14edt: Difference between revisions

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+subsets and supersets; +see also
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-23 18:04:33 UTC</tt>.<br>
: The original revision id was <tt>541891896</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">This is the simplest edt with a distinct form for each rotation of the Anti-Lambda scale. It is 9edo with ~23 cent stretched octaves.and so is a stretched octave pelog scale,


||~ Degree ||~ cents ||~ notation ||
== Theory ==
|| 1/14 || 135.85 || Cp/D@ ||
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]].
|| 2/14 || 271.71 || D ||
|| 3/14 || 407.56 || E ||
|| 4/14 || 543.42 || Ep/F@ ||
|| 5/14 || 679.27 || F ||
|| 6/14 || 815.12 || G ||
|| 7/14 || 950.98 || Gp/H@ ||
|| 8/14 || 1086.83 || H ||
|| 9/14 || 1222.685 || J ||
|| 10/14 || 1358.54 || Jp/A@ ||
|| 11/14 || 1494.39 || A ||
|| 12/14 || 1630.25 || Ap/B@ ||
|| 13/14 || 1766.10 || B ||
|| 14/14 || 1901.955 || C ||</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;14edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the simplest edt with a distinct form for each rotation of the Anti-Lambda scale. It is 9edo with ~23 cent stretched octaves.and so is a stretched octave pelog scale,&lt;br /&gt;
&lt;br /&gt;


=== 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)}}


&lt;table class="wiki_table"&gt;
=== Subsets and supersets ===
    &lt;tr&gt;
Since 14 factors into primes as {{nowrap| 2 × 7 }}, 14edt has subset edts [[2edt]] and [[7edt]].  
        &lt;th&gt;Degree&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notation&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;135.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cp/D@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;407.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;543.42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ep/F@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;679.27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;815.12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;950.98&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gp/H@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1086.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;H&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1222.685&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;J&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1358.54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Jp/A@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1494.39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1630.25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ap/B@&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1766.10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1901.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Intervals ==
{| class="wikitable center-1 right-2 right-3"
|-
! #
! [[Cent]]s
! [[Hekt]]s
! Notation{{clarify}}
|-
| 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 ==
* [[9edo]] – relative edo
* [[23ed6]] – relative ed6
* [[32ed12]] – relative ed12
 
 
{{Todo|inline=1|expand}}
[[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"