35edo: Difference between revisions
Wikispaces>phylingual **Imported revision 329071004 - Original comment: ** |
Wikispaces>phylingual **Imported revision 329083054 - Original comment: ** |
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<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:phylingual|phylingual]] and made on <tt>2012-05-02 | : This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-02 23:11:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>329083054</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> | ||
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As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. | As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. | ||
35edo | 35edo can represent the 2.3.5.7.11.17 [[Just intonation subgroups|subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators. Therefore it is a very versatile whitewood tuning. | ||
A good beggining for start to play 35-EDO is with the Sub-diatonic scale (Pentadiatonic scale), that is a [[MOS]] of 3L2s: L s L L s; in 35-EDO is: 9 4 9 9 4 | A good beggining for start to play 35-EDO is with the Sub-diatonic scale (Pentadiatonic scale), that is a [[MOS]] of 3L2s: L s L L s; in 35-EDO is: 9 4 9 9 4 | ||
==Intervals== | ==Intervals== | ||
|| Degrees of 35-EDO || Cents value || | || Degrees of 35-EDO || Cents value || Ratios in 2.3.5.7.11.17 subgroup || Ratios in 2.9.5.7.11.17 subgroup || | ||
|| 0 || 0 || | || 0 || 0 || 1/1 || || | ||
|| 1 || 34,29 || | || 1 || 34,29 || || || | ||
|| 2 || 68,57 || | || 2 || 68,57 || || || | ||
|| 3 || 102,86 || | || 3 || 102,86 || 17/16 || 17/16, 18/17 || | ||
|| 4 || 137,14 || | || 4 || 137,14 || 12/11 || || | ||
|| 5 || 171,43 || | || 5 || 171,43 || 11/10 || 10/9, 11/10 || | ||
|| 6 || 205,71 || | || 6 || 205,71 || || 9/8 || | ||
|| 7 || 240 || | || 7 || 240 || 8/7 || 8/7 || | ||
|| 8 || 274,29 || | || 8 || 274,29 || 7/6, 20/17 || 20/17 || | ||
|| 9 || 308,57 || | || 9 || 308,57 || 6/5 || || | ||
|| 10 || 342,86 || | || 10 || 342,86 || 17/14 || 11/9, 17/14 || | ||
|| 11 || 377,14 || | || 11 || 377,14 || 5/4 || 5/4 || | ||
|| 12 || 411,43 || | || 12 || 411,43 || 14/11 || 14/11 || | ||
|| 13 || 445,71 || | || 13 || 445,71 || 22/17 || 9/7, 22/17 || | ||
|| 14 || 480 || | || 14 || 480 || || || | ||
|| 15 || 514,29 || | || 15 || 514,29 || 4/3 || || | ||
|| 16 || 548,57 || | || 16 || 548,57 || 11/8 || 11/8 || | ||
|| 17 || 582,86 || | || 17 || 582,86 || 7/5, 24/17 || 7/8 || | ||
|| 18 || 617,14 || | || 18 || 617,14 || 10/7, 17/12 || 10/7 || | ||
|| 19 || 651,43 || | || 19 || 651,43 || 16/11 || 16/11 || | ||
|| 20 || 685,71 || | || 20 || 685,71 || 3/2 || || | ||
|| 21 || 720 || | || 21 || 720 || || || | ||
|| 22 || 754,29 || | || 22 || 754,29 || 17/11 || 14/9, 17/11 || | ||
|| 23 || 788,57 || | || 23 || 788,57 || 11/7 || 11/7 || | ||
|| 24 || 822,86 || | || 24 || 822,86 || 8/5 || 8/5 || | ||
|| 25 || 857,15 || | || 25 || 857,15 || || 18/11 || | ||
|| 26 || 891,43 || | || 26 || 891,43 || 5/3 || || | ||
|| 27 || 925,71 || | || 27 || 925,71 || 12/7, 17/10 || 17/10 || | ||
|| 28 || 960 || | || 28 || 960 || 7/4 || 7/4 || | ||
|| 29 || 994,29 || | || 29 || 994,29 || || 16/9 || | ||
|| 30 || 1028,57 || | || 30 || 1028,57 || 20/11 || 20/11, 9/5 || | ||
|| 31 || 1062,86 || | || 31 || 1062,86 || 11/6 || || | ||
|| 32 || 1097,14 || | || 32 || 1097,14 || 32/17 || 32/17, 17/9 || | ||
|| 33 || 1131,43 || | || 33 || 1131,43 || || || | ||
|| 34 || 1165,71 ||</pre></div> | || 34 || 1165,71 || || ||</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>35edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x35 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4100;">35 tone equal temperament</span></h1> | <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>35edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x35 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4100;">35 tone equal temperament</span></h1> | ||
