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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:xenwolf|xenwolf]] and made on <tt>2011-06-27 03:34:41 UTC</tt>.<br>
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| : The original revision id was <tt>238906141</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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=
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| **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 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. |
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| ==Compositions== | | === Harmonics === |
| [[http://www.seraph.it/XenoTunes3.html|Repetitions 1]] [[http://www.seraph.it/XenoTunes3_files/repetitions1.mp3|play]] by Carlo Serafini</pre></div>
| | {{Harmonics in equal|4|3|2}} |
| <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"><html><head><title>4edf</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal division of the perfect fifth (3/2) into 4 equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Equal division of the perfect fifth (3/2) into 4 equal parts</h1>
| | == Intervals == |
| <br />
| | |
| <strong>4edf</strong> divides the <a class="wiki_link" href="/Perfect%20fifth">Perfect fifth</a> into 4 <a class="wiki_link" href="/equal">equal</a> intervals, each 175.489 <a class="wiki_link" href="/cent">cent</a>s in size.<br />
| | {| class="wikitable center-1 right-2 center-3" |
| This division is said to be used in traditional scales of Georgia. See the <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100326" rel="nofollow">discussion on the Yahoo tuning list</a>.<br />
| | |- |
| <br />
| | ! # |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Equal division of the perfect fifth (3/2) into 4 equal parts-Compositions"></a><!-- ws:end:WikiTextHeadingRule:2 -->Compositions</h2>
| | ! Cents |
| <a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3.html" rel="nofollow">Repetitions 1</a> <a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3_files/repetitions1.mp3" rel="nofollow">play</a> by Carlo Serafini</body></html></pre></div>
| | ! 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]] |
| Prime factorization
|
22
|
| Step size
|
175.489 ¢
|
| Octave
|
7\4edf (1228.42 ¢)
(semiconvergent)
|
| Twelfth
|
11\4edf (1930.38 ¢)
(semiconvergent)
|
| Consistency limit
|
6
|
| Distinct consistency limit
|
5
|
| Special properties
|
|
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