35edo: Difference between revisions
Wikispaces>keenanpepper **Imported revision 330244846 - Original comment: ** |
Wikispaces>phylingual **Imported revision 330266656 - 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:phylingual|phylingual]] and made on <tt>2012-05-04 20:20:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>330266656</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 8: | Line 8: | ||
<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">35-tET or 35-[[xenharmonic/edo|EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[xenharmonic/cent|34.29¢]] each. | <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">35-tET or 35-[[xenharmonic/edo|EDO]] refers to a tuning system which divides the octave into 35 steps of approximately [[xenharmonic/cent|34.29¢]] each. | ||
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[xenharmonic/macrotonal edos|macrotonal edos]]: [[xenharmonic/5edo|5edo]] and [[xenharmonic/7edo|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 can also represent the 2.3.5.7.11.17 [[xenharmonic/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 among whitewood tunings it is very versatile, you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9, and if you ignore [[xenharmonic/22edo|22edo]]'s consistent representation of both subgroups. 35edo has the optimal patent val for [[xenharmonic/Greenwoodmic temperaments|greenwood]] and [[xenharmonic/Greenwoodmic temperaments#Secund|secund]] temperaments. | As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[xenharmonic/macrotonal edos|macrotonal edos]]: [[xenharmonic/5edo|5edo]] and [[xenharmonic/7edo|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 can also represent the 2.3.5.7.11.17 [[xenharmonic/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 among whitewood tunings it is very versatile, you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[xenharmonic/22edo|22edo]]'s | ||
more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for [[xenharmonic/Greenwoodmic temperaments|greenwood]] and [[xenharmonic/Greenwoodmic temperaments#Secund|secund]] temperaments. | |||
A good beggining for start to play 35-EDO is with the Sub-diatonic scale, that is a [[xenharmonic/MOS|MOS]] of 3L2s: 9 4 9 9 4. | A good beggining for start to play 35-EDO is with the Sub-diatonic scale, that is a [[xenharmonic/MOS|MOS]] of 3L2s: 9 4 9 9 4. | ||
| Line 17: | Line 18: | ||
|| Degrees of 35-EDO || Cents value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with 9 || | || Degrees of 35-EDO || Cents value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with 9 || | ||
|| 0 || 0 || 1/1 || || || | || 0 || 0 || 1/1 || || || | ||
|| 1 || 34.29 || | || 1 || 34.29 || 50/49, 121/119 || 36/35 || 81/80 || | ||
|| 2 || 68.57 || | || 2 || 68.57 || 128/125 || 25/24 || || | ||
|| 3 || 102.86 || 17/16 || || 18/17 || | || 3 || 102.86 || 17/16 || || 18/17 || | ||
|| 4 || 137.14 || || 12/11 || || | || 4 || 137.14 || || 12/11 || || | ||
| Line 38: | Line 39: | ||
|| 20 || 685.71 || || 3/2 || || | || 20 || 685.71 || || 3/2 || || | ||
|| 21 || 720 || || || || | || 21 || 720 || || || || | ||
|| 22 || 754.29 || 17/11 || | || 22 || 754.29 || 17/11 || 25/24 || 14/9 || | ||
|| 23 || 788.57 || 11/7 || || || | || 23 || 788.57 || 11/7 || || || | ||
|| 24 || 822.86 || 8/5 || || || | || 24 || 822.86 || 8/5 || || || | ||
| Line 54: | Line 55: | ||
||~ Periods | ||~ Periods | ||
per octave ||~ Generator ||~ Temperaments || | per octave ||~ Generator ||~ Temperaments | ||
|| 1 || 1\35 || || | with flat 3/2 ||~ <span style="text-align: center;">Temperaments</span> | ||
|| 1 || 2\35 || || | <span style="text-align: center;">with sharp 3/2</span> || | ||
|| 1 || 3\35 || Ripple || | || 1 || 1\35 || || || | ||
|| 1 || 4\35 || [[xenharmonic/Greenwoodmic temperaments#Secund|Secund]] || | || 1 || 2\35 || || || | ||
|| 1 || 6\35 || | || 1 || 3\35 || || [[Ripple]] || | ||
|| 1 || 8\35 || Messed-up [[Orwell]] || | || 1 || 4\35 || [[xenharmonic/Greenwoodmic temperaments#Secund|Secund]] || || | ||
|| 1 || 9\35 || [[xenharmonic/Myna|Myna]] || | || 1 || 6\35 |||| Messed-up [[Subgroup temperaments#Baldy|Baldy]] || | ||
|| 1 || 11\35 || [[ | || 1 || 8\35 || || Messed-up [[Orwell]] || | ||
|| 1 || 12\35 || || | || 1 || 9\35 || [[xenharmonic/Myna|Myna]] || || | ||
|| 1 || 13\35 || [[xenharmonic/Sensipent family|Sensipent]] || | || 1 || 11\35 || [[Magic family#Muggles|Muggles]] || || | ||
|| 1 || 16\35 || || | || 1 || 12\35 || || [[Avicennmic temperaments#Roman|Roman]] || | ||
|| 1 || 17\35 || || | || 1 || 13\35 || || [[xenharmonic/Sensipent family|Sensipent]] but //not// [[Sensi]] || | ||
