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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>
'''33ed4''' is the [[ed4|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #080;">Equivocal Tuning</span>'''.
: This revision was by author [[User:jauernig|jauernig]] and made on <tt>2015-01-09 18:20:44 UTC</tt>.<br>
: The original revision id was <tt>536805560</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">33ed4 is the Equal Divisions of the Double Octave into 33 narrow chromatic semitones each of 72.727 [[xenharmonic/cent|cent]]s. It takes out every second step of 33edo and falls between 16edo and 17edo. So even degree 16 or degree 17 can play the role of the octave, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of equivocal tuning.


It has a 9/5 which is 0.6 cents sharp, a 7/5 which is 0.7 cents flat, and a 9/7 which is 1.3 cents sharp. Therefore it is closely related to 13edt, the Bohlen-Pierce scale, although it has no pure 3/1, which is 11.1 cents flat.
It has a [[9/5]] which is 0.6{{c}} sharp, a [[7/5]] which is 0.7{{c}} flat, and a [[9/7]] which is 1.3{{c}} sharp. Therefore it is closely related to [[13edt]], the [[Bohlen–Pierce scale]], although it has no pure [[3/1]], which is 11.1 cents flat. The lack of a [[3/2|pure fifth]] makes it also interesting.


Furthermore it has some 11-limit, 13-limit, 17-limit and even 23-limit which are very close (most of them under or nearby 1 cent).
Furthermore it has some [[11-limit]], [[13-limit]], [[17-limit]] and even [[23-limit]] which are very close (most of them under or nearby 1{{c}}).


Intervals
== Intervals ==
{| class="wikitable right-all mw-collapsible"
|+ style="font-size: 105%;" | Intervals of 33ed4
|-
! Degree
! Cents
! Nearest JI<br />interval
! Cents
! Difference<br />in cents
|-
| 1
| 72.7
| 24/23
| 73.7
| −1.0
|-
| 2
| 145.5
| 25/23
| 144.4
| 1.1
|-
| 3
| 218.2
| 17/15
| 216.6
| 1.6
|-
| 4
| 290.9
| 13/11
| 289.2
| 1.7
|-
| 5
| 363.6
| 16/13
| 359.5
| 4.1
|- style="font-weight: bold"
| 6
| 436.4
| 9/7
| 435.1
| 1.3
|-
| 7
| 509.1
| 51/38
| 509.4
| −0.3
|- style="font-weight: bold"
| 8
| 581.8
| 7/5
| 582.5
| −0.7
|-
| 9
| 654.5
| 19/13
| 657.0
| −2.5
|-
| 10
| 727.3
| 35/23
| 726.9
| 0.4
|-
| 11
| 800.0
| 27/17
| 800.9
| −0.9
|-
| 12
| 872.7
| 53/32
| 873.5
| −0.8
|-
| 13
| 945.5
| 19/11
| 946.2
| −0.7
|- style="font-weight: bold"
| 14
| 1018.2
| 9/5
| 1017.6
| 0.6
|-
| 15
| 1090.9
| 15/8
| 1088.3
| 2.6
|- style="font-weight: bold; color: #080"
| 16
| 1163.6
| 45/23
| 1161.9
| 1.7
|- style="font-weight: bold; color: #080"
| 17
| 1236.4
| 49/24
| 1235.7
| 0.7
|-
| 18
| 1309.1
| 32/15
| 1311.7
| −2.6
|- style="font-weight: bold"
| 19
| 1381.8
| 20/9
| 1382.4
| −0.6
|-
| 20
| 1454.5
| 44/19
| 1453.8
| 0.7
|-
| 21
| 1527.3
| 29/12
| 1527.6
| −0.3
|-
| 22
| 1600.0
| 68/27
| 1599.1
| 0.9
|-
| 23
| 1672.7
| 21/8
| 1670.8
| 1.9
|-
| 24
| 1745.5
| 52/19
| 1743.0
| 2.5
|- style="font-weight: bold"
| 25
| 1818.2
| 20/7
| 1817.5
| 0.7
|-
| 26
| 1890.9
| 116/39
| 1887.1
| 3.8
|- style="font-weight: bold"
| 27
| 1963.6
| 28/9
| 1964.9
| −1.3
|-
| 28
| 2036.4
| 13/4
| 2040.5
| −4.1
|-
| 29
| 2109.1
| 44/13
| 2110.8
| −1.7
|-
| 30
| 2181.8
| 60/17
| 2183.3
| −1.5
|-
| 31
| 2254.5
| 114/31
| 2254.4
| 0.1
|-
| 32
| 2327.3
| 23/6
| 2326.3
| 1.0
|- style="font-weight: bold"
| 33
| 2400.0
| 4/1
| 2400.0
| 0.0
|}


degree cents nearest JI interval in cent diff
== Harmonics ==
1 72,7 24/23 73,7 -1,0
{{Harmonics in equal
2 145,5 25/23 144,4 1,1
| steps = 33
3 218,2 17/15 216,6 1,6
| num = 4
4 290,9 13/11 289,2 1,7
| denom = 1
5 363,6 16/13 359,5 4,1
}}
6 436,4 9/ 7 435,1 1,3
{{Harmonics in equal
7 509,1 51/38 509,4 -0,3
| steps = 33
8 581,8 7/ 5 582,5 -0,7
| num = 4
9 654,5 19/13 657,0 -2,5
| denom = 1
10 727,3 35/23 726,9 0,4
| start = 12
11 800,0 27/17 800,9 -0,9
| collapsed = 1
12 872,7 53/32 873,5 -0,8
}}
13 945,5 19/11 946,2 -0,7
 
