35edo: Difference between revisions
Wikispaces>clamengh **Imported revision 518729662 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 545672580 - 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: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-28 23:01:13 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>545672580</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> | ||
Line 15: | Line 15: | ||
(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.) | (Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.) | ||
|| Degrees || Cents value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with sharp 3 || Ratios with patent 9 || | || Degrees || Cents value | ||
DMS value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with sharp 3 || Ratios with patent 9 || | |||
|| 0 || 0 || **1/1** || (see comma table) || || || | || 0 || 0 || **1/1** || (see comma table) || || || | ||
|| 1 || 34.29 || **50/49**, **121/119**, 33/32 || **36/35** || 25/24 || **81/80** || | || 1 || 34.29 | ||
|| 2 || 68.57 || 128/125 || **25/24** || 81/80 || || | 10°<span style="background-color: #ffffff;">17'9"</span> || **50/49**, **121/119**, 33/32 || **36/35** || 25/24 || **81/80** || | ||
|| 3 || 102.86 || **17/16** || **15/14** || **16/15** || **18/17** || | || 2 || 68.57 | ||
|| 4 || 137.14 || || **12/11**, 16/15 || || || | 20°<span style="background-color: #ffffff;">34'17"</span> || 128/125 || **25/24** || 81/80 || || | ||
|| 5 || 171.43 || **11/10** || || 12/11 || **10/9** || | || 3 || 102.86 | ||
|| 6 || 205.71 || || || || **9/8** || | 30°<span style="background-color: #ffffff;">51'26"</span> || **17/16** || **15/14** || **16/15** || **18/17** || | ||
|| 7 || 240 || **8/7** || || 7/6 || || | || 4 || 137.14 | ||
|| 8 || 274.29 || **20/17** || **7/6** || || || | 41°<span style="background-color: #ffffff;">8'34"</span> || || **12/11**, 16/15 || || || | ||
|| 9 || 308.57 || || **6/5** || || || | || 5 || 171.43 | ||
|| 10 || 342.86 || **17/14** || || 6/5 || **11/9** || | <span style="background-color: #ffffff;">51°25'43"</span> || **11/10** || || 12/11 || **10/9** || | ||
|| 11 || 377.14 || **5/4** || || || || | || 6 || 205.71 | ||
|| 12 || 411.43 || **14/11** || || || || | 61°<span style="background-color: #ffffff;">42'51"</span> || || || || **9/8** || | ||
|| 13 || 445.71 || **22/17**, 32/25 || || || **9/7** || | || 7 || 240 | ||
|| 14 || 480 || || || 4/3, **21/16** || || | 72° || **8/7** || || 7/6 || || | ||
|| 15 || 514.29 || || **4/3** || || || | || 8 || 274.29 | ||
|| 16 || 548.57 || **11/8** || || || || | 82°<span style="background-color: #ffffff;">17'9"</span> || **20/17** || **7/6** || || || | ||
|| 17 || 582.86 || **7/5** || **24/17** || 17/12 || || | || 9 || 308.57 | ||
|| 18 || 617.14 || **10/7** || **17/12** || 24/17 || || | 92°<span style="background-color: #ffffff;">34'17"</span> || || **6/5** || || || | ||
|| 19 || 651.43 || **16/11** || || || || | || 10 || 342.86 | ||
|| 20 || 685.71 || || **3/2** || || || | <span style="background-color: #ffffff;">102°51'26"</span> || **17/14** || || 6/5 || **11/9** || | ||
|| 21 || 720 || || || 3/2, **32/21** || || | || 11 || 377.14 | ||
|| 22 || 754.29 || **17/11**, 25/16 || || || **14/9** || | 113°<span style="background-color: #ffffff;">8'34"</span> || **5/4** || || || || | ||
|| 23 || 788.57 || **11/7** || || || || | || 12 || 411.43 | ||
|| 24 || 822.86 || **8/5** || || || || | 123°<span style="background-color: #ffffff;">25'43"</span> || **14/11** || || || || | ||
|| 25 || 857. | || 13 || 445.71 | ||
|| 26 || 891.43 || || **5/3** || || || | 133°<span style="background-color: #ffffff;">42'51"</span> || **22/17**, 32/25 || || || **9/7** || | ||
|| 27 || 925.71 || **17/10** || **12/7** || || || | || 14 || 480 | ||
