [[1/1]]
|-
| 1
| 200
| major 2nd
| M2
| E
| [[8/7]], [[9/8]], [[10/9]]
|-
| 2
| 400
| major 3rd
| M3
| F#
| [[5/4]], [[9/7]]
|-
| 3
| 600
| aug 4th, dim 5th
| A4, d5
| G#, Ab
| [[7/5]], [[10/7]]
|-
| 4
| 800
| minor 6th
| m6
| Bb
| [[8/5]], [[14/9]]
|-
| 5
| 1000
| minor 7th
| m7
| C
| [[7/4]], [[9/5]], [[16/9]]
|-
| 6
| 1200
| perfect 8ve
| P8
| D
| [[2/1]]
|}
<nowiki>*</nowiki> based on treating 6edo as a 2.5.7.9 subgroup temperament; other approaches are possible.


== Commas ==
== Commas ==


6 EDO [[tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 6 10 14 17 21 22 }}.  
6edo [[tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 6 10 14 17 21 22 }}.  


{| class="commatable wikitable center-1 center-2 right-4 center-5"
{| class="commatable wikitable center-1 center-2 right-4 center-5"
Line 129: Line 192:
| 138.57
| 138.57
| tho 2nd
| tho 2nd
| tridecimal neutral second
| Tridecimal neutral second
|}
|}
<references/>
<references/>
Line 135: Line 198:
==Music==
==Music==


*[http://www.uvnitr.cz/flaoyg/forgotten_works/dvandva.html Dvandva] by Milan Guštar.
{| class="wikitable sortable"
*[http://micro.soonlabel.com/6edo/the-good-boundless-03.mp3 The Good Boundless] by Chris Vaisvil
!Title
*[https://soundcloud.com/uz1kt3k/prelude-in-6et Prelude In 6ET &#124; SoundCloud] by [[Aaron Andrew Hunt]]
!Composer
*[https://soundcloud.com/uz1kt3k/invention-in-6et Invention In 6ET &#124; SoundCloud] by Aaron Andrew Hunt
!Year
!Genre
!Additional links
|-
|[http://www.uvnitr.cz/flaoyg/forgotten_works/dvandva.html "Dvandva"]
|Milan Guštar
|1987/2007
|Folk
|
|-
|[http://micro.soonlabel.com/6edo/the-good-boundless-03.mp3 ''The Good Boundless'']
|[[Chris Vaisvil]]
|2011 (?)
|Jazz
|[http://chrisvaisvil.com/the-good-boundless/ Lyrics (personal website)]
|-
|[https://soundcloud.com/uz1kt3k/prelude-in-6et ''Prelude in 6ET'']
|[[Aaron Andrew Hunt]]
|2015
|Neobaroque
|
|-
|[https://soundcloud.com/uz1kt3k/invention-in-6et ''Invention in 6ET'']
|[[Aaron Andrew Hunt]]
|2015
|Neobaroque
|
|-
|data-sort-value="Exiting (from Edolian)"|[https://www.youtube.com/watch?v=AleKBhXifzY "Exiting"] (from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''])
|NullPointerException Music
|2020
|Classical
|
|-
|data-sort-value="Bowser breaks into Arnold Schoenberg's house and steals six of the twelve Tone Crystals (every other one), activating The 666666-Year-Curse Mechanism (from STAFFcirc vol. 7)"|"[https://soundcloud.com/sexytoadsandfrogsfriendcircle/6-chimeratio-bowser-breaks Bowser breaks into Arnold Schoenberg's house and steals six of the twelve Tone Crystals (every other one), activating The 666666-Year-Curse Mechanism]" (from [https://soundcloud.com/sexytoadsandfrogsfriendcircle/sets/staffcirc-vol-7-terra-octava ''STAFFcirc vol. 7''])
|Chimeratio
|2021
|Electronic
|[https://sexytoadsandfrogsfriendcircle.bandcamp.com/album/staffcirc-vol-7-terra-octava Album (Bandcamp)]
|}


[[Category:6-tone]]
[[Category:6-tone]]
Retrieved from "https://en.xen.wiki/w/6edo"