4ed4/3: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Propose merge (very similar tunings)
Merged 125cET and 11ed11/5, marked for cleanup
 
Line 1: Line 1:
{{todo|merge articles|inline=1|text=Merge [[4ed4/3]] and [[1ed125c]]?}}
{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}
{{ED intro}}
Line 20: Line 19:
}}
}}


== Similar tunings ==
=== 125cET ===
'''125-cent equal temperament''' ('''125cET''', also known as '''1ed125c''' or '''APS125¢'''), is an [[equal]] [[nonoctave]] scale generated by making a continuous chain of intervals of exactly 125¢. It is a stretched tuning of 4ed4/3, with its step size wider by about 0.5{{c}}.


{{Stub}}
==== Intervals ====
{| class="wikitable mw-collapsible mw-collapsed"
|+
! | Degree
! | Cents
! | Associated ratios
! | Interval name
|-
| | 0
| | 0
| | [[1/1]]
| | unison
|-
| | 1
| | 125
| | [[14/13]], [[15/14]]
| | 2/3-tone, trienthird
|-
| | 2
| | 250
| | [[15/13]], [[22/19]]
| | semifourth
|-
| | 3
| | 375
| | [[5/4]]
| | narrow perde segah, marvelous major third, near just major third
|-
| | 4
| | 500
| | [[4/3]]
| | perfect fourth
|-
| | 5
| | 625
| | [[10/7]], [[23/16]]
| | pental diminished fifth, classic diminshed fifth
|-
| | 6
| | 750
| | [[17/11]], [[20/13]]
| | septendecimal subminor sixth
|-
| | 7
| | 875
| | [[5/3]]
| | major sixth
|-
| | 8
| | 1000
| | [[16/9]]
| | Pythagorean minor seventh
|-
| | 9
| | 1125
| | [[21/11]], [[23/12]]
| | classic ([[5-limit|5-limit]]) diminished octave
|-
| | 10
| | 1250
| | [[33/16]]
| |
|}
 
=== 11ed11/5 ===
{{ED intro|11ed11/5}} It is a compressed tuning of 4ed4/3, with its step size narrower by about 0.4{{c}}.
 
==== Intervals ====
{| class="wikitable mw-collapsible mw-collapsed"
|+
!Step
!Interval (¢)
!JI approximated
!Simplified ratios
|-
|1
|124.09
|29/27
|
|-
|2
|248.18
|22/19
|
|-
|3
|372.27
|31/25
|
|-
|4
|496.37
|8/6, 29/22
|4/3
|-
|5
|620.46
|52/36
|13/9
|-
|6
|744.55
|80/52
|20/13
|-
|7
|868.46
|10/6, 36/22
|5/3, 18/11
|-
|8
|992.73
|39/22, 55/31, 64/36
|16/9
|-
|9
|1116.82
|19/10
|
|-
|10
|1240.91
|39/19
|
|-
|11
|1365.00
|11/5
|
|}
The subgroup interpretation used is 11/5.6.8.10.19.25.27.29.31.39.45.52. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 10*11/5=22, 25*11/5=55.
 
{{todo|cleanup|inline=1|comment=Reorganize interval tables?}}
 
== Music ==
=== 125cET ===
; [[Chris Vaisvil]]
* [http://chrisvaisvil.com/canyon-diablo-fall/ Canyon Diablo Fall]
* [http://chrisvaisvil.com/crossing-over-125cet/ Crossing Over]
 
=== 11ed11/5 ===
; [[Francium]]
* "Will Go Down" from ''Holy Carp'' (2025) – [https://open.spotify.com/track/7xIEOPptbuOnJ9oDuPQAOE Spotify] | [https://francium223.bandcamp.com/track/will-go-down Bandcamp] | [https://www.youtube.com/watch?v=4UpHb0IGPL8 YouTube]

Latest revision as of 08:36, 28 June 2026

← 3ed4/3 4ed4/3 5ed4/3 →
Prime factorization 22 (highly composite)
Step size 124.511 ¢ 
Octave 10\4ed4/3 (1245.11 ¢) (→ 5\2ed4/3)
Twelfth 15\4ed4/3 (1867.67 ¢)
(semiconvergent)
Consistency limit 2
Distinct consistency limit 2

4 equal divisions of 4/3 (abbreviated 4ed4/3) is a nonoctave tuning system that divides the interval of 4/3 into 4 equal parts of about 125 ¢ each. Each step represents a frequency ratio of (4/3)1/4, or the 4th root of 4/3.

