35edo: Difference between revisions

Revision as of 08:33, 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¢. 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.

=Intervals= 


|| 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 || 36/35 || 25/24 || 81/80 ||
|| 2 || di || 68.57 || 128/125 || 25/24 ||   ||   ||
|| 3 || ra || 102.86 || 17/16 ||   || 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 ||   ||   || 9/7 ||
|| 14 || fo || 480 ||   ||   || 4/3 ||   ||
|| 15 || fa(h) || 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 || sa || 685.71 ||   || 3/2 ||   ||   ||
|| 21 || so(h) || 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 ||   || 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, with 7/6 and 9/7) ||
|| 5 || 2\35 ||   || [[Blackwood]] (unfair, favoring 6/5) ||
|| 5 || 3\35 ||   || [[Blackwood]] (fair, favoring 5/4) ||
|| 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¢. 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 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:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h1>
 <br />
<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>1/1<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>50/49, 121/119<br />
</td>
        <td>36/35<br />
</td>
        <td>25/24<br />
</td>
        <td>81/80<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>di<br />
</td>
        <td>68.57<br />
</td>
        <td>128/125<br />
</td>
        <td>25/24<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>ra<br />
</td>
        <td>102.86<br />
</td>
        <td>17/16<br />
</td>
        <td><br />
</td>
        <td>16/15<br />
</td>
        <td>18/17<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>ru<br />
</td>
        <td>137.14<br />
</td>
        <td><br />
</td>
        <td>12/11, 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>11/10<br />
</td>
        <td><br />
</td>
        <td>12/11<br />
</td>
        <td>10/9<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>9/8<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>ri<br />
</td>
        <td>240<br />
</td>
        <td>8/7<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>20/17<br />
</td>
        <td>7/6<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>6/5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>mu<br />
</td>
        <td>342.86<br />
</td>
        <td>17/14<br />
</td>
        <td><br />
</td>
        <td>6/5<br />
</td>
        <td>11/9<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>mi<br />
</td>
        <td>377.14<br />
</td>
        <td>5/4<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>14/11<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>22/17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9/7<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(h)<br />
</td>
        <td>514.29<br />
</td>
        <td><br />
</td>
        <td>4/3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>fu<br />
</td>
        <td>548.57<br />
</td>
        <td>11/8<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>7/5<br />
</td>
        <td>24/17<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>10/7<br />
</td>
        <td>17/12<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>16/11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>sa<br />
</td>
        <td>685.71<br />
</td>
        <td><br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>so(h)<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>17/11, 25/16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>14/9<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>lo<br />
</td>
        <td>788.57<br />
</td>
        <td>11/7<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>8/5<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>18/11<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>la<br />
</td>
        <td>891.43<br />
</td>
        <td><br />
</td>
        <td>5/3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>li<br />
</td>
        <td>925.71<br />
</td>
        <td>17/10<br />
</td>
        <td>12/7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>ta<br />
</td>
        <td>960<br />
</td>
        <td>7/4<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>16/9<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>to<br />
</td>
        <td>1028.57<br />
</td>
        <td>20/11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9/5<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>tu<br />
</td>
        <td>1062.86<br />
</td>