|| 28 || 960 || **7/4** || || || || | 144° || || || 4/3, **21/16** || || | ||
|| 29 || 994.29 || || || || **16/9** || | || 15 || 514.29 | ||
|| 30 || 1028.57 || **20/11** || || || **9/5** || | <span style="background-color: #ffffff;">154°17'9"</span> || || **4/3** || || || | ||
|| 31 || 1062.86 || || **11/6**, 15/8 || || || | || 16 || 548.57 | ||
|| 32 || 1097.14 || **32/17** || **28/15** || **15/8** || **17/9** || | 164°<span style="background-color: #ffffff;">34'17"</span> || **11/8** || || || || | ||
|| | || 17 || 582.86 | ||
|| 34 || 1165.71 || || || || || | 174°<span style="background-color: #ffffff;">51'26"</span> || **7/5** || **24/17** || 17/12 || || | ||
|| 18 || 617.14 | |||
185°<span style="background-color: #ffffff;">8'34"</span> || **10/7** || **17/12** || 24/17 || || | |||
|| 19 || 651.43 | |||
195°<span style="background-color: #ffffff;">25'43"</span> || **16/11** || || || || | |||
|| 20 || 685.71 | |||
<span style="background-color: #ffffff;">205°42'51"</span> || || **3/2** || || || | |||
|| 21 || 720 | |||
216° || || || 3/2, **32/21** || || | |||
|| 22 || 754.29 | |||
226°<span style="background-color: #ffffff;">17'9"</span> || **17/11**, 25/16 || || || **14/9** || | |||
|| 23 || 788.57 | |||
236°<span style="background-color: #ffffff;">34'17"</span> || **11/7** || || || || | |||
|| 24 || 822.86 | |||
246°<span style="background-color: #ffffff;">51'26"</span> || **8/5** || || || || | |||
|| 25 || 857.14 | |||
<span style="background-color: #ffffff;">257°8'34"</span> || **28/17** || || 5/3 || **18/11** || | |||
|| 26 || 891.43 | |||
267°<span style="background-color: #ffffff;">25'43"</span> || || **5/3** || || || | |||
|| 27 || 925.71 | |||
277°<span style="background-color: #ffffff;">42'51"</span> || **17/10** || **12/7** || || || | |||
|| 28 || 960 | |||
288° || **7/4** || || || || | |||
|| 29 || 994.29 | |||
298°<span style="background-color: #ffffff;">17'9"</span> || || || || **16/9** || | |||
|| 30 || 1028.57 | |||
<span style="background-color: #ffffff;">308°34'17"</span> || **20/11** || || || **9/5** || | |||
|| 31 || 1062.86 | |||
318°<span style="background-color: #ffffff;">51'26"</span> || || **11/6**, 15/8 || || || | |||
|| 32 || 1097.14 | |||
329°<span style="background-color: #ffffff;">8'34"</span> || **32/17** || **28/15** || **15/8** || **17/9** || | |||
|| 3 || 1131.43 | |||
339°<span style="background-color: #ffffff;">25'43"</span> || || || || || | |||
|| 34 || 1165.71 | |||
349°<span style="background-color: #ffffff;">42'51"</span> || || || || || | |||
=Rank two temperaments= | =Rank two temperaments= | ||
||~ Periods | ||~ Periods | ||
per octave ||~ Generator ||~ Temperaments with | per octave ||~ Generator ||~ Temperaments with | ||
flat 3/2 (patent val) ||~ <span style="display: block; text-align: center;">Temperaments | flat 3/2 (patent val) ||~ <span style="display: block; text-align: center;">Temperaments with sharp 3/2 (35b val)</span> || | ||
|| 1 || 1\35 || || || | || 1 || 1\35 || || || | ||
|| 1 || 2\35 || || || | || 1 || 2\35 || || || | ||
Line 110: | Line 145: | ||
</td> | </td> | ||
<td>Cents value<br /> | <td>Cents value<br /> | ||
DMS value<br /> | |||
</td> | </td> | ||
<td>Ratios in 2.5.7.11.17 subgroup<br /> | <td>Ratios in 2.5.7.11.17 subgroup<br /> | ||
Line 138: | Line 174: | ||
</td> | </td> | ||
<td>34.29<br /> | <td>34.29<br /> | ||
10°<span style="background-color: #ffffff;">17'9&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>50/49</strong>, <strong>121/119</strong>, 33/32<br /> | <td><strong>50/49</strong>, <strong>121/119</strong>, 33/32<br /> | ||
Line 152: | Line 189: | ||
</td> | </td> | ||
<td>68.57<br /> | <td>68.57<br /> | ||
20°<span style="background-color: #ffffff;">34'17&quot;</span><br /> | |||
</td> | </td> | ||
<td>128/125<br /> | <td>128/125<br /> | ||
