62edo: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 340003066 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 368789204 - Original comment: ** |
||
Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-09-29 03:50:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>368789204</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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: #790080; font-family: | <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: #790080; font-family: "Times New Roman",Times,serif; font-size: 113%;">62 tone equal temperament</span>= | ||
62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. | 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. | ||
Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel. | Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel. | ||
===**62-EDO Intervals**=== | ===**62-EDO Intervals**=== | ||
Line 18: | Line 18: | ||
* **‡** = Semisharp (1/4-tone up) | * **‡** = Semisharp (1/4-tone up) | ||
* **b** = Flat (5/8-tone down) | * **b** = Flat (5/8-tone down) | ||
* **◊** = Node ( | * **◊** = Node (sharp/flat blindspot 1/2-tone) | ||
* **#** = Sharp (5/8-tone up) | * **#** = Sharp (5/8-tone up) | ||
* **v** = Semiflat (1/4-tone down) | * **v** = Semiflat (1/4-tone down) | ||
Line 86: | Line 86: | ||
|| 61 || 1180.64516 || 1⌐ (9‡) || ||</pre></div> | || 61 || 1180.64516 || 1⌐ (9‡) || ||</pre></div> | ||
<h4>Original HTML content:</h4> | <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>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #790080; font-family: | <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>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #790080; font-family: "Times New Roman",Times,serif; font-size: 113%;">62 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | ||
<br /> | <br /> | ||
Using the 35\62 generator, which leads to the &lt;62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &lt;62 97 143 172| supports hornbostel. <br /> | Using the 35\62 generator, which leads to the &lt;62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively &lt;62 97 143 172| supports hornbostel.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3> | ||
Line 102: | Line 102: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><ul><li><strong>Ɨ</strong> = Thick (1/8-tone up)</li><li><strong>‡</strong> = Semisharp (1/4-tone up)</li><li><strong>b</strong> = Flat (5/8-tone down)</li><li><strong>◊</strong> = Node ( | <td><ul><li><strong>Ɨ</strong> = Thick (1/8-tone up)</li><li><strong>‡</strong> = Semisharp (1/4-tone up)</li><li><strong>b</strong> = Flat (5/8-tone down)</li><li><strong>◊</strong> = Node (sharp/flat blindspot 1/2-tone)</li><li><strong>#</strong> = Sharp (5/8-tone up)</li><li><strong>v</strong> = Semiflat (1/4-tone down)</li><li><strong>⌐</strong> = Thin (1/8-tone down)</li></ul></td> | ||
</tr> | </tr> | ||
<tr> | <tr> |
Revision as of 03:50, 29 September 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Osmiorisbendi and made on 2012-09-29 03:50:31 UTC.
