Xenharmonic Wiki

6edf: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
 
(19 intermediate revisions by 8 users not shown)
Line 1: Line 1:
=Equal division of the perfect fifth (3/2) into 6 equal parts=
{{Infobox ET}}
(a.k.a. "6th root of 3/2")
{{ED intro}} It corresponds to 10.2571 [[edo]].  


The single step of 6-edf is 116.9925 cents. This is very close to the size of the [[Regular_Temperaments#miracle|miracle]] generator, and thus this scale is close to the "nonoctave miracle" scale...
== Theory ==
6edf is related to the [[miracle]] temperament, which [[tempering out|tempers out]] [[225/224]] and [[1029/1024]] in the 7-limit.


==Compositions==
=== Harmonics ===
[http://www.seraph.it/dep/det/metashakti.mp3 Metashakti] by [[Carlo_Serafini|Carlo Serafini]]
{{Harmonics in equal|6|3|2}}


==Intervals==
== Intervals ==


{| class="wikitable"
{| class="wikitable center-1 right-2 center-4"
|-
|-
| | degrees
! #
| | cents ~ cents octave-reduced
! Cents
! Approximate Ratios
! [[1L 3s (fifth-equivalent)|Neptunian]]<br>Notation
|-
|-
| | 0
| 0
| | 0 (perfect unison, 1:1)
| 0
| [[1/1]]
| C
|-
|-
| | 1
| 1
| | 117
| 117
| [[16/15]], [[15/14]]
| C#
|-
|-
| | 2
| 2
| | 234
| 234
| [[8/7]]
| Db
|-
|-
| | 3
| 3
| | 351
| 351
| [[11/9]], [[27/22]]
| D
|-
|-
| | 4
| 4
| | 468
| 468
| [[21/16]]
| E
|-
|-
| | 5
| 5
| | 585
| 585
| [[7/5]], [[45/32]]
| F
|-
|-
| | 6
| 6
| | 702 (just perfect fifth, 3:2)
| 702
| [[3/2]]
| C
|-
|-
| | 7
| 7
| | 819
| 819
| [[8/5]], [[21/13]]
| C#
|-
|-
| | 8
| 8
| | 936
| 936
| [[12/7]], [[55/32]]
| Db
|-
|-
| | 9
| 9
| | 1053
| 1053
| [[11/6]]
| D
|-
|-
| | 10
| 10
| | 1170
| 1170
| [[49/25]], [[160/81]], [[2/1]]
| E
|-
|-
| | 11
| 11
| | 1287 ~ 87
| 1287
|  
| F
|-
|-
| | 12
| 12
| | 1404 ~ 204 (just major whole tone/ninth, 9:4)
| 1404
| 9/4
| C
|-
|-
| | 13
| 13
| | 1521 ~ 321
| 1521
|
| C#
|-
|-
| | 14
| 14
| | 1638 ~ 438
| 1638
|
| Db
|-
|-
| | 15
| 15
| | 1755 ~ 555
| 1755
|11/4
| D
|-
|-
| | 16
| 16
| | 1872 ~ 672
| 1872
|
| E
|-
|-
| | 17
| 17
| | 1988 ~ 788
| 1988
|
| F
|-
|-
| | 18
| 18
| | 2106 ~ 906 (Pythagorean major sixth, 27:8)
| 2106
| 27/8
| C
|-
|-
| | 19
| 19
| | 2223 ~ 1023
| 2223
|
| C#
|-
|-
| | 20
| 20
| | 2340 ~ 1140
| 2340
|
| Db
|-
|-
| | 21
| 21
| | 2457 ~ 57
| 2457
|
| D
|-
|-
| | 22
| 22
| | 2574 ~ 174
| 2574
|
| E
|-
|-
| | 23
| 23
| | 2691 ~ 291
| 2691
|
| F
|-
|-
| | 24
| 24
| | 2808 ~ 408 (Pythagorean major third, 81:16)
| 2808
| 81/16
| C
|}
|}
[[Category:edf]]
 
[[Category:edonoi]]
== Music ==
[[Category:listen]]
; [[Carlo Serafini]]
* [http://www.seraph.it/dep/det/metashakti.mp3 ''Metashakti'']
 
; [[XэнкøрX]]
* [https://youtu.be/OSQljL4ANf8 "The Blame Game"] from ''State of the World (XLP)'' (2023)
 
[[Category:Listen]]
 
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/6edf"