Line 166: | Line 204: | ||
</td> | </td> | ||
<td>102.86<br /> | <td>102.86<br /> | ||
30°<span style="background-color: #ffffff;">51'26&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>17/16</strong><br /> | <td><strong>17/16</strong><br /> | ||
Line 180: | Line 219: | ||
</td> | </td> | ||
<td>137.14<br /> | <td>137.14<br /> | ||
41°<span style="background-color: #ffffff;">8'34&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 194: | Line 234: | ||
</td> | </td> | ||
<td>171.43<br /> | <td>171.43<br /> | ||
<span style="background-color: #ffffff;">51°25'43&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>11/10</strong><br /> | <td><strong>11/10</strong><br /> | ||
Line 208: | Line 249: | ||
</td> | </td> | ||
<td>205.71<br /> | <td>205.71<br /> | ||
61°<span style="background-color: #ffffff;">42'51&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 222: | Line 264: | ||
</td> | </td> | ||
<td>240<br /> | <td>240<br /> | ||
72°<br /> | |||
</td> | </td> | ||
<td><strong>8/7</strong><br /> | <td><strong>8/7</strong><br /> | ||
Line 236: | Line 279: | ||
</td> | </td> | ||
<td>274.29<br /> | <td>274.29<br /> | ||
82°<span style="background-color: #ffffff;">17'9&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>20/17</strong><br /> | <td><strong>20/17</strong><br /> | ||
Line 250: | Line 294: | ||
</td> | </td> | ||
<td>308.57<br /> | <td>308.57<br /> | ||
92°<span style="background-color: #ffffff;">34'17&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 264: | Line 309: | ||
</td> | </td> | ||
<td>342.86<br /> | <td>342.86<br /> | ||
<span style="background-color: #ffffff;">102°51'26&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>17/14</strong><br /> | <td><strong>17/14</strong><br /> | ||
Line 278: | Line 324: | ||
</td> | </td> | ||
<td>377.14<br /> | <td>377.14<br /> | ||
113°<span style="background-color: #ffffff;">8'34&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>5/4</strong><br /> | <td><strong>5/4</strong><br /> | ||
Line 292: | Line 339: | ||
</td> | </td> | ||
<td>411.43<br /> | <td>411.43<br /> | ||
123°<span style="background-color: #ffffff;">25'43&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>14/11</strong><br /> | <td><strong>14/11</strong><br /> | ||
Line 306: | Line 354: | ||
</td> | </td> | ||
<td>445.71<br /> | <td>445.71<br /> | ||
133°<span style="background-color: #ffffff;">42'51&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>22/17</strong>, 32/25<br /> | <td><strong>22/17</strong>, 32/25<br /> | ||
Line 320: | Line 369: | ||
</td> | </td> | ||
<td>480<br /> | <td>480<br /> | ||
144°<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 334: | Line 384: | ||
</td> | </td> | ||
<td>514.29<br /> | <td>514.29<br /> | ||
<span style="background-color: #ffffff;">154°17'9&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 348: | Line 399: | ||
</td> | </td> | ||
<td>548.57<br /> | <td>548.57<br /> | ||
164°<span style="background-color: #ffffff;">34'17&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>11/8</strong><br /> | <td><strong>11/8</strong><br /> | ||
Line 362: | Line 414: | ||
</td> | </td> | ||
<td>582.86<br /> | <td>582.86<br /> | ||
174°<span style="background-color: #ffffff;">51'26&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>7/5</strong><br /> | <td><strong>7/5</strong><br /> | ||
Line 376: | Line 429: | ||
</td> | </td> | ||
<td>617.14<br /> | <td>617.14<br /> | ||
185°<span style="background-color: #ffffff;">8'34&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>10/7</strong><br /> | <td><strong>10/7</strong><br /> | ||
Line 390: | Line 444: | ||
</td> | </td> | ||
<td>651.43<br /> | <td>651.43<br /> | ||
