14edt: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''14edt''' is the 14 division of the tritave ([[3/2]]) with a step size of 135.854 [[cent]]. Is the simplest [[edt]] with a distinct form for each rotation of the Anti-Lambda scale. It can be seen as [[9edo]] with ~23 cent [[stretched octave]]s and so is a stretched octave pelog scale.
{{ED intro}}


{| class="wikitable"
== Theory ==
14edt is the simplest [[edt]] with a distinct form for each rotation of the [[5L 4s (3/1-equivalent)|antilambda]] scale. It can be seen as [[9edo]] with significantly [[stretched and compressed tuning|stretched]] [[octave]]s (~23{{c}}) and may be used as a tuning for [[Pelog]].
 
=== Harmonics ===
{{Harmonics in equal|14|3|1|intervals=integer|columns=11}}
{{Harmonics in equal|14|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 14edt (continued)}}
 
=== Subsets and supersets ===
Since 14 factors into primes as {{nowrap| 2 × 7 }}, 14edt has subset edts [[2edt]] and [[7edt]].
 
== Intervals ==
{| class="wikitable center-1 right-2 right-3"
|-
|-
! Degree
! #
! Cents
! [[Cent]]s
!Hekts
! [[Hekt]]s
! Notation
! Notation{{clarify}}
|-
|-
| 1
| 1
| 135.854
| 136
|92.857
| 93
| Cp/D\\
| Cp/D\\
|-
|-
| 2
| 2
| 271.708
| 272
|185.714
| 186
| D
| D
|-
|-
| 3
| 3
| 407.562
| 408
|278.571
| 279
| E
| E
|-
|-
| 4
| 4
| 543.416
| 543
|371.429
| 371
| Ep/F\\
| Ep/F\\
|-
|-
| 5
| 5
| 679.27
| 679
|464.286
| 464
| F
| F
|-
|-
| 6
| 6
| 815.124
| 815
|557.143
| 557
| G
| G
|-
|-
| 7
| 7
| 950.978
| 951
|650
| 650
| Gp/H\\
| Gp/H\\
|-
|-
| 8
| 8
| 1086.831
| 1087
|742.857
| 743
| H
| H
|-
|-
| 9
| 9
| 1222.685
| 1223
|835.714
| 836
| J
| J
|-
|-
| 10
| 10
| 1358.539
| 1359
|928.571
| 929
| Jp/A\\
| Jp/A\\
|-
|-
| 11
| 11
| 1494.393
| 1494
|1021.429
| 1021
| A
| A
|-
|-
| 12
| 12
| 1630.247
| 1630
|1114.286
| 1114
| Ap/B\\
| Ap/B\\
|-
|-
| 13
| 13
| 1766.101
| 1766
|1207.143
| 1207
| B
| B
|-
|-
| 14
| 14
| 1901.955
| 1902
|1300
| 1300
| C
| C
|}
|}


== Prime harmonics ==
== See also ==
{{Harmonics in equal|14|3|1|intervals=prime}}
* [[9edo]] – relative edo
* [[23ed6]] – relative ed6
* [[32ed12]] – relative ed12
 


[[Category:Edt]]
{{Todo|inline=1|expand}}
[[Category:Macrotonal]]
[[Category:Pelog]]

Latest revision as of 08:49, 27 May 2025

← 13edt 14edt 15edt →
Prime factorization 2 × 7
Step size 135.854 ¢ 
Octave 9\14edt (1222.69 ¢)
Consistency limit 7
Distinct consistency limit 6

14 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 14edt or 14ed3), is a nonoctave tuning system that divides the interval of 3/1 into 14 equal parts of about 136 ¢ each. Each step represents a frequency ratio of 31/14, or the 14th root of 3.

Theory

14edt is the simplest edt with a distinct form for each rotation of the antilambda scale. It can be seen as 9edo with significantly stretched octaves (~23 ¢) and may be used as a tuning for Pelog.

Harmonics

Approximation of harmonics in 14edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +22.7 +0.0 +45.4 +66.6 +22.7 +27.5 -67.8 +0.0 -46.5 +60.2 +45.4
Relative (%) +16.7 +0.0 +33.4 +49.0 +16.7 +20.3 -49.9 +0.0 -34.3 +44.3 +33.4
Steps
(reduced) 		9
(9) 		14
(0) 		18
(4) 		21
(7) 		23
(9) 		25
(11) 		26
(12) 		28
(0) 		29
(1) 		31
(3) 		32
(4)
Approximation of harmonics in 14edt (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +42.7 +50.2 +66.6 -45.1 -14.2 +22.7 +64.9 -23.9 +27.5 -53.0 +5.9 -67.8
Relative (%) +31.4 +37.0 +49.0 -33.2 -10.5 +16.7 +47.8 -17.6 +20.3 -39.0 +4.3 -49.9
Steps
(reduced) 		33
(5) 		34
(6) 		35
(7) 		35
(7) 		36
(8) 		37
(9) 		38
(10) 		38
(10) 		39
(11) 		39
(11) 		40
(12) 		40
(12)

Subsets and supersets

Since 14 factors into primes as 2 × 7, 14edt has subset edts 2edt and 7edt.

Intervals

# Cents Hekts Notation[clarification needed]
1 136 93 Cp/D\\
2 272 186 D
3 408 279 E
4 543 371 Ep/F\\
5 679 464 F
6 815 557 G
7 951 650 Gp/H\\
8 1087 743 H
9 1223 836 J
10 1359 929 Jp/A\\
11 1494 1021 A
12 1630 1114 Ap/B\\
13 1766 1207 B
14 1902 1300 C

See also


Todo: expand
Retrieved from "https://en.xen.wiki/index.php?title=14edt&oldid=197809"