35edo
IMPORTED REVISION FROM WIKISPACES
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Original Wikitext content:
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. 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. =Intervals= || 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 || || || || 1 || 34.29 || || || || || 2 || 68.57 || || || || || 3 || 102.86 || 17/16 || || 18/17 || || 4 || 137.14 || || 12/11 || || || 5 || 171.43 || 11/10 || || 10/9 || || 6 || 205.71 || || || 9/8 || || 7 || 240 || 8/7 || || || || 8 || 274.29 || 20/17 || 7/6 || || || 9 || 308.57 || || 6/5 || || || 10 || 342.86 || 17/14 || || 11/9 || || 11 || 377.14 || 5/4 || || || || 12 || 411.43 || 14/11 || || 14/11 || || 13 || 445.71 || 22/17 || || 9/7 || || 14 || 480 || || || || || 15 || 514.29 || || 4/3 || || || 16 || 548.57 || 11/8 || || || || 17 || 582.86 || 7/5 || 24/17 || || || 18 || 617.14 || 10/7 || 17/12 || || || 19 || 651.43 || 16/11 || || || || 20 || 685.71 || || 3/2 || || || 21 || 720 || || || || || 22 || 754.29 || 17/11 || || 14/9 || || 23 || 788.57 || 11/7 || || || || 24 || 822.86 || 8/5 || || || || 25 || 857.15 || || || 18/11 || || 26 || 891.43 || || 5/3 || || || 27 || 925.71 || 17/10 || 12/7 || || || 28 || 960 || 7/4 || || || || 29 || 994.29 || || || 16/9 || || 30 || 1028.57 || 20/11 || || 9/5 || || 31 || 1062.86 || || 11/6 || || || 32 || 1097.14 || 32/17 || || 17/9 || || 33 || 1131.43 || || || || || 34 || 1165.71 || || || || =Rank two temperaments= ||~ Periods per octave ||~ Generator ||~ Temperaments || || 1 || 3\35 || Ripple || || 1 || 4\35 || [[xenharmonic/Greenwoodmic temperaments#Secund|Secund]] || || 1 || 6\35 || || || 1 || 8\35 || || || 1 || 9\35 || [[xenharmonic/Myna|Myna]] || || 1 || 11\35 || [[xenharmonic/Magic|Magic]] || || 1 || 12\35 || || || 1 || 13\35 || [[Sensipent family|Sensipent]] || || 1 || 16\35 || || || 1 || 17\35 || || || || || || || 5 || 2\35 || || || || || || || 7 || 1\35 || [[xenharmonic/Apotome family|Whitewood]]/[[xenharmonic/Apotome family#Redwood|Redwood]] || || 7 || 2\35 || [[Greenwoodmic temperaments#Greenwood|Greenwood]] || ==<span style="background-color: #ffffff;">Commas</span>== <span style="background-color: #ffffff;">35EDO tempers out the following commas. (Note: This assumes the val </span><35 55 81 98 121 130|<span style="background-color: #ffffff;">.)</span> ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || ||= 2187/2048 ||< | -11 7 > ||> <span style="background-color: #ffffff; display: block; text-align: right;">113.69</span> ||= Apotome ||= Whitewood comma ||= || ||= <span style="background-color: #ffffff;">6561/6250</span> || <span style="background-color: #ffffff; display: block; text-align: left;"><span style="background-color: #ffffff;">| -1 8 -5 ></span></span> ||> <span style="background-color: #ffffff; display: block; text-align: right;">84.07</span> ||= Ripple comma ||= || || ||= <span style="background-color: #ffffff;">10077696/9765625</span> || | 9 9 -10 > ||> 54.46 ||= Mynic comma ||= || || ||= 3125/3072 || <span style="background-color: #ffffff; display: block; text-align: left;">| -10 -1 5 ></span> ||> <span style="background-color: #ffffff; display: block; text-align: right;">29.61</span> ||= <span style="background-color: #ffffff;">Small diesis</span> ||= <span style="background-color: #ffffff;">Magic comma</span> || || ||= <span style="background-color: #ffffff;">78732/78125</span> || | 2 9 -7 > ||> 13.40 ||= Medium semicomma ||= Sensipent comma || || ||= 405/392 || | -3 4 1 -2 > ||> 56.48 ||= Greenwoodma ||= || || ||= <span style="background-color: #ffffff; display: block; text-align: center;">16807/16384</span> || <span style="background-color: #ffffff;">| -14 0 0 5 ></span> ||> 44.13 ||= ||= || || ||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= || || ||= 126/125 || <span style="background-color: #ffffff;">| 1 2 -3 1 ></span> ||> 13.79 ||= Starling comma ||= <span style="background-color: #ffffff; display: block; text-align: center;">Septimal semicomma</span> || || ||= 99/98 || | -1 2 0 -2 1 > ||> 17.58 || Mothwellsma || || || ||= 66/65 || | 1 1 -1 0 1 -1 > ||> 26.43 || || || ||
Original HTML content:
<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 />
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 />
<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 />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h1>
<br />
<br />