- The original revision id was 368789204.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=<span style="color: #790080; font-family: "Times New Roman",Times,serif; font-size: 113%;">62 tone equal temperament</span>= 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel. ===**62-EDO Intervals**=== || **ARMODUE NOMENCLATURE 8;3 RELATION** || || * **Ɨ** = Thick (1/8-tone up) * **‡** = Semisharp (1/4-tone up) * **b** = Flat (5/8-tone down) * **◊** = Node (sharp/flat blindspot 1/2-tone) * **#** = Sharp (5/8-tone up) * **v** = Semiflat (1/4-tone down) * **⌐** = Thin (1/8-tone down) || || Degrees || Cents size || Armodue notation || || || 0 || 0 || 1 || || || 1 || 19.35484 || 1Ɨ || || || 2 || 38.70968 || 1‡ (9#) || || || 3 || 58.06452 || 2b || || || 4 || 77.41935 || 1◊2 || || || 5 || 96.77419 || 1# || || || 6 || 116.12903 || 2v || || || 7 || 135.48387 || 2⌐ || || || 8 || 154.83871 || 2 || || || 9 || 174.19355 || 2Ɨ || || || 10 || 193.54839 || 2‡ || || || 11 || 212.90323 || 3b || || || 12 || 232.25806 || 2◊3 || || || 13 || 251.6129 || 2# || || || 14 || 270.96774 || 3v || || || 15 || 290.32258 || 3⌐ || || || 16 || 309.67742 || 3 || || || 17 || 329.03226 || 3Ɨ || || || 18 || 348.3871 || 3‡ || || || 19 || 367.74194 || 4b || || || 20 || 387.09677 || 3◊4 || || || 21 || 406.45161 || 3# || || || 22 || 425.80645 || 4v (5b) || || || 23 || 445.16129 || 4⌐ || || || 24 || 464.51613 || 4 || || || 25 || 483.87097 || 4Ɨ (5v) || || || 26 || 503.22581 || 5⌐ (4‡) || || || 27 || 522.58065 || 5 || || || 28 || 541.93548 || 5Ɨ || || || 29 || 561.29032 || 5‡ (4#) || || || 30 || 580.64516 || 6b || || || 31 || 600 || 5◊6 || || || 32 || 619.35484 || 5# || || || 33 || 638.70968 || 6v || || || 34 || 658.06452 || 6⌐ || || || 35 || 677.41935 || 6 || || || 36 || 696.77419 || 6Ɨ || || || 37 || 716.12903 || 6‡ || || || 38 || 735.48387 || 7b || || || 39 || 754.83871 || 6◊7 || || || 40 || 774.19355 || 6# || || || 41 || 793.54839 || 7v || || || 42 || 812.90323 || 7⌐ || || || 43 || 832.25806 || 7 || || || 44 || 851.6129 || 7Ɨ || || || 45 || 870.96774 || 7‡ || || || 46 || 890.32258 || 8b || || || 47 || 909.67742 || 7◊8 || || || 48 || 929.03226 || 7# || || || 49 || 948.3871 || 8v || || || 50 || 967.74194 || 8⌐ || || || 51 || 987.09677 || 8 || || || 52 || 1006.45161 || 8Ɨ || || || 53 || 1025.80645 || 8‡ || || || 54 || 1045.16129 || 9b || || || 55 || 1064.51613 || 8◊9 || || || 56 || 1083.87097 || 8# || || || 57 || 1103.22581 || 9v (1b) || || || 58 || 1122.58065 || 9⌐ || || || 59 || 1141.93548 || 9 || || || 60 || 1161.29032 || 9Ɨ (1v) || || || 61 || 1180.64516 || 1⌐ (9‡) || ||
Original HTML content:
<html><head><title>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #790080; font-family: "Times New Roman",Times,serif; font-size: 113%;">62 tone equal temperament</span></h1> <br /> 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> <br /> Using the 35\62 generator, which leads to the <62 97 143 173| val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively <62 97 143 172| supports hornbostel.