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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | =<span style="color: #008523; font-family: 'Times New Roman',Times,serif; font-size: 113%;">55 tone equal temperament</span>= |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2012-04-16 07:02:46 UTC</tt>.<br>
| |
| : The original revision id was <tt>320984000</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">=<span style="color: #008523; font-family: 'Times New Roman',Times,serif; font-size: 113%;">55 tone equal temperament</span>=
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|
| **//55edo//** divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to [[1-6 Syntonic Comma Meantone|1/6 comma meantone]] (and is almost exactly 10/57 comma meantone.) [[http://en.wikipedia.org/wiki/Georg_Philipp_Telemann|Telemann]] suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by [[http://en.wikipedia.org/wiki/Leopold_Mozart|Leopold]] and [[http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart|Wolfgang Mozart]]. It can also be used for [[Meantone family|mohajira and liese]] temperaments.
| | '''''55edo''''' divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to [[1-6_Syntonic_Comma_Meantone|1/6 comma meantone]] (and is almost exactly 10/57 comma meantone.) [http://en.wikipedia.org/wiki/Georg_Philipp_Telemann Telemann] suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by [http://en.wikipedia.org/wiki/Leopold_Mozart Leopold] and [http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart Wolfgang Mozart]. It can also be used for [[Meantone_family|mohajira and liese]] temperaments. |
|
| |
|
| 5-limit commas: 81/80, <31 1 -14| | | 5-limit commas: 81/80, <31 1 -14| |
| Line 16: |
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| 11-limit commas: 81/80, 121/120, 176/175, 686/675 | | 11-limit commas: 81/80, 121/120, 176/175, 686/675 |
|
| |
|
| ==Intervals== | | ==Intervals== |
| || Degrees of 55-EDO || Cents value ||
| |
| || 0 || 0 ||
| |
| || 1 || 21.818 ||
| |
| || 2 || 43.636 ||
| |
| || 3 || 65.455 ||
| |
| || 4 || 87.273 ||
| |
| || 5 || 109.091 ||
| |
| || 6 || 130.909 ||
| |
| || 7 || 152.727 ||
| |
| || 8 || 174.545 ||
| |
| || 9 || 196.364 ||
| |
| || 10 || 218.182 ||
| |
| || 11 || 240.000 ||
| |
| || 12 || 261.818 ||
| |
| || 13 || 283.636 ||
| |
| || 14 || 305.455 ||
| |
| || 15 || 327.273 ||
| |
| || 16 || 349.091 ||
| |
| || 17 || 370.909 ||
| |
| || 18 || 392.727 ||
| |
| || 19 || 414.545 ||
| |
| || 20 || 436.364 ||
| |
| || 21 || 458.182 ||
| |
| || 22 || 480.000 ||
| |
| || 23 || 501.818 ||
| |
| || 24 || 523.636 ||
| |
| || 25 || 545.455 ||
| |
| || 26 || 567.273 ||
| |
| || 27 || 589.091 ||
| |
| || 28 || 610.909 ||
| |
| || 29 || 632.727 ||
| |
| || 30 || 654.545 ||
| |
| || 31 || 676.364 ||
| |
| || 32 || 698.182 ||
| |
| || 33 || 720.000 ||
| |
| || 34 || 741.818 ||
| |
| || 35 || 763.636 ||
| |
| || 36 || 785.455 ||
| |
| || 37 || 807.273 ||
| |
| || 38 || 829.091 ||
| |
| || 39 || 850.909 ||
| |
| || 40 || 872.727 ||
| |
| || 41 || 894.545 ||
| |
| || 42 || 916.364 ||
| |
| || 43 || 938.182 ||
| |
| || 44 || 960.000 ||
| |
| || 45 || 981.818 ||
| |
| || 46 || 1003.636 ||
| |
| || 47 || 1025.455 ||
| |
| || 48 || 1047.273 ||
| |
| || 49 || 1069.091 ||
| |
| || 50 || 1090.909 ||
| |
| || 51 || 1112.727 ||
| |
| || 52 || 1134.545 ||
| |
| || 53 || 1156.364 ||
| |
| || 54 || 1178.182 ||
| |
| || 55 || 1200.000 ||
| |
|
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|
| [[http://www.seraph.it/dep/int/AdagioKV540.mp3|Mozart - Adagio in B minor KV 540]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/706c4662272db7703def4d57edfcb955-119.html|blog entry]])
| | {| class="wikitable" |
| | |- |
| | | | Degrees of 55-EDO |