195°<span style="background-color: #ffffff;">25'43&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>16/11</strong><br /> | <td><strong>16/11</strong><br /> | ||
Line 404: | Line 459: | ||
</td> | </td> | ||
<td>685.71<br /> | <td>685.71<br /> | ||
<span style="background-color: #ffffff;">205°42'51&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 418: | Line 474: | ||
</td> | </td> | ||
<td>720<br /> | <td>720<br /> | ||
216°<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 432: | Line 489: | ||
</td> | </td> | ||
<td>754.29<br /> | <td>754.29<br /> | ||
226°<span style="background-color: #ffffff;">17'9&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>17/11</strong>, 25/16<br /> | <td><strong>17/11</strong>, 25/16<br /> | ||
Line 446: | Line 504: | ||
</td> | </td> | ||
<td>788.57<br /> | <td>788.57<br /> | ||
236°<span style="background-color: #ffffff;">34'17&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>11/7</strong><br /> | <td><strong>11/7</strong><br /> | ||
Line 460: | Line 519: | ||
</td> | </td> | ||
<td>822.86<br /> | <td>822.86<br /> | ||
246°<span style="background-color: #ffffff;">51'26&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>8/5</strong><br /> | <td><strong>8/5</strong><br /> | ||
Line 473: | Line 533: | ||
<td>25<br /> | <td>25<br /> | ||
</td> | </td> | ||
<td>857. | <td>857.14<br /> | ||
<span style="background-color: #ffffff;">257°8'34&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>28/17</strong><br /> | <td><strong>28/17</strong><br /> | ||
Line 488: | Line 549: | ||
</td> | </td> | ||
<td>891.43<br /> | <td>891.43<br /> | ||
267°<span style="background-color: #ffffff;">25'43&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 502: | Line 564: | ||
</td> | </td> | ||
<td>925.71<br /> | <td>925.71<br /> | ||
277°<span style="background-color: #ffffff;">42'51&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>17/10</strong><br /> | <td><strong>17/10</strong><br /> | ||
Line 516: | Line 579: | ||
</td> | </td> | ||
<td>960<br /> | <td>960<br /> | ||
288°<br /> | |||
</td> | </td> | ||
<td><strong>7/4</strong><br /> | <td><strong>7/4</strong><br /> | ||
Line 530: | Line 594: | ||
</td> | </td> | ||
<td>994.29<br /> | <td>994.29<br /> | ||
298°<span style="background-color: #ffffff;">17'9&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 544: | Line 609: | ||
</td> | </td> | ||
<td>1028.57<br /> | <td>1028.57<br /> | ||
<span style="background-color: #ffffff;">308°34'17&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>20/11</strong><br /> | <td><strong>20/11</strong><br /> | ||
Line 558: | Line 624: | ||
</td> | </td> | ||
<td>1062.86<br /> | <td>1062.86<br /> | ||
318°<span style="background-color: #ffffff;">51'26&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 572: | Line 639: | ||
</td> | </td> | ||
<td>1097.14<br /> | <td>1097.14<br /> | ||
329°<span style="background-color: #ffffff;">8'34&quot;</span><br /> | |||
</td> | </td> | ||
<td><strong>32/17</strong><br /> | <td><strong>32/17</strong><br /> | ||
Line 583: | Line 651: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>3<br /> | ||
</td> | </td> | ||
<td>1131.43<br /> | <td>1131.43<br /> | ||
339°<span style="background-color: #ffffff;">25'43&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 600: | Line 669: | ||
</td> | </td> | ||
<td>1165.71<br /> | <td>1165.71<br /> | ||
349°<span style="background-color: #ffffff;">42'51&quot;</span><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
Line 626: | Line 696: | ||
flat 3/2 (patent val)<br /> | flat 3/2 (patent val)<br /> | ||
</th> | </th> | ||
<th><span style="display: block; text-align: center;">Temperaments | <th><span style="display: block; text-align: center;">Temperaments with sharp 3/2 (35b val)</span><br /> | ||
</th> | </th> | ||
</tr> | </tr> |