35edo

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Revision as of 08:25, 6 December 2016 by Wikispaces>JosephRuhf (**Imported revision 601502570 - Original comment: **)
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The original revision id was 601502570.
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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¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent of error. 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 (7/5 and 17/11 stand out, having less than 1 cent error). 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, as well as 11-limit [[Magic family#Muggles-11-limit%7D|muggles]], and the 35f val is an excellent tuning for 13-limit muggles.

A good beginning 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= 

(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)
|| 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) ||   ||   ||
|| 1 || 34.29
10°<span style="background-color: #ffffff;">17'9"</span> || **50/49**, **121/119**, 33/32 || **36/35** || 25/24 || **81/80** ||
|| 2 || 68.57
20°<span style="background-color: #ffffff;">34'17"</span> || 128/125 || **25/24** || 81/80 ||   ||
|| 3 || 102.86
30°<span style="background-color: #ffffff;">51'26"</span> || **17/16** || **15/14** || **16/15** || **18/17** ||
|| 4 || 137.14
41°<span style="background-color: #ffffff;">8'34"</span> ||   || **12/11**, 16/15 ||   ||   ||
|| 5 || 171.43
<span style="background-color: #ffffff;">51°25'43"</span> || **11/10** ||   || 12/11 || **10/9** ||
|| 6 || 205.71
61°<span style="background-color: #ffffff;">42'51"</span> ||   ||   ||   || **9/8** ||
|| 7 || 240
72° || **8/7** ||   || 7/6 ||   ||
|| 8 || 274.29
82°<span style="background-color: #ffffff;">17'9"</span> || **20/17** || **7/6** ||   ||   ||
|| 9 || 308.57
92°<span style="background-color: #ffffff;">34'17"</span> ||   || **6/5** ||   ||   ||
|| 10 || 342.86
<span style="background-color: #ffffff;">102°51'26"</span> || **17/14** ||   || 6/5 || **11/9** ||
|| 11 || 377.14
113°<span style="background-color: #ffffff;">8'34"</span> || **5/4** ||   ||   ||   ||
|| 12 || 411.43
123°<span style="background-color: #ffffff;">25'43"</span> || **14/11** ||   ||   ||   ||
|| 13 || 445.71
133°<span style="background-color: #ffffff;">42'51"</span> || **22/17**, 32/25 ||   ||   || **9/7** ||
|| 14 || 480
144° ||   ||   || 4/3, **21/16** ||   ||
|| 15 || 514.29
<span style="background-color: #ffffff;">154°17'9"</span> ||   || **4/3** ||   ||   ||
|| 16 || 548.57
164°<span style="background-color: #ffffff;">34'17"</span> || **11/8** ||   ||   ||   ||
|| 17 || 582.86
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** ||
|| 33 || 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= 

||~ Periods
per octave ||~ Generator ||~ Temperaments with
flat 3/2 (patent val) ||~ <span style="display: block; text-align: center;">Temperaments with sharp 3/2 (35b val)</span> ||
|| 1 || 1\35 ||   ||   ||
|| 1 || 2\35 ||   ||   ||
|| 1 || 3\35 ||   || [[Ripple]] ||
|| 1 || 4\35 || [[xenharmonic/Greenwoodmic temperaments#Secund|Secund]] ||   ||
|| 1 || 6\35 |||| Messed-up [[Chromatic pairs#Baldy|Baldy]] ||
|| 1 || 8\35 ||   || Messed-up [[Orwell]] ||
|| 1 || 9\35 || [[xenharmonic/Myna|Myna]] ||   ||
|| 1 || 11\35 || [[Magic family#Muggles|Muggles]] ||   ||
|| 1 || 12\35 ||   || [[Avicennmic temperaments#Roman|Roman]] ||
|| 1 || 13\35 |||| Inconsistent 2.9'/7.5/3 [[Sensi]] ||
|| 1 || 16\35 ||   ||   ||
|| 1 || 17\35 ||   ||   ||
|| 5 || 1\35 ||   || [[Blackwood]] (favoring 7/6) ||
|| 5 || 2\35 ||   || [[Blackwood]] (favoring 6/5 and 20/17) ||
|| 5 || 3\35 ||   || [[Blackwood]] (favoring 5/4 and 17/14) ||
|| 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;">Scales</span>= 
== == 
==<span style="background-color: #ffffff;">Commas</span>== 
35EDO tempers out the following commas. (Note: This assumes the val <[[tel:35 55 81 98 121|35 55 81 98 121]] 130|.)
||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** ||
||= 2187/2048 || | -11 7 > ||> 113.69 ||= Apotome ||= Whitewood comma ||   ||
||= 6561/6250 || | -1 8 -5 > ||> 84.07 ||= Ripple comma ||=   ||   ||
||=   || | 9 9 -10 > ||> 54.46 ||= Mynic comma ||=   ||   ||
||= 3125/3072 || | -10 -1 5 > ||> 29.61 ||= Small diesis ||= Magic comma ||   ||
||= 405/392 || | -3 4 1 -2 > ||> 56.48 ||= Greenwoodma ||=   ||   ||
||= 16807/16384 || | -14 0 0 5 > ||> 44.13 ||=   ||=   ||   ||
||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicenna ||=   ||   ||
||= 126/125 || | 1 2 -3 1 > ||> 13.79 ||= Starling comma ||= Septimal semicomma ||   ||
||= 99/98 || | -1 2 0 -2 1 > ||> 17.58 ||= Mothwellsma ||=   ||   ||
||= 66/65 || | 1 1 -1 0 1 -1 > ||> 26.43 ||=   ||=   ||   ||
== == 