Intervals

Steps Cents Approximate ratios
0 0 1/1, 21/20
1 124.5 11/10, 13/12, 14/13, 18/17, 19/18, 20/19, 21/19
2 249 7/6, 10/9, 17/14, 17/15, 19/17
3 373.5 6/5, 9/7, 11/9, 13/11, 17/13, 20/17, 21/17
4 498 13/10, 14/11, 15/11, 18/13, 19/14, 19/15

Harmonics

Approximation of harmonics in 4ed4/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +45.1 -34.3 -34.3 -47.1 +10.8 -7.0 +10.8 +55.9 -2.0 -42.4 +55.9
Relative (%) +36.2 -27.5 -27.5 -37.8 +8.7 -5.6 +8.7 +44.9 -1.6 -34.1 +44.9
Steps
(reduced) 		10
(2) 		15
(3) 		19
(3) 		22
(2) 		25
(1) 		27
(3) 		29
(1) 		31
(3) 		32
(0) 		33
(1) 		35
(3)
Approximation of harmonics in 4ed4/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +41.9 +38.1 +43.2 +55.9 -49.0 -23.5 +7.4 +43.2 -41.3 +2.7 +50.2
Relative (%) +33.6 +30.6 +34.7 +44.9 -39.4 -18.8 +6.0 +34.7 -33.2 +2.1 +40.3
Steps
(reduced) 		36
(0) 		37
(1) 		38
(2) 		39
(3) 		39
(3) 		40
(0) 		41
(1) 		42
(2) 		42
(2) 		43
(3) 		44
(0)

Similar tunings

125cET

125-cent equal temperament (125cET, also known as 1ed125c or APS125¢), is an equal nonoctave scale generated by making a continuous chain of intervals of exactly 125¢. It is a stretched tuning of 4ed4/3, with its step size wider by about 0.5 ¢.

Intervals

Degree Cents Associated ratios Interval name
0 0 1/1 unison
1 125 14/13, 15/14 2/3-tone, trienthird
2 250 15/13, 22/19 semifourth
3 375 5/4 narrow perde segah, marvelous major third, near just major third
4 500 4/3 perfect fourth
5 625 10/7, 23/16 pental diminished fifth, classic diminshed fifth
6 750 17/11, 20/13 septendecimal subminor sixth
7 875 5/3 major sixth
8 1000 16/9 Pythagorean minor seventh
9 1125 21/11, 23/12 classic (5-limit) diminished octave
10 1250 33/16

11ed11/5

11 equal divisions of 11/5 (abbreviated 11ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 11 equal parts of about 124 ¢ each. Each step represents a frequency ratio of (11/5)1/11, or the 11th root of 11/5. It is a compressed tuning of 4ed4/3, with its step size narrower by about 0.4 ¢.

Intervals

Step Interval (¢) JI approximated Simplified ratios
1 124.09 29/27
2 248.18 22/19
3 372.27 31/25
4 496.37 8/6, 29/22 4/3
5 620.46 52/36 13/9
6 744.55 80/52 20/13
7 868.46 10/6, 36/22 5/3, 18/11
8 992.73 39/22, 55/31, 64/36 16/9
9 1116.82 19/10
10 1240.91 39/19
11 1365.00 11/5

The subgroup interpretation used is 11/5.6.8.10.19.25.27.29.31.39.45.52. Other interpretations are possible. Don't forget that fractions can multiply, e.g. 10*11/5=22, 25*11/5=55.

Todo: cleanup

Reorganize interval tables?

Music

125cET

Chris Vaisvil

11ed11/5

Francium
Retrieved from "https://en.xen.wiki/index.php?title=4ed4/3&oldid=232865"