<table class="wiki_table">
<tr>
<td>Degrees of 35-EDO<br />
</td>
<td>Cents value<br />
</td>
<td>Ratios in 2.5.7.11.17 subgroup<br />
</td>
<td>Ratios with flat 3<br />
</td>
<td>Ratios with 9<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td>1/1<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>34.29<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>68.57<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>102.86<br />
</td>
<td>17/16<br />
</td>
<td><br />
</td>
<td>18/17<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>137.14<br />
</td>
<td><br />
</td>
<td>12/11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>171.43<br />
</td>
<td>11/10<br />
</td>
<td><br />
</td>
<td>10/9<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>205.71<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>9/8<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>240<br />
</td>
<td>8/7<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>274.29<br />
</td>
<td>20/17<br />
</td>
<td>7/6<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>308.57<br />
</td>
<td><br />
</td>
<td>6/5<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>342.86<br />
</td>
<td>17/14<br />
</td>
<td><br />
</td>
<td>11/9<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>377.14<br />
</td>
<td>5/4<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>411.43<br />
</td>
<td>14/11<br />
</td>
<td><br />
</td>
<td>14/11<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>445.71<br />
</td>
<td>22/17<br />
</td>
<td><br />
</td>
<td>9/7<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>480<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>514.29<br />
</td>
<td><br />
</td>
<td>4/3<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>548.57<br />
</td>
<td>11/8<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>582.86<br />
</td>
<td>7/5<br />
</td>
<td>24/17<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>617.14<br />
</td>
<td>10/7<br />
</td>
<td>17/12<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>651.43<br />
</td>
<td>16/11<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>685.71<br />
</td>
<td><br />
</td>
<td>3/2<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>720<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>754.29<br />
</td>
<td>17/11<br />
</td>
<td><br />
</td>
<td>14/9<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>788.57<br />
</td>
<td>11/7<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>822.86<br />
</td>
<td>8/5<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>857.15<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>18/11<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>891.43<br />
</td>
<td><br />
</td>
<td>5/3<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>925.71<br />
</td>
<td>17/10<br />
</td>
<td>12/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>960<br />
</td>
<td>7/4<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>994.29<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>16/9<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>1028.57<br />
</td>
<td>20/11<br />
</td>
<td><br />
</td>
<td>9/5<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>1062.86<br />
</td>
<td><br />
</td>
<td>11/6<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>1097.14<br />
</td>
<td>32/17<br />
</td>
<td><br />
</td>
<td>17/9<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>1131.43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>1165.71<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank two temperaments</h1>
<br />
<br />
<table class="wiki_table">
<tr>
<th>Periods<br />
per octave<br />
</th>
<th>Generator<br />
</th>
<th>Temperaments<br />
</th>
</tr>
<tr>
<td>1<br />
</td>
<td>3\35<br />
</td>
<td>Ripple<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>4\35<br />
</td>
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund">Secund</a><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>6\35<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>8\35<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>9\35<br />
</td>
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Myna">Myna</a><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>11\35<br />
</td>
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Magic">Magic</a><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>12\35<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>13\35<br />