| | | | Cents value |
| | |- |
| | | | 0 |
| | | | 0 |
| | |- |
| | | | 1 |
| | | | 21.818 |
| | |- |
| | | | 2 |
| | | | 43.636 |
| | |- |
| | | | 3 |
| | | | 65.455 |
| | |- |
| | | | 4 |
| | | | 87.273 |
| | |- |
| | | | 5 |
| | | | 109.091 |
| | |- |
| | | | 6 |
| | | | 130.909 |
| | |- |
| | | | 7 |
| | | | 152.727 |
| | |- |
| | | | 8 |
| | | | 174.545 |
| | |- |
| | | | 9 |
| | | | 196.364 |
| | |- |
| | | | 10 |
| | | | 218.182 |
| | |- |
| | | | 11 |
| | | | 240.000 |
| | |- |
| | | | 12 |
| | | | 261.818 |
| | |- |
| | | | 13 |
| | | | 283.636 |
| | |- |
| | | | 14 |
| | | | 305.455 |
| | |- |
| | | | 15 |
| | | | 327.273 |
| | |- |
| | | | 16 |
| | | | 349.091 |
| | |- |
| | | | 17 |
| | | | 370.909 |
| | |- |
| | | | 18 |
| | | | 392.727 |
| | |- |
| | | | 19 |
| | | | 414.545 |
| | |- |
| | | | 20 |
| | | | 436.364 |
| | |- |
| | | | 21 |
| | | | 458.182 |
| | |- |
| | | | 22 |
| | | | 480.000 |
| | |- |
| | | | 23 |
| | | | 501.818 |
| | |- |
| | | | 24 |
| | | | 523.636 |
| | |- |
| | | | 25 |
| | | | 545.455 |
| | |- |
| | | | 26 |
| | | | 567.273 |
| | |- |
| | | | 27 |
| | | | 589.091 |
| | |- |
| | | | 28 |
| | | | 610.909 |
| | |- |
| | | | 29 |
| | | | 632.727 |
| | |- |
| | | | 30 |
| | | | 654.545 |
| | |- |
| | | | 31 |
| | | | 676.364 |
| | |- |
| | | | 32 |
| | | | 698.182 |
| | |- |
| | | | 33 |
| | | | 720.000 |
| | |- |
| | | | 34 |
| | | | 741.818 |
| | |- |
| | | | 35 |
| | | | 763.636 |
| | |- |
| | | | 36 |
| | | | 785.455 |
| | |- |
| | | | 37 |
| | | | 807.273 |
| | |- |
| | | | 38 |
| | | | 829.091 |
| | |- |
| | | | 39 |
| | | | 850.909 |
| | |- |
| | | | 40 |
| | | | 872.727 |
| | |- |
| | | | 41 |
| | | | 894.545 |
| | |- |
| | | | 42 |
| | | | 916.364 |
| | |- |
| | | | 43 |
| | | | 938.182 |
| | |- |
| | | | 44 |
| | | | 960.000 |
| | |- |
| | | | 45 |
| | | | 981.818 |
| | |- |
| | | | 46 |
| | | | 1003.636 |
| | |- |
| | | | 47 |
| | | | 1025.455 |
| | |- |
| | | | 48 |
| | | | 1047.273 |
| | |- |
| | | | 49 |
| | | | 1069.091 |
| | |- |
| | | | 50 |
| | | | 1090.909 |
| | |- |
| | | | 51 |
| | | | 1112.727 |
| | |- |
| | | | 52 |
| | | | 1134.545 |
| | |- |
| | | | 53 |
| | | | 1156.364 |
| | |- |
| | | | 54 |
| | | | 1178.182 |
| | |- |
| | | | 55 |
| | | | 1200.000 |
| | |} |
|
| |
|
| [[http://tonalsoft.com/monzo/55edo/55edo.aspx|"Mozart's tuning: 55edo"]] (containing another listening example) in the [[tonalsoft encyclopedia]]</pre></div>
| | [http://www.seraph.it/dep/int/AdagioKV540.mp3 Mozart - Adagio in B minor KV 540] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/706c4662272db7703def4d57edfcb955-119.html blog entry]) |
| <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>55edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x55 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #008523; font-family: 'Times New Roman',Times,serif; font-size: 113%;">55 tone equal temperament</span></h1>
| |
| <br />
| |
| <strong><em>55edo</em></strong> divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to <a class="wiki_link" href="/1-6%20Syntonic%20Comma%20Meantone">1/6 comma meantone</a> (and is almost exactly 10/57 comma meantone.) <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Philipp_Telemann" rel="nofollow">Telemann</a> suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Leopold_Mozart" rel="nofollow">Leopold</a> and <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Wolfgang_Amadeus_Mozart" rel="nofollow">Wolfgang Mozart</a>. It can also be used for <a class="wiki_link" href="/Meantone%20family">mohajira and liese</a> temperaments.<br />
| |
| <br />
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| 5-limit commas: 81/80, &lt;31 1 -14|<br />
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| <br />