==Music== 
[[@http://soonlabel.com/xenharmonic/archives/2348|Little Prelude & Fugue, "The Bijingle" by Claudi Meneghin]]
[[@http://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3|Self-Destructing Mechanical Forest]] by Chuckles McGee (in Secund[9])

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¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent of error. 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 (7/5 and 17/11 stand out, having less than 1 cent error). 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 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, as well as 11-limit <a class="wiki_link" href="/Magic%20family#Muggles-11-limit%7D">muggles</a>, and the 35f val is an excellent tuning for 13-limit muggles.<br />
<br />
A good beginning 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:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h1>
 <br />
(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)<br />


<table class="wiki_table">
    <tr>
        <td>Degrees<br />
</td>
        <td>Cents value<br />
DMS value<br />
</td>
        <td>Ratios in 2.5.7.11.17 subgroup<br />
</td>
        <td>Ratios with flat 3<br />
</td>
        <td>Ratios with sharp 3<br />
</td>
        <td>Ratios with patent 9<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td><strong>1/1</strong><br />
</td>
        <td>(see comma table)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>34.29<br />
10°<span style="background-color: #ffffff;">17'9&quot;</span><br />
</td>
        <td><strong>50/49</strong>, <strong>121/119</strong>, 33/32<br />
</td>
        <td><strong>36/35</strong><br />
</td>
        <td>25/24<br />
</td>
        <td><strong>81/80</strong><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>68.57<br />
20°<span style="background-color: #ffffff;">34'17&quot;</span><br />
</td>
        <td>128/125<br />
</td>
        <td><strong>25/24</strong><br />
</td>
        <td>81/80<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>102.86<br />
30°<span style="background-color: #ffffff;">51'26&quot;</span><br />
</td>
        <td><strong>17/16</strong><br />
</td>
        <td><strong>15/14</strong><br />
</td>
        <td><strong>16/15</strong><br />
</td>
        <td><strong>18/17</strong><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>137.14<br />
41°<span style="background-color: #ffffff;">8'34&quot;</span><br />
</td>
        <td><br />
</td>
        <td><strong>12/11</strong>, 16/15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>171.43<br />
<span style="background-color: #ffffff;">51°25'43&quot;</span><br />
</td>
        <td><strong>11/10</strong><br />
</td>
        <td><br />
</td>
        <td>12/11<br />
</td>
        <td><strong>10/9</strong><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>205.71<br />
61°<span style="background-color: #ffffff;">42'51&quot;</span><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><strong>9/8</strong><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>240<br />
72°<br />
</td>
        <td><strong>8/7</strong><br />
</td>
        <td><br />
</td>
        <td>7/6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>274.29<br />
82°<span style="background-color: #ffffff;">17'9&quot;</span><br />
</td>
        <td><strong>20/17</strong><br />
</td>
        <td><strong>7/6</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>308.57<br />
92°<span style="background-color: #ffffff;">34'17&quot;</span><br />
</td>
        <td><br />
</td>
        <td><strong>6/5</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>342.86<br />
<span style="background-color: #ffffff;">102°51'26&quot;</span><br />
</td>
        <td><strong>17/14</strong><br />
</td>
        <td><br />
</td>
        <td>6/5<br />
</td>
        <td><strong>11/9</strong><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>377.14<br />
113°<span style="background-color: #ffffff;">8'34&quot;</span><br />
</td>
        <td><strong>5/4</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>411.43<br />
123°<span style="background-color: #ffffff;">25'43&quot;</span><br />
</td>
        <td><strong>14/11</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>445.71<br />
133°<span style="background-color: #ffffff;">42'51&quot;</span><br />
</td>
