4edf: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''4EDF''' is the [[EDF|equal division of the just perfect fifth]] into four parts of 175.489 [[cent|cents]] each, corresponding to 6.8380 [[edo]]. It is related to the [[Tetracot family|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.
{{ED intro}} It corresponds to 6.8380[[edo]].  


This division is said to be used in traditional scales of [[Georgian|Georgia]].
== Theory ==
See the [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100326.html#100326 discussion on the Yahoo tuning list].
4edf is related to the [[tetracot]] temperament, which [[tempering out|tempers out]] [[20000/19683]] in the 5-limit.
 
=== Harmonics ===
{{Harmonics in equal|4|3|2}}


== Intervals ==
== Intervals ==


{| class="wikitable"
{| class="wikitable center-1 right-2 center-3"
|-
|-
! degree
! #
! cents value
! Cents
! octave-reduced cents value
! Tetratonic<br>Notation
! [[1L 3s (fifth-equivalent)|Neptunian]] notation
|-
|-
| colspan="2" | 0
| 0
|
| 0.0
| C
| C
|-
|-
| 1
| 1
| 175.489
| 175.5
|
| D
| D
|-
|-
| 2
| 2
| 350.978
| 351.0
|
| E
| E
|-
|-
| 3
| 3
| 526.466
| 526.5
|
| F  
| F  
|-
|-
| 4
| 4
| 701.955
| 702.0
|
| C
| C
|-
|-
| 5
| 5
| 877.444
| 877.4
|
| D
| D
|-
|-
| 6
| 6
| 1052.933
| 1052.9
|
| E
| E
|-
! colspan="4" | second octave
|-
|-
| 7
| 7
| 1228.421
| 1228.4
| 28.421
| F
| F
|-
|-
| 8
| 8
| 1403.910
| 1403.9
| 203.910
| C
| C
|-
! colspan="4" |nonet
|-
|-
| 9
| 9
| 1579.399
| 1579.4
| 379.399
| D
| D
|-
|-
| 10
| 10
| 1754.888
| 1754.9
| 554.888
| E
| E
|-
|-
| 11
| 11
| 1930.376
| 1930.4
| 730.376
| F
| F
|-
|-
| 12
| 12
| 2105.865
| 2105.9
| 905.865
| C
| C
|-
|-
| 13
| 13
| 2281.354
| 2281.4
| 1081.354
| D
| D
|-
! colspan="4" | third octave
|-
|-
| 14
| 14
| 2456.843
| 2456.8
| 56.843
| E
| E
|}
|}


== Compositions ==
== Music ==
* [http://www.seraph.it/dep/det/repetitions1.mp3 Repetitions 1] [http://www.youtube.com/watch?v=XEklMo0tIW0 Repetitions 1 video] by [[Carlo Serafini]]
; [[Carlo Serafini]]
* ''Repetitions 1'' – [http://www.seraph.it/dep/det/repetitions1.mp3 play] | [https://www.youtube.com/watch?v=XEklMo0tIW0 YouTube]


[[Category:Edf]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Nonoctave]]

Latest revision as of 06:09, 10 May 2024

← 3edf 4edf 5edf →
Prime factorization 22
Step size 175.489 ¢ 
Octave 7\4edf (1228.42 ¢)
(semiconvergent)
Twelfth 11\4edf (1930.38 ¢)
(semiconvergent)
Consistency limit 6
Distinct consistency limit 5
Special properties

4 equal divisions of the perfect fifth (abbreviated 4edf or 4ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 4 equal parts of about 175 ¢ each. Each step represents a frequency ratio of (3/2)1/4, or the 4th root of 3/2. It corresponds to 6.8380edo.

Theory

4edf is related to the tetracot temperament, which tempers out 20000/19683 in the 5-limit.

Harmonics

Approximation of harmonics in 4edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +28.4 +28.4 +56.8 +21.5 +56.8 -34.5 +85.3 +56.8 +49.9 +60.4 +85.3
Relative (%) +16.2 +16.2 +32.4 +12.3 +32.4 -19.7 +48.6 +32.4 +28.5 +34.4 +48.6
Steps
(reduced) 		7
(3) 		11
(3) 		14
(2) 		16
(0) 		18
(2) 		19
(3) 		21
(1) 		22
(2) 		23
(3) 		24
(0) 		25
(1)

Intervals

# Cents Tetratonic
Notation
0 0.0 C
1 175.5 D
2 351.0 E
3 526.5 F
4 702.0 C
5 877.4 D
6 1052.9 E
7 1228.4 F
8 1403.9 C
9 1579.4 D
10 1754.9 E
11 1930.4 F
12 2105.9 C
13 2281.4 D
14 2456.8 E

Music

Carlo Serafini
Retrieved from "https://en.xen.wiki/index.php?title=4edf&oldid=142776"