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| 7-limit commas: 81/80, 686/675, 6144/6125<br />
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| <br />
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| 11-limit commas: 81/80, 121/120, 176/175, 686/675<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x55 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
| |
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| <table class="wiki_table">
| | [http://tonalsoft.com/monzo/55edo/55edo.aspx "Mozart's tuning: 55edo"] (containing another listening example) in the [[tonalsoft_encyclopedia|tonalsoft encyclopedia]] [[Category:55edo]] |
| <tr>
| | [[Category:edo]] |
| <td>Degrees of 55-EDO<br />
| | [[Category:intervals]] |
| </td>
| | [[Category:meantone]] |
| <td>Cents value<br />
| | [[Category:theory]] |
| </td>
| | [[Category:todo:unify_precision]] |
| </tr>
| |
| <tr>
| |
| <td>0<br />
| |
| </td>
| |
| <td>0<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>21.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>43.636<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>65.455<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>87.273<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>109.091<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>130.909<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>152.727<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>174.545<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>196.364<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>218.182<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>240.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>261.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>283.636<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>305.455<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
| |
| </td>
| |
| <td>327.273<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>349.091<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
| |
| </td>
| |
| <td>370.909<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18<br />
| |
| </td>
| |
| <td>392.727<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19<br />
| |
| </td>
| |
| <td>414.545<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
| |
| </td>
| |
| <td>436.364<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21<br />
| |
| </td>
| |
| <td>458.182<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>480.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>501.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
| |
| </td>
| |
| <td>523.636<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25<br />
| |
| </td>
| |
| <td>545.455<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26<br />
| |
| </td>
| |
| <td>567.273<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>589.091<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28<br />
| |
| </td>
| |
| <td>610.909<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>632.727<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
| |
| <td>654.545<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
| |
| </td>
| |
| <td>676.364<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
| |
| </td>
| |
| <td>698.182<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
| |
| </td>
| |
| <td>720.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34<br />
| |
| </td>
| |
| <td>741.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
| |
| </td>
| |
| <td>763.636<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36<br />
| |
| </td>
| |
| <td>785.455<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
| |
| <td>807.273<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38<br />
| |
| </td>
| |