| Line 60: | Line 60: | ||
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic <a class="wiki_link" href="/macrotonal%20edos">macrotonal edos</a>: <a class="wiki_link" href="/5edo">5edo</a> and <a class="wiki_link" href="/7edo">7edo</a>. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢.<br /> | As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic <a class="wiki_link" href="/macrotonal%20edos">macrotonal edos</a>: <a class="wiki_link" href="/5edo">5edo</a> and <a class="wiki_link" href="/7edo">7edo</a>. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢.<br /> | ||
<br /> | <br /> | ||
35edo | 35edo can represent the 2.3.5.7.11.17 <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators. Therefore it is a very versatile whitewood tuning.<br /> | ||
<br /> | <br /> | ||
A good beggining for start to play 35-EDO is with the Sub-diatonic scale (Pentadiatonic scale), that is a <a class="wiki_link" href="/MOS">MOS</a> of 3L2s: L s L L s; in 35-EDO is: 9 4 9 9 4<br /> | A good beggining for start to play 35-EDO is with the Sub-diatonic scale (Pentadiatonic scale), that is a <a class="wiki_link" href="/MOS">MOS</a> of 3L2s: L s L L s; in 35-EDO is: 9 4 9 9 4<br /> | ||
| Line 72: | Line 72: | ||
</td> | </td> | ||
<td>Cents value<br /> | <td>Cents value<br /> | ||
</td> | |||
<td>Ratios in 2.3.5.7.11.17 subgroup<br /> | |||
</td> | |||
<td>Ratios in 2.9.5.7.11.17 subgroup<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 78: | Line 82: | ||
</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
</td> | |||
<td>1/1<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 84: | Line 92: | ||
</td> | </td> | ||
<td>34,29<br /> | <td>34,29<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 90: | Line 102: | ||
</td> | </td> | ||
<td>68,57<br /> | <td>68,57<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 96: | Line 112: | ||
</td> | </td> | ||
<td>102,86<br /> | <td>102,86<br /> | ||
</td> | |||
<td>17/16<br /> | |||
</td> | |||
<td>17/16, 18/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 102: | Line 122: | ||
</td> | </td> | ||
<td>137,14<br /> | <td>137,14<br /> | ||
</td> | |||
<td>12/11<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 108: | Line 132: | ||
</td> | </td> | ||
<td>171,43<br /> | <td>171,43<br /> | ||
</td> | |||
<td>11/10<br /> | |||
</td> | |||
<td>10/9, 11/10<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 114: | Line 142: | ||
</td> | </td> | ||
<td>205,71<br /> | <td>205,71<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td>9/8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 120: | Line 152: | ||
</td> | </td> | ||
<td>240<br /> | <td>240<br /> | ||
</td> | |||
<td>8/7<br /> | |||
</td> | |||
<td>8/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 126: | Line 162: | ||
</td> | </td> | ||
<td>274,29<br /> | <td>274,29<br /> | ||
</td> | |||
<td>7/6, 20/17<br /> | |||
</td> | |||
<td>20/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 132: | Line 172: | ||
</td> | </td> | ||
<td>308,57<br /> | <td>308,57<br /> | ||
</td> | |||
<td>6/5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 138: | Line 182: | ||
</td> | </td> | ||
<td>342,86<br /> | <td>342,86<br /> | ||
</td> | |||
<td>17/14<br /> | |||
</td> | |||
<td>11/9, 17/14<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 144: | Line 192: | ||
</td> | </td> | ||
<td>377,14<br /> | <td>377,14<br /> | ||
</td> | |||
<td>5/4<br /> | |||
</td> | |||
<td>5/4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 150: | Line 202: | ||
</td> | </td> | ||
<td>411,43<br /> | <td>411,43<br /> | ||
</td> | |||
<td>14/11<br /> | |||
</td> | |||
<td>14/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 156: | Line 212: | ||
