4edf: Difference between revisions

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**Imported revision 17888191 - 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>2008-02-26 11:44:28 UTC</tt>.<br>
 
: The original revision id was <tt>17888191</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
4edf is related to the [[tetracot]] temperament, which [[tempering out|tempers out]] [[20000/19683]] in the 5-limit.
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>
=== Harmonics ===
<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=
{{Harmonics in equal|4|3|2}}
==Compositions==  
 
[[http://www.seraph.it/XenoTunes3.html|Repetitions 1]] by Carlo Serafini </pre></div>
== Intervals ==
<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;
{| class="wikitable center-1 right-2 center-3"
&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-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Compositions&lt;/h2&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3.html" rel="nofollow"&gt;Repetitions 1&lt;/a&gt; by Carlo Serafini&lt;/body&gt;&lt;/html&gt;</pre></div>
! #
! Cents
! Tetratonic<br>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]]
* ''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"