|| 5 || 1\35 || || | || 1 || 16\35 || || || | ||
|| 5 || 2\35 || [[Blackwood]] || | || 1 || 17\35 || || || | ||
|| 5 || 3\35 || | || 5 || 1\35 || || || | ||
|| 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] || | || 5 || 2\35 || || Bad [[Blackwood]] || | ||
|| 7 || 2\35 || [[xenharmonic/Greenwoodmic temperaments#Greenwood|Greenwood]] || | || 5 || 3\35 || || || | ||
|| 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] || || | |||
|| 7 || 2\35 || [[xenharmonic/Greenwoodmic temperaments#Greenwood|Greenwood]] || || | |||
==<span style="background-color: #ffffff;">Commas</span>== | ==<span style="background-color: #ffffff;">Commas</span>== | ||
35EDO tempers out the following commas. (Note: This assumes the val <35 55 81 98 121 130|.) | 35EDO tempers out the following commas. (Note: This assumes the val <35 55 81 98 121 130|.) | ||
||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** || | ||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** || | ||
||= 2187/2048 || | -11 7 > ||> 113.69 ||= Apotome ||= Whitewood comma || || | ||= 2187/2048 || | -11 7 > ||> 113.69 ||= Apotome ||= Whitewood comma || || | ||
| Line 95: | Line 95: | ||
<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>35-tET or 35-<a class="wiki_link" href="http://xenharmonic.wikispaces.com/edo">EDO</a> refers to a tuning system which divides the octave into 35 steps of approximately <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">34.29¢</a> each.<br /> | <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>35-tET or 35-<a class="wiki_link" href="http://xenharmonic.wikispaces.com/edo">EDO</a> refers to a tuning system which divides the octave into 35 steps of approximately <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent">34.29¢</a> each.<br /> | ||
<br /> | <br /> | ||
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic <a class="wiki_link" href="http://xenharmonic.wikispaces.com/macrotonal%20edos">macrotonal edos</a>: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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¢. 35edo can also represent the 2.3.5.7.11.17 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 among whitewood tunings it is very versatile, you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9, and if you ignore <a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo">22edo</a>'s consistent representation of both subgroups. 35edo has the optimal patent val for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments">greenwood</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">secund</a> temperaments.<br /> | As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic <a class="wiki_link" href="http://xenharmonic.wikispaces.com/macrotonal%20edos">macrotonal edos</a>: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo">5edo</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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¢. 35edo can also represent the 2.3.5.7.11.17 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 among whitewood tunings it is very versatile, you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore <a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo">22edo</a>'s<br /> | ||
more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments">greenwood</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">secund</a> temperaments.<br /> | |||
<br /> | <br /> | ||
A good beggining for start to play 35-EDO is with the Sub-diatonic scale, that is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOS">MOS</a> of 3L2s: 9 4 9 9 4.<br /> | A good beggining for start to play 35-EDO is with the Sub-diatonic scale, that is a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOS">MOS</a> of 3L2s: 9 4 9 9 4.<br /> | ||
| Line 134: | Line 135: | ||
<td>34.29<br /> | <td>34.29<br /> | ||
</td> | </td> | ||
<td><br /> | <td>50/49, 121/119<br /> | ||
</td> | </td> | ||
<td><br /> | <td>36/35<br /> | ||
</td> | </td> | ||
<td><br /> | <td>81/80<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 146: | Line 147: | ||
<td>68.57<br /> | <td>68.57<br /> | ||
</td> | </td> | ||
<td><br /> | <td>128/125<br /> | ||
</td> | </td> | ||
<td><br /> | <td>25/24<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 388: | Line 389: | ||
<td>17/11<br /> | <td>17/11<br /> | ||
</td> | </td> | ||
<td><br /> | <td>25/24<br /> | ||
</td> | </td> | ||
<td>14/9<br /> | <td>14/9<br /> | ||
| Line 551: | Line 552: | ||
</th> | </th> | ||
<th>Temperaments<br /> | <th>Temperaments<br /> | ||