14 1018,2 9/ 5 1017,6 0,6
== Music ==
15 1090,9 15/ 8 1088,3 2,6
* [http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] — Set of compositions by Ahornberg
16 1163,6 45/23 1161,9 1,7
 
17 1236,4 49/24 1235,7 0,7
[[Category:Equal-step tuning]]
18 1309,1 32/15 1311,7 -2,6
{{todo|expand}}
19 1381,8 20/ 9 1382,4 -0,6
20 1454,5 44/19 1453,8 0,7
21 1527,3 29/12 1527,6 -0,3
22 1600,0 68/27 1599,1 0,9
23 1672,7 21/8 1670,8 1,9
24 1745,5 52/19 1743,0 2,5
25 1818,2 20/ 7 1817,5 0,7
26 1890,9 116/39 1887,1 3,8
27 1963,6 28/ 9 1964,9 -1,3
28 2036,4 13/ 4 2040,5 -4,1
29 2109,1 44/13 2110,8 -1,7
30 2181,8 60/17 2183,3 -1,5
31 2254,5 114/31 2254,4 0,1
32 2327,3 23/ 6 2326,3 1,0
33 2400,0 4/ 1 2400,0 0,0</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;33ed4&lt;/title&gt;&lt;/head&gt;&lt;body&gt;33ed4 is the Equal Divisions of the Double Octave into 33 narrow chromatic semitones each of 72.727 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent"&gt;cent&lt;/a&gt;s. It takes out every second step of 33edo and falls between 16edo and 17edo. So even degree 16 or degree 17 can play the role of the octave, depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of equivocal tuning.&lt;br /&gt;
&lt;br /&gt;
It has a 9/5 which is 0.6 cents sharp, a 7/5 which is 0.7 cents flat, and a 9/7 which is 1.3 cents sharp. Therefore it is closely related to 13edt, the Bohlen-Pierce scale, although it has no pure 3/1, which is 11.1 cents flat.&lt;br /&gt;
&lt;br /&gt;
Furthermore it has some 11-limit, 13-limit, 17-limit and even 23-limit which are very close (most of them under or nearby 1 cent).&lt;br /&gt;
&lt;br /&gt;
Intervals&lt;br /&gt;
&lt;br /&gt;
degree cents nearest JI interval in cent diff&lt;br /&gt;
1 72,7 24/23 73,7 -1,0&lt;br /&gt;
2 145,5 25/23 144,4 1,1&lt;br /&gt;
3 218,2 17/15 216,6 1,6&lt;br /&gt;
4 290,9 13/11 289,2 1,7&lt;br /&gt;
5 363,6 16/13 359,5 4,1&lt;br /&gt;
6 436,4 9/ 7 435,1 1,3&lt;br /&gt;
7 509,1 51/38 509,4 -0,3&lt;br /&gt;
8 581,8 7/ 5 582,5 -0,7&lt;br /&gt;
9 654,5 19/13 657,0 -2,5&lt;br /&gt;
10 727,3 35/23 726,9 0,4&lt;br /&gt;
11 800,0 27/17 800,9 -0,9&lt;br /&gt;
12 872,7 53/32 873,5 -0,8&lt;br /&gt;
13 945,5 19/11 946,2 -0,7&lt;br /&gt;
14 1018,2 9/ 5 1017,6 0,6&lt;br /&gt;
15 1090,9 15/ 8 1088,3 2,6&lt;br /&gt;
16 1163,6 45/23 1161,9 1,7&lt;br /&gt;
17 1236,4 49/24 1235,7 0,7&lt;br /&gt;
18 1309,1 32/15 1311,7 -2,6&lt;br /&gt;
19 1381,8 20/ 9 1382,4 -0,6&lt;br /&gt;
20 1454,5 44/19 1453,8 0,7&lt;br /&gt;
21 1527,3 29/12 1527,6 -0,3&lt;br /&gt;
22 1600,0 68/27 1599,1 0,9&lt;br /&gt;
23 1672,7 21/8 1670,8 1,9&lt;br /&gt;
24 1745,5 52/19 1743,0 2,5&lt;br /&gt;
25 1818,2 20/ 7 1817,5 0,7&lt;br /&gt;
26 1890,9 116/39 1887,1 3,8&lt;br /&gt;
27 1963,6 28/ 9 1964,9 -1,3&lt;br /&gt;
28 2036,4 13/ 4 2040,5 -4,1&lt;br /&gt;
29 2109,1 44/13 2110,8 -1,7&lt;br /&gt;
30 2181,8 60/17 2183,3 -1,5&lt;br /&gt;
31 2254,5 114/31 2254,4 0,1&lt;br /&gt;
32 2327,3 23/ 6 2326,3 1,0&lt;br /&gt;
33 2400,0 4/ 1 2400,0 0,0&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/33ed4"