35edo: Difference between revisions

Revision as of 08:54, 6 May 2012

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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. 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 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 || Solfege || Cents value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with sharp 3 || Ratios with 9 ||
|| 0 || do || 0 || **1/1** || (see comma table) ||   ||   ||
|| 1 || du || 34.29 || **50/49**, **121/119**, 33/32 || **36/35** || 25/24 || **81/80** ||
|| 2 || di || 68.57 || 128/125 || **25/24** || 81/80 ||   ||
|| 3 || ra || 102.86 || **17/16** || **15/14** || **16/15** || **18/17** ||
|| 4 || ru || 137.14 ||   || **12/11**, 16/15 ||   ||   ||
|| 5 || ro || 171.43 || **11/10** ||   || 12/11 || **10/9** ||
|| 6 || re || 205.71 ||   ||   ||   || **9/8** ||
|| 7 || ri || 240 || **8/7** ||   || 7/6 ||   ||
|| 8 || ma || 274.29 || **20/17** || **7/6** ||   ||   ||
|| 9 || me || 308.57 ||   || **6/5** ||   ||   ||
|| 10 || mu || 342.86 || **17/14** ||   || 6/5 || **11/9** ||
|| 11 || mi || 377.14 || **5/4** ||   ||   ||   ||
|| 12 || mo || 411.43 || **14/11** ||   ||   ||   ||
|| 13 || fe || 445.71 || **22/17**, 32/25 ||   ||   || **9/7** ||
|| 14 || fo || 480 ||   ||   || 4/3 ||   ||
|| 15 || fa || 514.29 ||   || **4/3** ||   ||   ||
|| 16 || fu || 548.57 || **11/8** ||   ||   ||   ||
|| 17 || fi || 582.86 || **7/5** || **24/17** || 17/12 ||   ||
|| 18 || se || 617.14 || **10/7** || **17/12** || 24/17 ||   ||
|| 19 || su || 651.43 || **16/11** ||   ||   ||   ||
|| 20 || so || 685.71 ||   || **3/2** ||   ||   ||
|| 21 || sa || 720 ||   ||   || 3/2 ||   ||
|| 22 || si || 754.29 || **17/11**, 25/16 ||   ||   || **14/9** ||
|| 23 || lo || 788.57 || **11/7** ||   ||   ||   ||
|| 24 || le || 822.86 || **8/5** ||   ||   ||   ||
|| 25 || lu || 857.15 ||   ||   || 5/3 || **18/11** ||
|| 26 || la || 891.43 ||   || **5/3** ||   ||   ||
|| 27 || li || 925.71 || **17/10** || **12/7** ||   ||   ||
|| 28 || ta || 960 || **7/4** ||   ||   ||   ||
|| 29 || te || 994.29 ||   ||   ||   || **16/9** ||
|| 30 || to || 1028.57 || **20/11** ||   ||   || **9/5** ||
|| 31 || tu || 1062.86 ||   || **11/6**, 15/8 ||   ||   ||
|| 32 || ti || 1097.14 || **32/17** || **28/15** || **15/8** || **17/9** ||
|| 33 || de || 1131.43 ||   ||   ||   ||   ||
|| 34 || da || 1165.71 ||   ||   ||   ||   ||
=Rank two temperaments= 

||~ Periods
per octave ||~ Generator ||~ Temperaments with
flat 3/2 (patent val) ||~ <span style="display: block; text-align: center;">Temperaments with</span><span style="display: block; text-align: center;">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 ||   || [[xenharmonic/Sensipent family|Sensipent]] but //not// [[Sensi]] ||
|| 1 || 16\35 ||   ||   ||
|| 1 || 17\35 ||   ||   ||
|| 5 || 1\35 ||   || [[Blackwood]] (very unfair, favoring 7/6) ||
|| 5 || 2\35 ||   || [[Blackwood]] (unfair, favoring 6/5 and 20/17) ||
|| 5 || 3\35 ||   || [[Blackwood]] (fair, 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;">Commas</span>== 
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** ||
||= 2187/2048 || | -11 7 > ||> 113.69 ||= Apotome ||= Whitewood comma ||   ||
||= 6561/6250 || | -1 8 -5 > ||> 84.07 ||= Ripple comma ||=   ||   ||
||= 10077696/9765625 || | 9 9 -10 > ||> 54.46 ||= Mynic comma ||=   ||   ||
||= 3125/3072 || | -10 -1 5 > ||> 29.61 ||= Small diesis ||= Magic comma ||   ||
||= 78732/78125 || | 2 9 -7 > ||> 13.40 ||= Medium semicomma ||= Sensipent 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 ||= Avicennma ||=   ||   ||
||= 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 ||=   ||=   ||   ||
== == 

