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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>
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| : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-01-01 04:44:18 UTC</tt>.<br>
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| : The original revision id was <tt>288953957</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">=10 equal divisions of the 5th harmonic=
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| Half of [[20ed5]] (obviously). But it has important characteristics of its own:
| | In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to. |
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| | It is especially important as a structural framework for the [[5.7.11.13 subgroup]]. |
| | |
| | == Harmonics == |
| | {{Harmonics in equal |
| | | steps = 10 |
| | | num = 5 |
| | | denom = 1 |
| | }} |
| | {{Harmonics in equal |
| | | steps = 10 |
| | | num = 5 |
| | | denom = 1 |
| | | start = 12 |
| | | collapsed = 1 |
| | }} |
|
| |
|
| In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.
| | == Intervals == |
| | {| class="wikitable" |
| | |+ |
| | !Degree |
| | !Cents |
| | !5.7.11.13 intervals |
| | |- |
| | |0 |
| | |0.000 |
| | |1/1 |
| | |- |
| | |1 |
| | |278.631 |
| | |13/11, 55/49 |
| | |- |
| | |2 |
| | |557.263 |
| | |7/5 |
| | |- |
| | |3 |
| | |835.894 |
| | |11/7 |
| | |- |
| | |4 |
| | |1114.525 |
| | |13/7, 25/13 |
| | |- |
| | |5 |
| | |1393.157 |
| | |11/5, 25/11 |
| | |- |
| | |6 |
| | |1671.788 |
| | |13/5, 35/13 |
| | |- |
| | |7 |
| | |1950.420 |
| | |35/11 |
| | |- |
| | |8 |
| | |2229.051 |
| | |49/13 |
| | |- |
| | |9 |
| | |2507.682 |
| | |49/11 |
| | |- |
| | |10 |
| | |2786.314 |
| | |5/1 |
| | |} |
|
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| As 5ed5 is the simplest [[hyperpyth]] tuning, analogous to [[5edo]] and [[4edt]] in their own spheres, this, its double, can be compared, structurally, to, [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.
| | == Subsets and supersets == |
| | Half of [[20ed5]]. |
|
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|
| Adding octaves, strangely enough, relates this tuning to [[53edo]].
| | As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals. |
|
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| 0: 1/1
| | Octaves can be added by dividing the step in three to get [[13edo]] with octaves 7 cents sharp. If octaves are instead made just, prime 7 becomes very flat, as well as prime 5 to a lesser extent. Alternatively, the step can be divided in ten to get [[43edo]]. |
| 1: 278.631 cents 13/11
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| 2: 557.263 cents 7/5
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| 3: 835.894 cents
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| 4: 1114.525 cents "9/5"
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| 5: 1393.157 cents 11/5 | |
| 6: 1671.788 cents 13/5
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| 7: 1950.420 cents
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| 8: 2229.051 cents "17/5"
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| 9: 2507.682 cents 21/5
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| 10: 5/1
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| Music: | | == Music == |
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| [[http://www.youtube.com/watch?v=tjD7Es05zuI|Weird Blues]] -- Kosmorsky</pre></div>
| | [http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky |
| <h4>Original HTML content:</h4>
| | [[Category:5th_harmonic]] |
| <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>10ed5</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x10 equal divisions of the 5th harmonic"></a><!-- ws:end:WikiTextHeadingRule:0 -->10 equal divisions of the 5th harmonic</h1>
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| <br />
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| Half of <a class="wiki_link" href="/20ed5">20ed5</a> (obviously). But it has important characteristics of its own:<br />
| |
| <br />
| |