        <td><strong>22/17</strong>, 32/25<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><strong>9/7</strong><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>480<br />
144°<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4/3, <strong>21/16</strong><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>514.29<br />
<span style="background-color: #ffffff;">154°17'9&quot;</span><br />
</td>
        <td><br />
</td>
        <td><strong>4/3</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>548.57<br />
164°<span style="background-color: #ffffff;">34'17&quot;</span><br />
</td>
        <td><strong>11/8</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>582.86<br />
174°<span style="background-color: #ffffff;">51'26&quot;</span><br />
</td>
        <td><strong>7/5</strong><br />
</td>
        <td><strong>24/17</strong><br />
</td>
        <td>17/12<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>617.14<br />
185°<span style="background-color: #ffffff;">8'34&quot;</span><br />
</td>
        <td><strong>10/7</strong><br />
</td>
        <td><strong>17/12</strong><br />
</td>
        <td>24/17<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>651.43<br />
195°<span style="background-color: #ffffff;">25'43&quot;</span><br />
</td>
        <td><strong>16/11</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>685.71<br />
<span style="background-color: #ffffff;">205°42'51&quot;</span><br />
</td>
        <td><br />
</td>
        <td><strong>3/2</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>720<br />
216°<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/2, <strong>32/21</strong><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>754.29<br />
226°<span style="background-color: #ffffff;">17'9&quot;</span><br />
</td>
        <td><strong>17/11</strong>, 25/16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><strong>14/9</strong><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>788.57<br />
236°<span style="background-color: #ffffff;">34'17&quot;</span><br />
</td>
        <td><strong>11/7</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>822.86<br />
246°<span style="background-color: #ffffff;">51'26&quot;</span><br />
</td>
        <td><strong>8/5</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>857.14<br />
<span style="background-color: #ffffff;">257°8'34&quot;</span><br />
</td>
        <td><strong>28/17</strong><br />
</td>
        <td><br />
</td>
        <td>5/3<br />
</td>
        <td><strong>18/11</strong><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>891.43<br />
267°<span style="background-color: #ffffff;">25'43&quot;</span><br />
</td>
        <td><br />
</td>
        <td><strong>5/3</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>925.71<br />
277°<span style="background-color: #ffffff;">42'51&quot;</span><br />
</td>
        <td><strong>17/10</strong><br />
</td>
        <td><strong>12/7</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>960<br />
288°<br />
</td>
        <td><strong>7/4</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>994.29<br />
298°<span style="background-color: #ffffff;">17'9&quot;</span><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><strong>16/9</strong><br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>1028.57<br />
<span style="background-color: #ffffff;">308°34'17&quot;</span><br />
</td>
        <td><strong>20/11</strong><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><strong>9/5</strong><br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>1062.86<br />
318°<span style="background-color: #ffffff;">51'26&quot;</span><br />
</td>
        <td><br />
</td>
        <td><strong>11/6</strong>, 15/8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>1097.14<br />
329°<span style="background-color: #ffffff;">8'34&quot;</span><br />
</td>
        <td><strong>32/17</strong><br />
</td>
        <td><strong>28/15</strong><br />
</td>
        <td><strong>15/8</strong><br />
</td>
        <td><strong>17/9</strong><br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>1131.43<br />
339°<span style="background-color: #ffffff;">25'43&quot;</span><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>1165.71<br />
349°<span style="background-color: #ffffff;">42'51&quot;</span><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank two temperaments</h1>
 <br />


