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**Imported revision 624205195 - Original comment: **
Move the only nontrivial sentence to the theory section
 
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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}} It corresponds to 6.8380[[edo]].  
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-12-23 15:11:35 UTC</tt>.<br>
: The original revision id was <tt>624205195</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">=Equal division of the perfect fifth (3/2) into 4 equal parts=


**4edf** divides the [[Perfect fifth]] into 4 [[equal]] intervals, each 175.489 [[cent]]s in size.
== Theory ==
This division is said to be used in traditional scales of [[Georgian|Georgia]]. See the [[http://launch.groups.yahoo.com/group/tuning/message/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.


==Intervals==  
=== Harmonics ===
||~ degree ||~ cents value ||~ octave-reduced cents value ||
{{Harmonics in equal|4|3|2}}
|| 0 || 0 ||  ||
|| 1 || 175.489 ||  ||
|| 2 || 350.978 ||  ||
|| 3 || 526.466 ||  ||
|| 4 || 701.955 ||  ||
|| 5 || 877.444 ||  ||
|| 6 || 1052.933 ||  ||
||~ second octave ||~  ||~  ||
|| 7 || 1228.421 || 28.421 ||
|| 8 || 1403.910 || 203.910 ||
|| 9 || 1579.399 || 379.399 ||
|| 10 || 1754.888 || 554.888 ||
|| 11 || 1930.376 || 730.376 ||
|| 12 || 2105.865 || 905.865 ||
|| 13 || 2281.354 || 1081.354 ||
||~ third octave ||~  ||~  ||
|| 14 || 2456.843 || 56.843 ||


==Compositions==
== Intervals ==
[[http://www.seraph.it/dep/det/repetitions1.mp3|Repetitions 1]] [[http://www.youtube.com/watch?v=XEklMo0tIW0|Repetitions 1 video]] by [[Carlo Serafini]]</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;4edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Equal division of the perfect fifth (3/2) into 4 equal parts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Equal division of the perfect fifth (3/2) into 4 equal parts&lt;/h1&gt;
&lt;br /&gt;
&lt;strong&gt;4edf&lt;/strong&gt; divides the &lt;a class="wiki_link" href="/Perfect%20fifth"&gt;Perfect fifth&lt;/a&gt; into 4 &lt;a class="wiki_link" href="/equal"&gt;equal&lt;/a&gt; intervals, each 175.489 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s in size.&lt;br /&gt;
This division is said to be used in traditional scales of &lt;a class="wiki_link" href="/Georgian"&gt;Georgia&lt;/a&gt;. See the &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100326" rel="nofollow"&gt;discussion on the Yahoo tuning list&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Equal division of the perfect fifth (3/2) into 4 equal parts-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals&lt;/h2&gt;


&lt;table class="wiki_table"&gt;
{| class="wikitable center-1 right-2 center-3"
    &lt;tr&gt;
|-
        &lt;th&gt;degree&lt;br /&gt;
! #
&lt;/th&gt;
! Cents
        &lt;th&gt;cents value&lt;br /&gt;
! Tetratonic<br>Notation
&lt;/th&gt;
|-
        &lt;th&gt;octave-reduced cents value&lt;br /&gt;
| 0
&lt;/th&gt;
| 0.0
    &lt;/tr&gt;
| C
    &lt;tr&gt;
|-
        &lt;td&gt;0&lt;br /&gt;
| 1
&lt;/td&gt;
| 175.5
        &lt;td&gt;0&lt;br /&gt;
| D
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| 2
&lt;/td&gt;
| 351.0
    &lt;/tr&gt;
| E
    &lt;tr&gt;
|-
        &lt;td&gt;1&lt;br /&gt;
| 3
&lt;/td&gt;
| 526.5
        &lt;td&gt;175.489&lt;br /&gt;
| F
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| 4
&lt;/td&gt;
| 702.0
    &lt;/tr&gt;
| C
    &lt;tr&gt;
|-
        &lt;td&gt;2&lt;br /&gt;
| 5
&lt;/td&gt;
| 877.4
        &lt;td&gt;350.978&lt;br /&gt;
| D
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| 6
&lt;/td&gt;
| 1052.9
    &lt;/tr&gt;
| E
    &lt;tr&gt;
|-
        &lt;td&gt;3&lt;br /&gt;
| 7
&lt;/td&gt;
| 1228.4
        &lt;td&gt;526.466&lt;br /&gt;
| F
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| 8
&lt;/td&gt;
| 1403.9
    &lt;/tr&gt;
| C
    &lt;tr&gt;
|-
        &lt;td&gt;4&lt;br /&gt;
| 9
&lt;/td&gt;
| 1579.4
        &lt;td&gt;701.955&lt;br /&gt;
| D
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| 10
&lt;/td&gt;
| 1754.9
    &lt;/tr&gt;
| E
    &lt;tr&gt;
|-
        &lt;td&gt;5&lt;br /&gt;
| 11
&lt;/td&gt;
| 1930.4
        &lt;td&gt;877.444&lt;br /&gt;
| F
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| 12
&lt;/td&gt;
| 2105.9
    &lt;/tr&gt;
| C
    &lt;tr&gt;
|-
        &lt;td&gt;6&lt;br /&gt;
| 13
&lt;/td&gt;
| 2281.4
        &lt;td&gt;1052.933&lt;br /&gt;
| D
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| 14
&lt;/td&gt;
| 2456.8
    &lt;/tr&gt;
| E
    &lt;tr&gt;
|}
        &lt;th&gt;second octave&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1228.421&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;28.421&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1403.910&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.910&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1579.399&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;379.399&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1754.888&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;554.888&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1930.376&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;730.376&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2105.865&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;905.865&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2281.354&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1081.354&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th&gt;third octave&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2456.843&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;56.843&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
== Music ==
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Equal division of the perfect fifth (3/2) into 4 equal parts-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Compositions&lt;/h2&gt;
; [[Carlo Serafini]]
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/repetitions1.mp3" rel="nofollow"&gt;Repetitions 1&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=XEklMo0tIW0" rel="nofollow"&gt;Repetitions 1 video&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
* ''Repetitions 1'' – [http://www.seraph.it/dep/det/repetitions1.mp3 play] | [https://www.youtube.com/watch?v=XEklMo0tIW0 YouTube]
 
[[Category:Listen]]

Latest revision as of 06:09, 10 May 2024

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

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"