| In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.<br />
| |
| <br />
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| As 5ed5 is the simplest <a class="wiki_link" href="/hyperpyth">hyperpyth</a> tuning, analogous to <a class="wiki_link" href="/5edo">5edo</a> and <a class="wiki_link" href="/4edt">4edt</a> in their own spheres, this, its double, can be compared, structurally, to, <a class="wiki_link" href="/10edo">10edo</a>. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.<br />
| |
| <br />
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| Adding octaves, strangely enough, relates this tuning to <a class="wiki_link" href="/53edo">53edo</a>.<br />
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| <br />
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| 0: 1/1<br />
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| 1: 278.631 cents 13/11<br />
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| 2: 557.263 cents 7/5<br />
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| 3: 835.894 cents<br />
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| 4: 1114.525 cents &quot;9/5&quot;<br />
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| 5: 1393.157 cents 11/5<br />
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| 6: 1671.788 cents 13/5<br />
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| 7: 1950.420 cents<br />
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| 8: 2229.051 cents &quot;17/5&quot;<br />
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| 9: 2507.682 cents 21/5<br />
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| 10: 5/1<br />
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| <br />
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| Music:<br />
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| <br />
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| <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=tjD7Es05zuI" rel="nofollow">Weird Blues</a> -- Kosmorsky</body></html></pre></div>
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| Prime factorization
|
2 × 5
|
| Step size
|
278.631 ¢
|
| Octave
|
4\10ed5 (1114.53 ¢) (→ 2\5ed5)
|
| Twelfth
|
7\10ed5 (1950.42 ¢)
(semiconvergent)
|
| Consistency limit
|
3
|
| Distinct consistency limit
|
3
|
In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.
It is especially important as a structural framework for the 5.7.11.13 subgroup.
Harmonics
Approximation of harmonics in 10ed5
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Error
|
Absolute (¢)
|
-85
|
+48
|
+108
|
+0
|
-37
|
-25
|
+22
|
+97
|
-85
|
+28
|
-122
|
| Relative (%)
|
-30.7
|
+17.4
|
+38.6
|
+0.0
|
-13.3
|
-9.1
|
+8.0
|
+34.8
|
-30.7
|
+10.1
|
-44.0
|
Steps
(reduced)
|
4
(4)
|
7
(7)
|
9
(9)
|
10
(0)
|
11
(1)
|
12
(2)
|
13
(3)
|
14
(4)
|
14
(4)
|
15
(5)
|
15
(5)
|
Approximation of harmonics in 10ed5
| Harmonic
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
| Error
|
Absolute (¢)
|
+18
|
-111
|
+48
|
-63
|
+110
|
+11
|
-82
|
+108
|
+23
|
-57
|
-134
|
| Relative (%)
|
+6.3
|
-39.7
|
+17.4
|
-22.7
|
+39.6
|
+4.1
|
-29.5
|
+38.6
|
+8.3
|
-20.6
|
-48.2
|
Steps
(reduced)
|
16
(6)
|
16
(6)
|
17
(7)
|
17
(7)
|
18
(8)
|
18
(8)
|
18
(8)
|
19
(9)
|
19
(9)
|
19
(9)
|
19
(9)
|
Intervals
| Degree
|
Cents
|
5.7.11.13 intervals
|
| 0
|
0.000
|
1/1
|
| 1
|
278.631
|
13/11, 55/49
|
| 2
|
557.263
|
7/5
|
| 3
|
835.894
|
11/7
|
| 4
|
1114.525
|
13/7, 25/13
|
| 5
|
1393.157
|
11/5, 25/11
|
| 6
|
1671.788
|
13/5, 35/13
|
| 7
|
1950.420
|
35/11
|
| 8
|
2229.051
|
49/13
|
| 9
|
2507.682
|
49/11
|
| 10
|
2786.314
|
5/1
|
Subsets and supersets
Half of 20ed5.
As 5ed5 is the simplest hyperpyth tuning (analogous to 5edo and 4edt in their own spheres) this, its double, can be compared structurally to 10edo. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.
Octaves can be added by dividing the step in three to get 13edo with octaves 7 cents sharp. If octaves are instead made just, prime 7 becomes very flat, as well as prime 5 to a lesser extent. Alternatively, the step can be divided in ten to get 43edo.
Music
Weird Blues -- Kosmorsky