</td>
<td><a class="wiki_link" href="/Sensipent%20family">Sensipent</a><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>16\35<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>17\35<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>2\35<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>1\35<br />
</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>
</tr>
<tr>
<td>7<br />
</td>
<td>2\35<br />
</td>
<td><a class="wiki_link" href="/Greenwoodmic%20temperaments#Greenwood">Greenwood</a><br />
</td>
</tr>
</table>
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Rank two temperaments-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;">Commas</span></h2>
<span style="background-color: #ffffff;">35EDO tempers out the following commas. (Note: This assumes the val </span><35 55 81 98 121 130|<span style="background-color: #ffffff;">.)</span><br />
<br />
<table class="wiki_table">
<tr>
<th>Comma<br />
</th>
<th>Monzo<br />
</th>
<th>Value (Cents)<br />
</th>
<th>Name 1<br />
</th>
<th>Name 2<br />
</th>
<th>Name 3<br />
</th>
</tr>
<tr>
<td style="text-align: center;">2187/2048<br />
</td>
<td style="text-align: left;">| -11 7 ><br />
</td>
<td style="text-align: right;"><span style="background-color: #ffffff; display: block; text-align: right;">113.69</span><br />
</td>
<td style="text-align: center;">Apotome<br />
</td>
<td style="text-align: center;">Whitewood comma<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><span style="background-color: #ffffff;">6561/6250</span><br />
</td>
<td><span style="background-color: #ffffff; display: block; text-align: left;"><span style="background-color: #ffffff;">| -1 8 -5 ></span></span><br />
</td>
<td style="text-align: right;"><span style="background-color: #ffffff; display: block; text-align: right;">84.07</span><br />
</td>
<td style="text-align: center;">Ripple comma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><span style="background-color: #ffffff;">10077696/9765625</span><br />
</td>
<td>| 9 9 -10 ><br />
</td>
<td style="text-align: right;">54.46<br />
</td>
<td style="text-align: center;">Mynic comma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">3125/3072<br />
</td>
<td><span style="background-color: #ffffff; display: block; text-align: left;">| -10 -1 5 ></span><br />
</td>
<td style="text-align: right;"><span style="background-color: #ffffff; display: block; text-align: right;">29.61</span><br />
</td>
<td style="text-align: center;"><span style="background-color: #ffffff;">Small diesis</span><br />
</td>
<td style="text-align: center;"><span style="background-color: #ffffff;">Magic comma</span><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><span style="background-color: #ffffff;">78732/78125</span><br />
</td>
<td>| 2 9 -7 ><br />
</td>
<td style="text-align: right;">13.40<br />
</td>
<td style="text-align: center;">Medium semicomma<br />
</td>
<td style="text-align: center;">Sensipent comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">405/392<br />
</td>
<td>| -3 4 1 -2 ><br />
</td>
<td style="text-align: right;">56.48<br />
</td>
<td style="text-align: center;">Greenwoodma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">16807/16384</span><br />
</td>
<td><span style="background-color: #ffffff;">| -14 0 0 5 ></span><br />
</td>
<td style="text-align: right;">44.13<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">525/512<br />
</td>
<td>| -9 1 2 1 ><br />
</td>
<td style="text-align: right;">43.41<br />
</td>
<td style="text-align: center;">Avicennma<br />
</td>
<td style="text-align: center;"><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">126/125<br />
</td>
<td><span style="background-color: #ffffff;">| 1 2 -3 1 ></span><br />
</td>
<td style="text-align: right;">13.79<br />
</td>
<td style="text-align: center;">Starling comma<br />
</td>
<td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">Septimal semicomma</span><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">99/98<br />
</td>
<td>| -1 2 0 -2 1 ><br />
</td>
<td style="text-align: right;">17.58<br />
</td>
<td>Mothwellsma<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td style="text-align: center;">66/65<br />
</td>
<td>| 1 1 -1 0 1 -1 ><br />
</td>
<td style="text-align: right;">26.43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>