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x62 tone equal temperament--62-EDO Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 --><strong>62-EDO Intervals</strong></h3> <br /> <table class="wiki_table"> <tr> <td><strong>ARMODUE NOMENCLATURE 8;3 RELATION</strong><br /> </td> </tr> <tr> <td><ul><li><strong>Ɨ</strong> = Thick (1/8-tone up)</li><li><strong>‡</strong> = Semisharp (1/4-tone up)</li><li><strong>b</strong> = Flat (5/8-tone down)</li><li><strong>◊</strong> = Node (sharp/flat blindspot 1/2-tone)</li><li><strong>#</strong> = Sharp (5/8-tone up)</li><li><strong>v</strong> = Semiflat (1/4-tone down)</li><li><strong>⌐</strong> = Thin (1/8-tone down)</li></ul></td> </tr> <tr> <td>Degrees<br /> </td> <td>Cents size<br /> </td> <td>Armodue notation<br /> </td> <td><br /> </td> </tr> <tr> <td>0<br /> </td> <td>0<br /> </td> <td>1<br /> </td> <td><br /> </td> </tr> <tr> <td>1<br /> </td> <td>19.35484<br /> </td> <td>1Ɨ<br /> </td> <td><br /> </td> </tr> <tr> <td>2<br /> </td> <td>38.70968<br /> </td> <td>1‡ (9#)<br /> </td> <td><br /> </td> </tr> <tr> <td>3<br /> </td> <td>58.06452<br /> </td> <td>2b<br /> </td> <td><br /> </td> </tr> <tr> <td>4<br /> </td> <td>77.41935<br /> </td> <td>1◊2<br /> </td> <td><br /> </td> </tr> <tr> <td>5<br /> </td> <td>96.77419<br /> </td> <td>1#<br /> </td> <td><br /> </td> </tr> <tr> <td>6<br /> </td> <td>116.12903<br /> </td> <td>2v<br /> </td> <td><br /> </td> </tr> <tr> <td>7<br /> </td> <td>135.48387<br /> </td> <td>2⌐<br /> </td> <td><br /> </td> </tr> <tr> <td>8<br /> </td> <td>154.83871<br /> </td> <td>2<br /> </td> <td><br /> </td> </tr> <tr> <td>9<br /> </td> <td>174.19355<br /> </td> <td>2Ɨ<br /> </td> <td><br /> </td> </tr> <tr> <td>10<br /> </td> <td>193.54839<br /> </td> <td>2‡<br /> </td> <td><br /> </td> </tr> <tr> <td>11<br /> </td> <td>212.90323<br /> </td> <td>3b<br /> </td> <td><br /> </td> </tr> <tr> <td>12<br /> </td> <td>232.25806<br /> </td> <td>2◊3<br /> </td> <td><br /> </td> </tr> <tr> <td>13<br /> </td> <td>251.6129<br /> </td> <td>2#<br /> </td> <td><br /> </td> </tr> <tr> <td>14<br /> </td> <td>270.96774<br /> </td> <td>3v<br /> </td> <td><br /> </td> </tr> <tr> <td>15<br /> </td> <td>290.32258<br /> </td> <td>3⌐<br /> </td> <td><br /> </td> </tr> <tr> <td>16<br /> </td> <td>309.67742<br /> </td> <td>3<br /> </td> <td><br /> </td> </tr> <tr> <td>17<br /> </td> <td>329.03226<br /> </td> <td>3Ɨ<br /> </td> <td><br /> </td> </tr> <tr> <td>18<br /> </td> <td>348.3871<br /> </td> <td>3‡<br /> </td> <td><br /> </td> </tr> <tr> <td>19<br /> </td> <td>367.74194<br /> </td> <td>4b<br /> </td> <td><br /> </td> </tr> <tr> <td>20<br /> </td> <td>387.09677<br /> </td> <td>3◊4<br /> </td> <td><br /> </td> </tr> <tr> <td>21<br /> </td> <td>406.45161<br /> </td> <td>3#<br /> </td> <td><br /> </td> </tr> <tr> <td>22<br /> </td> <td>425.80645<br /> </td> <td>4v (5b)<br /> </td> <td><br /> </td> </tr> <tr> <td>23<br /> </td> <td>445.16129<br /> </td> <td>4⌐<br /> </td> <td><br /> </td> </tr> <tr> <td>24<br /> </td> <td>464.51613<br /> </td> <td>4<br /> </td> <td><br /> </td> </tr> <tr> <td>25<br /> </td> <td>483.87097<br /> </td> <td>4Ɨ (5v)<br /> </td> <td><br /> </td> </tr> <tr> <td>26<br /> </td> <td>503.22581<br /> </td> <td>5⌐ (4‡)<br /> </td> <td><br /> </td> </tr> <tr> <td>27<br /> </td> <td>522.58065<br /> </td> <td>5<br /> </td> <td><br /> </td> </tr> <tr> <td>28<br /> </td> <td>541.93548<br /> </td> <td>5Ɨ<br /> </td> <td><br /> </td> </tr> <tr> <td>29<br /> </td> <td>561.29032<br /> </td> <td>5‡ (4#)<br /> </td> <td><br /> </td> </tr> <tr> <td>30<br /> </td> <td>580.64516<br /> </td> <td>6b<br /> </td> <td><br /> </td> </tr> <tr> <td>31<br /> </td> <td>600<br /> </td> <td>5◊6<br /> </td> <td><br /> </td> </tr> <tr> <td>32<br /> </td> <td>619.35484<br /> </td> <td>5#<br /> </td> <td><br /> </td> </tr> <tr> <td>33<br /> </td> <td>638.70968<br /> </td> <td>6v<br /> </td> <td><br /> </td> </tr> <tr> <td>34<br /> </td> <td>658.06452<br /> </td> <td>6⌐<br /> </td> <td><br /> </td> </tr> <tr> <td>35<br /> </td> <td>677.41935<br /> </td> <td>6<br /> </td> <td><br /> </td> </tr> <tr> <td>36<br /> </td> <td>696.77419<br /> </td> <td>6Ɨ<br /> </td> <td><br /> </td> </tr> <tr> <td>37<br /> </td> <td>716.12903<br /> </td> <td>6‡<br /> </td> <td><br /> </td> </tr> <tr> <td>38<br /> </td> <td>735.48387<br /> </td> <td>7b<br /> </td> <td><br /> </td> </tr> <tr> <td>39<br /> </td> <td>754.83871<br /> </td> <td>6◊7<br /> </td> <td><br /> </td> </tr> <tr> <td>40<br /> </td> <td>774.19355<br /> </td> <td>6#<br /> </td> <td><br /> </td> </tr> <tr> <td>41<br /> </td> <td>793.54839<br /> </td> <td>7v<br /> </td> <td><br /> </td> </tr> <tr> <td>42<br /> </td> <td>812.90323<br /> </td> <td>7⌐<br /> </td> <td><br /> </td> </tr> <tr> <td>43<br /> </td> <td>832.25806<br /> </td> <td>7<br /> </td> <td><br /> </td> </tr> <tr> <td>44<br /> </td> <td>851.6129<br /> </td> <td>7Ɨ<br /> </td> <td><br /> </td> </tr> <tr> <td>45<br /> </td> <td>870.96774<br /> </td> <td>7‡<br /> </td> <td><br /> </td> </tr> <tr> <td>46<br /> </td> <td>890.32258<br /> </td> <td>8b<br /> </td> <td><br /> </td> </tr> <tr> <td>47<br /> </td> <td>909.67742<br /> </td> <td>7◊8<br /> </td> <td><br /> </td> </tr> <tr> <td>48<br /> </td> <td>929.03226<br /> </td> <td>7#<br /> </td> <td><br /> </td> </tr> <tr> <td>49<br /> </td> <td>948.3871<br /> </td> <td>8v<br /> </td> <td><br /> </td> </tr> <tr> <td>50<br /> </td> <td>967.74194<br /> </td> <td>8⌐<br /> </td> <td><br /> </td> </tr> <tr> <td>51<br /> </td> <td>987.09677<br /> </td> <td>8<br /> </td> <td><br /> </td> </tr> <tr> <td>52<br /> </td> <td>1006.45161<br /> </td> <td>8Ɨ<br /> </td> <td><br /> </td> </tr> <tr> <td>53<br /> </td> <td>1025.80645<br /> </td> <td>8‡<br /> </td> <td><br /> </td> </tr> <tr> <td>54<br /> </td> <td>1045.16129<br /> </td> <td>9b<br /> </td> <td><br /> </td> </tr> <tr> <td>55<br /> </td> <td>1064.51613<br /> </td> <td>8◊9<br /> </td> <td><br /> </td> </tr> <tr> <td>56<br /> </td> <td>1083.87097<br /> </td> <td>8#<br /> </td> <td><br /> </td> </tr> <tr> <td>57<br /> </td> <td>1103.22581<br /> </td> <td>9v (1b)<br /> </td> <td><br /> </td> </tr> <tr> <td>58<br /> </td> <td>1122.58065<br /> </td> <td>9⌐<br /> </td> <td><br /> </td> </tr> <tr> <td>59<br /> </td> <td>1141.93548<br /> </td> <td>9<br /> </td> <td><br /> </td> </tr> <tr> <td>60<br /> </td> <td>1161.29032<br /> </td> <td>9Ɨ (1v)<br /> </td> <td><br /> </td> </tr> <tr> <td>61<br /> </td> <td>1180.64516<br /> </td> <td>1⌐ (9‡)<br /> </td> <td><br /> </td> </tr> </table> </body></html>