with flat 3/2<br /> | |||
</th> | |||
<th><span style="text-align: center;">Temperaments</span><br /> | |||
<span style="text-align: center;">with sharp 3/2</span><br /> | |||
</th> | </th> | ||
</tr> | </tr> | ||
| Line 557: | Line 562: | ||
</td> | </td> | ||
<td>1\35<br /> | <td>1\35<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 565: | Line 572: | ||
</td> | </td> | ||
<td>2\35<br /> | <td>2\35<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 574: | Line 583: | ||
<td>3\35<br /> | <td>3\35<br /> | ||
</td> | </td> | ||
<td>Ripple<br /> | <td><br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Ripple">Ripple</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 583: | Line 594: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">Secund</a><br /> | <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">Secund</a><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 590: | Line 603: | ||
<td>6\35<br /> | <td>6\35<br /> | ||
</td> | </td> | ||
<td><br /> | <td colspan="2">Messed-up <a class="wiki_link" href="/Subgroup%20temperaments#Baldy">Baldy</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 597: | Line 610: | ||
</td> | </td> | ||
<td>8\35<br /> | <td>8\35<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td>Messed-up <a class="wiki_link" href="/Orwell">Orwell</a><br /> | <td>Messed-up <a class="wiki_link" href="/Orwell">Orwell</a><br /> | ||
| Line 607: | Line 622: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Myna">Myna</a><br /> | <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Myna">Myna</a><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 614: | Line 631: | ||
<td>11\35<br /> | <td>11\35<br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href=" | <td><a class="wiki_link" href="/Magic%20family#Muggles">Muggles</a><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 623: | Line 642: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td><a class="wiki_link" href="/Avicennmic%20temperaments#Roman">Roman</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 630: | Line 651: | ||
<td>13\35<br /> | <td>13\35<br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensipent%20family">Sensipent</a><br /> | <td><br /> | ||
</td> | |||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Sensipent%20family">Sensipent</a> but <em>not</em> <a class="wiki_link" href="/Sensi">Sensi</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 637: | Line 660: | ||
</td> | </td> | ||
<td>16\35<br /> | <td>16\35<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 645: | Line 670: | ||
</td> | </td> | ||
<td>17\35<br /> | <td>17\35<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 653: | Line 680: | ||
</td> | </td> | ||
<td>1\35<br /> | <td>1\35<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 662: | Line 691: | ||
<td>2\35<br /> | <td>2\35<br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/Blackwood">Blackwood</a><br /> | <td><br /> | ||
</td> | |||
<td>Bad <a class="wiki_link" href="/Blackwood">Blackwood</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 669: | Line 700: | ||
</td> | </td> | ||
<td>3\35<br /> | <td>3\35<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 677: | Line 712: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family">Whitewood</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family#Redwood">Redwood</a><br /> | <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family">Whitewood</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Apotome%20family#Redwood">Redwood</a><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 685: | Line 722: | ||
</td> | </td> | ||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Greenwood">Greenwood</a><br /> | <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Greenwood">Greenwood</a><br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 691: | Line 730: | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Rank two temperaments-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;">Commas</span></h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Rank two temperaments-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;">Commas</span></h2> | ||
35EDO tempers out the following commas. (Note: This assumes the val &lt;35 55 81 98 121 130|.)<br /> | 35EDO tempers out the following commas. (Note: This assumes the val &lt;35 55 81 98 121 130|.)<br /> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
| Line 867: | Line 903: | ||
</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h2> | ||
</body></html></pre></div> | </body></html></pre></div> | ||