Wikispaces>Andrew_Heathwaite |
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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{todo|merge articles|inline=1|text=Merge into [[37ed4]]?}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | '''65-cent equal temperament''' ('''65cET''', also known as '''1ed65c''' or '''APS65¢'''), is an [[equal]] [[nonoctave]] scale generated by making a continuous chain of intervals of exactly 65¢. It is a good tuning in the 2.3.5.7.11.13.27 subgroup, and is closely related to [[37edo]] and [[37ed4]]. 37 degrees of 1ed65c is exactly 2405¢, which is the 4/1 double octave plus 5¢. Thus, 1ed65c can be seen as a stretched version of 37ed4. |
| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-11-19 21:46:07 UTC</tt>.<br>
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| : The original revision id was <tt>277297748</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">65cET is an [[equal]] [[nonoctave]] scale generated by making a continuous chain of intervals of exactly 65¢. It is a good tuning in the 2.3.5.7.11.13.27 subgroup, and is closely related to [[37edo]] and [[37ED4]]. A characteristic pentad of 65cET is 8:10:13:14:22. 37 degrees of 65cET is exactly 2405¢, which is the 4/1 double octave plus 5¢. Thus, 65cET can be seen as a stretched version of 37ED4.
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|
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| ==Intervals== | | == Theory == |
| | A characteristic pentad of 1ed65c is 8:10:13:14:22 and it's utonal inversion. |
|
| |
|
| ||~ Degree of 65cET ||~ Cents Value ||
| | === Harmonics === |
| || 0 || 0 ||
| | {{harmonics in cet|65}} |
| || 1 || 65 ||
| |
| || 2 || 130 ||
| |
| || 3 || 195 ||
| |
| || 4 || 260 ||
| |
| || 5 || 325 ||
| |
| || 6 || 390 ||
| |
| || 7 || 455 ||
| |
| || 8 || 520 ||
| |
| || 9 || 585 ||
| |
| || 10 || 650 ||
| |
| || 11 || 715 ||
| |
| || 12 || 780 ||
| |
| || 13 || 845 ||
| |
| || 14 || 910 ||
| |
| || 15 || 975 ||
| |
| || 16 || 1040 ||
| |
| || 17 || 1105 ||
| |
| || 18 || 1170 ||
| |
| || 19 || 1235 ||
| |
| || 20 || 1300 ||
| |
| || 21 || 1365 ||
| |
| || 22 || 1430 ||
| |
| || 23 || 1495 ||
| |
| || 24 || 1560 ||
| |
| || 25 || 1625 ||
| |
| || 26 || 1690 ||
| |
| || 27 || 1755 ||
| |
| || 28 || 1820 ||
| |
| || 29 || 1885 ||
| |
| || 30 || 1950 ||
| |
| || 31 || 2015 ||
| |
| || 32 || 2080 ||
| |
| || 33 || 2145 ||
| |
| || 34 || 2210 ||
| |
| || 35 || 2275 ||
| |
| || 36 || 2340 ||
| |
| || 37 || 2405 ||</pre></div>
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| <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>65cET</title></head><body>65cET is an <a class="wiki_link" href="/equal">equal</a> <a class="wiki_link" href="/nonoctave">nonoctave</a> scale generated by making a continuous chain of intervals of exactly 65¢. It is a good tuning in the 2.3.5.7.11.13.27 subgroup, and is closely related to <a class="wiki_link" href="/37edo">37edo</a> and <a class="wiki_link" href="/37ED4">37ED4</a>. A characteristic pentad of 65cET is 8:10:13:14:22. 37 degrees of 65cET is exactly 2405¢, which is the 4/1 double octave plus 5¢. Thus, 65cET can be seen as a stretched version of 37ED4.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h2>
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| <br />
| |
|
| |
|
| | == Intervals == |
| | {| class="wikitable" |
| | |- |
| | ! | Degree of 1ed65c |
| | ! | Cents Value |
| | |- |
| | | | 0 |
| | | | 0 |
| | |- |
| | | | 1 |
| | | | 65 |
| | |- |
| | | | 2 |
| | | | 130 |
| | |- |
| | | | 3 |
| | | | 195 |
| | |- |
| | | | 4 |
| | | | 260 |
| | |- |
| | | | 5 |
| | | | 325 |
| | |- |
| | | | 6 |
| | | | 390 |
| | |- |
| | | | 7 |
| | | | 455 |
| | |- |
| | | | 8 |
| | | | 520 |
| | |- |
| | | | 9 |
| | | | 585 |
| | |- |
| | | | 10 |
| | | | 650 |
| | |- |
| | | | 11 |
| | | | 715 |
| | |- |
| | | | 12 |
| | | | 780 |
| | |- |
| | | | 13 |
| | | | 845 |
| | |- |
| | | | 14 |
| | | | 910 |
| | |- |
| | | | 15 |
| | | | 975 |
| | |- |
| | | | 16 |
| | | | 1040 |
| | |- |
| | | | 17 |
| | | | 1105 |
| | |- |
| | | | 18 |
| | | | 1170 |
| | |- |
| | | | 19 |
| | | | 1235 |
| | |- |
| | | | 20 |
| | | | 1300 |
| | |- |
| | | | 21 |
| | | | 1365 |
| | |- |
| | | | 22 |
| | | | 1430 |
| | |- |
| | | | 23 |
| | | | 1495 |
| | |- |
| | | | 24 |
| | | | 1560 |
| | |- |
| | | | 25 |
| | | | 1625 |
| | |- |
| | | | 26 |
| | | | 1690 |
| | |- |
| | | | 27 |
| | | | 1755 |
| | |- |
| | | | 28 |
| | | | 1820 |
| | |- |
| | | | 29 |
| | | | 1885 |
| | |- |
| | | | 30 |
| | | | 1950 |
| | |- |
| | | | 31 |
| | | | 2015 |
| | |- |
| | | | 32 |
| | | | 2080 |
| | |- |
| | | | 33 |
| | | | 2145 |
| | |- |
| | | | 34 |
