14edt: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{ED intro}} It is the simplest [[edt]] with a distinct form for each rotation of the [[Anti-Lambda]] 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]].
{{ED intro}}  
 
== 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|Approximation of harmonics in 14edt (continued)}}


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable center-1 right-2 right-3"
|-
|-
! Degree
! #
! Cents
! [[Cent]]s
! [[Hekt]]s
! [[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 ==
{{Harmonics in equal|14|3|1|intervals=prime}}


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

Revision as of 08:47, 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
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)

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


Todo: expand
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