== ==

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. 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 />
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>Solfege<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 sharp 3<br />
</td>
        <td>Ratios with 9<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>do<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>du<br />
</td>
        <td>34.29<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>di<br />
</td>
        <td>68.57<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>ra<br />
</td>
        <td>102.86<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>ru<br />
</td>
        <td>137.14<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>ro<br />
</td>
        <td>171.43<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>re<br />
</td>
        <td>205.71<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>ri<br />
</td>
        <td>240<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>ma<br />
</td>
        <td>274.29<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>me<br />
</td>
        <td>308.57<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>mu<br />
</td>
        <td>342.86<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>mi<br />
</td>
        <td>377.14<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>mo<br />
</td>
        <td>411.43<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>fe<br />
</td>
        <td>445.71<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>fo<br />
</td>
        <td>480<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>fa<br />
</td>
        <td>514.29<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>fu<br />
</td>
        <td>548.57<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>fi<br />
</td>
        <td>582.86<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>se<br />
</td>
        <td>617.14<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>su<br />
</td>
        <td>651.43<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>so<br />
</td>
        <td>685.71<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>sa<br />
</td>
        <td>720<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>si<br />
</td>
        <td>754.29<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>lo<br />
</td>
        <td>788.57<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>le<br />
</td>
        <td>822.86<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>lu<br />
</td>
        <td>857.15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5/3<br />
</td>
        <td><strong>18/11</strong><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>la<br />
</td>
        <td>891.43<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>li<br />
</td>
        <td>925.71<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>ta<br />
</td>
        <td>960<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>te<br />
</td>
        <td>994.29<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>to<br />
</td>
        <td>1028.57<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>tu<br />
</td>
        <td>1062.86<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>ti<br />
</td>
        <td>1097.14<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>de<br />
</td>
        <td>1131.43<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>da<br />
</td>
        <td>1165.71<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</span><span style="display: block; text-align: center;">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><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>
    </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> (very unfair, 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> (unfair, 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> (fair, 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;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 />


<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;">10077696/9765625<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;">78732/78125<br />
</td>
        <td>| 2 9 -7 &gt;<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 &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;">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>| 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:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2>
 <br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h2>
</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-05-06 08:50:45 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-06 08:54:17 UTC</tt>.<br>
-: The original revision id was <tt>330635360</tt>.<br>
+: The original revision id was <tt>330635850</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>
@@ 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.
-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
+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. 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.
@@ Line 19: / Line 19: @@
 || 0 || do || 0 || **1/1** || (see comma table) ||   ||   ||
 || 1 || du || 34.29 || **50/49**, **121/119**, 33/32 || **36/35** || 25/24 || **81/80** ||
-|| 2 || di || 68.57 || 128/125 || **25/24** ||   ||   ||
+|| 2 || di || 68.57 || 128/125 || **25/24** || 81/80 ||   ||
-|| 3 || ra || 102.86 || **17/16** ||   || **16/15** || **18/17** ||
+|| 3 || ra || 102.86 || **17/16** || **15/14** || **16/15** || **18/17** ||
 || 4 || ru || 137.14 ||   || **12/11**, 16/15 ||   ||   ||
 || 5 || ro || 171.43 || **11/10** ||   || 12/11 || **10/9** ||
@@ Line 49: / Line 49: @@
 || 30 || to || 1028.57 || **20/11** ||   ||   || **9/5** ||
 || 31 || tu || 1062.86 ||   || **11/6**, 15/8 ||   ||   ||
-|| 32 || ti || 1097.14 || **32/17** ||   || **15/8** || **17/9** ||
+|| 32 || ti || 1097.14 || **32/17** || **28/15** || **15/8** || **17/9** ||
 || 33 || de || 1131.43 ||   ||   ||   ||   ||
 || 34 || da || 1165.71 ||   ||   ||   ||   ||
@@ Line 94: / Line 94: @@
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;35edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;35-tET or 35-&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/edo"&gt;EDO&lt;/a&gt; refers to a tuning system which divides the octave into 35 steps of approximately &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/cent"&gt;34.29¢&lt;/a&gt; each.&lt;br /&gt;
 &lt;br /&gt;
-As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/macrotonal%20edos"&gt;macrotonal edos&lt;/a&gt;: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo"&gt;5edo&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo"&gt;7edo&lt;/a&gt;. 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 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt; 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 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo"&gt;22edo&lt;/a&gt;'s&lt;br /&gt;
+As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/macrotonal%20edos"&gt;macrotonal edos&lt;/a&gt;: &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/5edo"&gt;5edo&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/7edo"&gt;7edo&lt;/a&gt;. 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 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt; 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 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/22edo"&gt;22edo&lt;/a&gt;'s&lt;br /&gt;
 more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments"&gt;greenwood&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Greenwoodmic%20temperaments#Secund"&gt;secund&lt;/a&gt; temperaments.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 164: / Line 164: @@
          &lt;td&gt;&lt;strong&gt;25/24&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;81/80&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 178: / Line 178: @@
          &lt;td&gt;&lt;strong&gt;17/16&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;15/14&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;16/15&lt;/strong&gt;&lt;br /&gt;
@@ Line 642: / Line 642: @@
          &lt;td&gt;&lt;strong&gt;32/17&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;28/15&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;15/8&lt;/strong&gt;&lt;br /&gt;

35edo: Difference between revisions

Revision as of 08:54, 6 May 2012

IMPORTED REVISION FROM WIKISPACES

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