| <td>829.091<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
| |
| <td>850.909<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
| |
| </td>
| |
| <td>872.727<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41<br />
| |
| </td>
| |
| <td>894.545<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
| |
| </td>
| |
| <td>916.364<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43<br />
| |
| </td>
| |
| <td>938.182<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td>960.000<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
| |
| </td>
| |
| <td>981.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46<br />
| |
| </td>
| |
| <td>1003.636<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
| |
| </td>
| |
| <td>1025.455<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48<br />
| |
| </td>
| |
| <td>1047.273<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
| |
| </td>
| |
| <td>1069.091<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50<br />
| |
| </td>
| |
| <td>1090.909<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>51<br />
| |
| </td>
| |
| <td>1112.727<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52<br />
| |
| </td>
| |
| <td>1134.545<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53<br />
| |
| </td>
| |
| <td>1156.364<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54<br />
| |
| </td>
| |
| <td>1178.182<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>55<br />
| |
| </td>
| |
| <td>1200.000<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <a class="wiki_link_ext" href="http://www.seraph.it/dep/int/AdagioKV540.mp3" rel="nofollow">Mozart - Adagio in B minor KV 540</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/706c4662272db7703def4d57edfcb955-119.html" rel="nofollow">blog entry</a>)<br />
| |
| <br />
| |
| <a class="wiki_link_ext" href="http://tonalsoft.com/monzo/55edo/55edo.aspx" rel="nofollow">&quot;Mozart's tuning: 55edo&quot;</a> (containing another listening example) in the <a class="wiki_link" href="/tonalsoft%20encyclopedia">tonalsoft encyclopedia</a></body></html></pre></div>
| |
55 tone equal temperament
55edo divides the octave into 55 parts of 21.818 cents. It can be used for a meantone tuning, and is close to 1/6 comma meantone (and is almost exactly 10/57 comma meantone.) Telemann suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by Leopold and Wolfgang Mozart. It can also be used for mohajira and liese temperaments.
5-limit commas: 81/80, <31 1 -14|
7-limit commas: 81/80, 686/675, 6144/6125
11-limit commas: 81/80, 121/120, 176/175, 686/675
Intervals
| Degrees of 55-EDO
|
Cents value
|
| 0
|
0
|
| 1
|
21.818
|
| 2
|
43.636
|
| 3
|
65.455
|
| 4
|
87.273
|
| 5
|
109.091
|
| 6
|
130.909
|
| 7
|
152.727
|
| 8
|
174.545
|
| 9
|
196.364
|
| 10
|
218.182
|
| 11
|
240.000
|
| 12
|
261.818
|
| 13
|
283.636
|
| 14
|
305.455
|
| 15
|
327.273
|
| 16
|
349.091
|
| 17
|
370.909
|
| 18
|
392.727
|
| 19
|
414.545
|
| 20
|
436.364
|
| 21
|
458.182
|
| 22
|
480.000
|
| 23
|
501.818
|
| 24
|
523.636
|
| 25
|
545.455
|
| 26
|
567.273
|
| 27
|
589.091
|
| 28
|
610.909
|
| 29
|
632.727
|
| 30
|
654.545
|
| 31
|
676.364
|
| 32
|
698.182
|
| 33
|
720.000
|
| 34
|
741.818
|
| 35
|
763.636
|
| 36
|
785.455
|
| 37
|
807.273
|
| 38
|
829.091
|
| 39
|
850.909
|
| 40
|
872.727
|
| 41
|
894.545
|
| 42
|
916.364
|
| 43
|
938.182
|
| 44
|
960.000
|
| 45
|
981.818
|
| 46
|
1003.636
|
| 47
|
1025.455
|
| 48
|
1047.273
|
| 49
|
1069.091
|
| 50
|
1090.909
|
| 51
|
1112.727
|
| 52
|
1134.545
|
| 53
|
1156.364
|
| 54
|
1178.182
|
| 55
|
1200.000
|
Mozart - Adagio in B minor KV 540 by Carlo Serafini (blog entry)
"Mozart's tuning: 55edo" (containing another listening example) in the tonalsoft encyclopedia