</td> | </td> | ||
<td>445,71<br /> | <td>445,71<br /> | ||
</td> | |||
<td>22/17<br /> | |||
</td> | |||
<td>9/7, 22/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 162: | Line 222: | ||
</td> | </td> | ||
<td>480<br /> | <td>480<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 168: | Line 232: | ||
</td> | </td> | ||
<td>514,29<br /> | <td>514,29<br /> | ||
</td> | |||
<td>4/3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 174: | Line 242: | ||
</td> | </td> | ||
<td>548,57<br /> | <td>548,57<br /> | ||
</td> | |||
<td>11/8<br /> | |||
</td> | |||
<td>11/8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 180: | Line 252: | ||
</td> | </td> | ||
<td>582,86<br /> | <td>582,86<br /> | ||
</td> | |||
<td>7/5, 24/17<br /> | |||
</td> | |||
<td>7/8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 186: | Line 262: | ||
</td> | </td> | ||
<td>617,14<br /> | <td>617,14<br /> | ||
</td> | |||
<td>10/7, 17/12<br /> | |||
</td> | |||
<td>10/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 192: | Line 272: | ||
</td> | </td> | ||
<td>651,43<br /> | <td>651,43<br /> | ||
</td> | |||
<td>16/11<br /> | |||
</td> | |||
<td>16/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 198: | Line 282: | ||
</td> | </td> | ||
<td>685,71<br /> | <td>685,71<br /> | ||
</td> | |||
<td>3/2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 204: | Line 292: | ||
</td> | </td> | ||
<td>720<br /> | <td>720<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 210: | Line 302: | ||
</td> | </td> | ||
<td>754,29<br /> | <td>754,29<br /> | ||
</td> | |||
<td>17/11<br /> | |||
</td> | |||
<td>14/9, 17/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 216: | Line 312: | ||
</td> | </td> | ||
<td>788,57<br /> | <td>788,57<br /> | ||
</td> | |||
<td>11/7<br /> | |||
</td> | |||
<td>11/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 222: | Line 322: | ||
</td> | </td> | ||
<td>822,86<br /> | <td>822,86<br /> | ||
</td> | |||
<td>8/5<br /> | |||
</td> | |||
<td>8/5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 228: | Line 332: | ||
</td> | </td> | ||
<td>857,15<br /> | <td>857,15<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td>18/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 234: | Line 342: | ||
</td> | </td> | ||
<td>891,43<br /> | <td>891,43<br /> | ||
</td> | |||
<td>5/3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 240: | Line 352: | ||
</td> | </td> | ||
<td>925,71<br /> | <td>925,71<br /> | ||
</td> | |||
<td>12/7, 17/10<br /> | |||
</td> | |||
<td>17/10<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 246: | Line 362: | ||
</td> | </td> | ||
<td>960<br /> | <td>960<br /> | ||
</td> | |||
<td>7/4<br /> | |||
</td> | |||
<td>7/4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 252: | Line 372: | ||
</td> | </td> | ||
<td>994,29<br /> | <td>994,29<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td>16/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 258: | Line 382: | ||
</td> | </td> | ||
<td>1028,57<br /> | <td>1028,57<br /> | ||
</td> | |||
<td>20/11<br /> | |||
</td> | |||
<td>20/11, 9/5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 264: | Line 392: | ||
</td> | </td> | ||
<td>1062,86<br /> | <td>1062,86<br /> | ||
</td> | |||
<td>11/6<br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 270: | Line 402: | ||
</td> | </td> | ||
<td>1097,14<br /> | <td>1097,14<br /> | ||
</td> | |||
<td>32/17<br /> | |||
</td> | |||
<td>32/17, 17/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 276: | Line 412: | ||
</td> | </td> | ||
<td>1131,43<br /> | <td>1131,43<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 282: | Line 422: | ||
</td> | </td> | ||
<td>1165,71<br /> | <td>1165,71<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||