| | | | 2210 |
| | |- |
| | | | 35 |
| | | | 2275 |
| | |- |
| | | | 36 |
| | | | 2340 |
| | |- |
| | | | 37 |
| | | | 2405 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | == Music == |
| <tr>
| | * [http://chrisvaisvil.com/?p=2319 Slumber of Thought] by [[Chris Vaisvil]] |
| <th>Degree of 65cET<br />
| | * [http://micro.soonlabel.com/65cET_37ed4/20120527-65ct-malathion.mp3 Malathion in 65cET] by Chris Vaisvil |
| </th>
| |
| <th>Cents Value<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>0<br />
| |
| </td>
| |
| <td>0<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>65<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>130<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>195<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>260<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>325<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>390<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>455<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>520<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>585<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>650<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>715<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>780<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>845<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>910<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
| |
| </td>
| |
| <td>975<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>1040<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
| |
| </td>
| |
| <td>1105<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18<br />
| |
| </td>
| |
| <td>1170<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19<br />
| |
| </td>
| |
| <td>1235<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
| |
| </td>
| |
| <td>1300<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21<br />
| |
| </td>
| |
| <td>1365<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>1430<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>1495<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
| |
| </td>
| |
| <td>1560<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25<br />
| |
| </td>
| |
| <td>1625<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26<br />
| |
| </td>
| |
| <td>1690<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>1755<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28<br />
| |
| </td>
| |
| <td>1820<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>1885<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
| |
| <td>1950<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
| |
| </td>
| |
| <td>2015<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
| |
| </td>
| |
| <td>2080<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
| |
| </td>
| |
| <td>2145<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34<br />
| |
| </td>
| |
| <td>2210<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
| |
| </td>
| |
| <td>2275<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36<br />
| |
| </td>
| |
| <td>2340<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
| |
| <td>2405<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | [[Category:37ed4]] |
|
Todo: merge articles
Merge into 37ed4?
|
65-cent equal temperament (65cET, also known as 1ed65c or APS65¢), is an equal nonoctave scale generated by making a continuous chain of intervals of exactly 65¢. It is a good tuning in the 2.3.5.7.11.13.27 subgroup, and is closely related to 37edo and 37ed4. 37 degrees of 1ed65c is exactly 2405¢, which is the 4/1 double octave plus 5¢. Thus, 1ed65c can be seen as a stretched version of 37ed4.
Theory
A characteristic pentad of 1ed65c is 8:10:13:14:22 and it's utonal inversion.
Harmonics
Approximation of harmonics in 1ed65c
| Harmonic
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Error
|
Absolute (¢)
|
-30.0
|
-17.0
|
+5.0
|
+8.7
|
+18.0
|
+11.2
|
-25.0
|
+31.1
|
-21.3
|
+8.7
|
-12.0
|
| Relative (%)
|
-46.2
|
-26.1
|
+7.7
|
+13.4
|
+27.8
|
+17.2
|
-38.5
|
+47.8
|
-32.8
|
+13.4
|
-18.4
|
| Step
|
18
|
29
|
37
|
43
|
48
|
52
|
55
|
59
|
61
|
64
|
66
|
Intervals
| Degree of 1ed65c
|
Cents Value
|
| 0
|
0
|
| 1
|
65
|
| 2
|
130
|
| 3
|
195
|
| 4
|
260
|
| 5
|
325
|
| 6
|
390
|
| 7
|
455
|
| 8
|
520
|
| 9
|
585
|
| 10
|
650
|
| 11
|
715
|
| 12
|
780
|
| 13
|
845
|
| 14
|
910
|
| 15
|
975
|
| 16
|
1040
|
| 17
|
1105
|
| 18
|
1170
|
| 19
|
1235
|
| 20
|
1300
|
| 21
|
1365
|
| 22
|
1430
|
| 23
|
1495
|
| 24
|
1560
|
| 25
|
1625
|
| 26
|
1690
|
| 27
|
1755
|
| 28
|
1820
|
| 29
|
1885
|
| 30
|
1950
|
| 31
|
2015
|
| 32
|
2080
|
| 33
|
2145
|
| 34
|
2210
|
| 35
|
2275
|
| 36
|
2340
|
| 37
|
2405
|
Music