<table class="wiki_table">
    <tr>
        <th>Periods<br />
per octave<br />
</th>
        <th>Generator<br />
</th>
        <th>Temperaments with<br />
flat 3/2 (patent val)<br />
</th>
        <th><span style="display: block; text-align: center;">Temperaments with sharp 3/2 (35b val)</span><br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1\35<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>2\35<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>3\35<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Ripple">Ripple</a><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>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>6\35<br />
</td>
        <td colspan="2">Messed-up <a class="wiki_link" href="/Chromatic%20pairs#Baldy">Baldy</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>8\35<br />
</td>
        <td><br />
</td>
        <td>Messed-up <a class="wiki_link" href="/Orwell">Orwell</a><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>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>11\35<br />
</td>
        <td><a class="wiki_link" href="/Magic%20family#Muggles">Muggles</a><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>12\35<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Avicennmic%20temperaments#Roman">Roman</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>13\35<br />
</td>
        <td colspan="2">Inconsistent 2.9'/7.5/3 <a class="wiki_link" href="/Sensi">Sensi</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>16\35<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>17\35<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>1\35<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Blackwood">Blackwood</a> (favoring 7/6)<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>2\35<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Blackwood">Blackwood</a> (favoring 6/5 and 20/17)<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>3\35<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="/Blackwood">Blackwood</a> (favoring 5/4 and 17/14)<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>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>2\35<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Greenwood">Greenwood</a><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;">Scales</span></h1>
 <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2>
 <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Scales-Commas"></a><!-- ws:end:WikiTextHeadingRule:8 --><span style="background-color: #ffffff;">Commas</span></h2>
 35EDO tempers out the following commas. (Note: This assumes the val &lt;<a class="wiki_link" href="http://tel.wikispaces.com/35%2055%2081%2098%20121">35 55 81 98 121</a> 130|.)<br />


<table class="wiki_table">
    <tr>
        <th><strong>Comma</strong><br />
</th>
        <th><strong>Monzo</strong><br />
</th>
        <th><strong>Value (Cents)</strong><br />
</th>
        <th><strong>Name 1</strong><br />
</th>
        <th><strong>Name 2</strong><br />
</th>
        <th><strong>Name 3</strong><br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;">2187/2048<br />
</td>
        <td>| -11 7 &gt;<br />
</td>
        <td style="text-align: right;">113.69<br />
</td>
        <td style="text-align: center;">Apotome<br />
</td>
        <td style="text-align: center;">Whitewood comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6561/6250<br />
</td>
        <td>| -1 8 -5 &gt;<br />
</td>
        <td style="text-align: right;">84.07<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;"><br />
</td>
        <td>| 9 9 -10 &gt;<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>| -10 -1 5 &gt;<br />
</td>
        <td style="text-align: right;">29.61<br />
</td>
        <td style="text-align: center;">Small diesis<br />
</td>
        <td style="text-align: center;">Magic comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">405/392<br />
</td>
        <td>| -3 4 1 -2 &gt;<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;">16807/16384<br />
</td>
        <td>| -14 0 0 5 &gt;<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 &gt;<br />
</td>
        <td style="text-align: right;">43.41<br />
</td>
        <td style="text-align: center;">Avicenna<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">126/125<br />
</td>
        <td>| 1 2 -3 1 &gt;<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;">Septimal semicomma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">99/98<br />
</td>
        <td>| -1 2 0 -2 1 &gt;<br />
</td>
        <td style="text-align: right;">17.58<br />
</td>
        <td style="text-align: center;">Mothwellsma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">66/65<br />
</td>
        <td>| 1 1 -1 0 1 -1 &gt;<br />
</td>
        <td style="text-align: right;">26.43<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><!-- ws:end:WikiTextHeadingRule:10 --> </h2>
 <br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Scales-Music"></a><!-- ws:end:WikiTextHeadingRule:12 -->Music</h2>
 <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/2348" rel="nofollow" target="_blank">Little Prelude &amp; Fugue, &quot;The Bijingle&quot; by Claudi Meneghin</a><br />
<a class="wiki_link_ext" href="http://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3" rel="nofollow" target="_blank">Self-Destructing Mechanical Forest</a> by Chuckles McGee (in Secund[9])</body></html>
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