        <td><br />
</td>
        <td>11/6, 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>32/17<br />
</td>
        <td><br />
</td>
        <td>15/8<br />
</td>
        <td>17/9<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><br />
<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, with 7/6 and 9/7)<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)<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)<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 08:10:00 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-06 08:33:32 UTC</tt>.<br>
-: The original revision id was <tt>330630328</tt>.<br>
+: The original revision id was <tt>330633216</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 16: / Line 16: @@
-|| Degrees || Solfege || Cents value || Ratios in 2.5.7.11.17 subgroup || Ratios with flat 3 || Ratios with 9 ||
+|| 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 ||   ||   ||
+|| 0 || do || 0 || 1/1 || (see comma table) ||   ||   ||
-|| 1 || du || 34.29 || 50/49, 121/119 || 36/35 || 81/80 ||
+|| 1 || du || 34.29 || 50/49, 121/119 || 36/35 || 25/24 || 81/80 ||
-|| 2 || di || 68.57 || 128/125 || 25/24 ||   ||
+|| 2 || di || 68.57 || 128/125 || 25/24 ||   ||   ||
-|| 3 || ra || 102.86 || 17/16 ||   || 18/17 ||
+|| 3 || ra || 102.86 || 17/16 ||   || 16/15 || 18/17 ||
-|| 4 || ru || 137.14 ||   || 12/11 ||   ||
+|| 4 || ru || 137.14 ||   || 12/11, 16/15 ||   ||   ||
-|| 5 || ro || 171.43 || 11/10 ||   || 10/9 ||
+|| 5 || ro || 171.43 || 11/10 ||   || 12/11 || 10/9 ||
-|| 6 || re || 205.71 ||   ||   || 9/8 ||
+|| 6 || re || 205.71 ||   ||   ||   || 9/8 ||
-|| 7 || ri || 240 || 8/7 ||   ||   ||
+|| 7 || ri || 240 || 8/7 ||   || 7/6 ||   ||
-|| 8 || ma || 274.29 || 20/17 || 7/6 ||   ||
+|| 8 || ma || 274.29 || 20/17 || 7/6 ||   ||   ||
-|| 9 || me || 308.57 ||   || 6/5 ||   ||
+|| 9 || me || 308.57 ||   || 6/5 ||   ||   ||
-|| 10 || mu || 342.86 || 17/14 ||   || 11/9 ||
+|| 10 || mu || 342.86 || 17/14 ||   || 6/5 || 11/9 ||
-|| 11 || mi || 377.14 || 5/4 ||   ||   ||
+|| 11 || mi || 377.14 || 5/4 ||   ||   ||   ||
-|| 12 || mo || 411.43 || 14/11 ||   || 14/11 ||
+|| 12 || mo || 411.43 || 14/11 ||   ||   ||   ||
-|| 13 || fe || 445.71 || 22/17 ||   || 9/7 ||
+|| 13 || fe || 445.71 || 22/17 ||   ||   || 9/7 ||
-|| 14 || fo || 480 ||   ||   ||   ||
+|| 14 || fo || 480 ||   ||   || 4/3 ||   ||
-|| 15 || fa || 514.29 ||   || 4/3 ||   ||
+|| 15 || fa(h) || 514.29 ||   || 4/3 ||   ||   ||
-|| 16 || fu || 548.57 || 11/8 ||   ||   ||
+|| 16 || fu || 548.57 || 11/8 ||   ||   ||   ||
-|| 17 || fi || 582.86 || 7/5 || 24/17 ||   ||
+|| 17 || fi || 582.86 || 7/5 || 24/17 || 17/12 ||   ||
-|| 18 || se || 617.14 || 10/7 || 17/12 ||   ||
+|| 18 || se || 617.14 || 10/7 || 17/12 || 24/17 ||   ||
-|| 19 || su || 651.43 || 16/11 ||   ||   ||
+|| 19 || su || 651.43 || 16/11 ||   ||   ||   ||
-|| 20 || sa || 685.71 ||   || 3/2 ||   ||
+|| 20 || sa || 685.71 ||   || 3/2 ||   ||   ||
-|| 21 || so || 720 ||   ||   ||   ||
+|| 21 || so(h) || 720 ||   ||   || 3/2 ||   ||
-|| 22 || si || 754.29 || 17/11 || 25/24 || 14/9 ||
+|| 22 || si || 754.29 || 17/11, 25/16 ||   ||   || 14/9 ||
-|| 23 || lo || 788.57 || 11/7 ||   ||   ||
+|| 23 || lo || 788.57 || 11/7 ||   ||   ||   ||
-|| 24 || le || 822.86 || 8/5 ||   ||   ||
+|| 24 || le || 822.86 || 8/5 ||   ||   ||   ||
-|| 25 || lu || 857.15 ||   ||   || 18/11 ||
+|| 25 || lu || 857.15 ||   ||   || 5/3 || 18/11 ||
-|| 26 || la || 891.43 ||   || 5/3 ||   ||
+|| 26 || la || 891.43 ||   || 5/3 ||   ||   ||
-|| 27 || li || 925.71 || 17/10 || 12/7 ||   ||
+|| 27 || li || 925.71 || 17/10 || 12/7 ||   ||   ||
-|| 28 || ta || 960 || 7/4 ||   ||   ||
+|| 28 || ta || 960 || 7/4 ||   ||   ||   ||
-|| 29 || te || 994.29 ||   ||   || 16/9 ||
+|| 29 || te || 994.29 ||   ||   ||   || 16/9 ||
-|| 30 || to || 1028.57 || 20/11 ||   || 9/5 ||
+|| 30 || to || 1028.57 || 20/11 ||   ||   || 9/5 ||
-|| 31 || tu || 1062.86 ||   || 11/6 ||   ||
+|| 31 || tu || 1062.86 ||   || 11/6, 15/8 ||   ||   ||
-|| 32 || ti || 1097.14 || 32/17 ||   || 17/9 ||
+|| 32 || ti || 1097.14 || 32/17 ||   || 15/8 || 17/9 ||
-|| 33 || de || 1131.43 ||   ||   ||   ||
+|| 33 || de || 1131.43 ||   ||   ||   ||   ||
-|| 34 || da || 1165.71 ||   ||   ||   ||
+|| 34 || da || 1165.71 ||   ||   ||   ||   ||
 =Rank two temperaments=
@@ Line 116: / Line 116: @@
 &lt;/td&gt;
          &lt;td&gt;Ratios with flat 3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Ratios with sharp 3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Ratios with 9&lt;br /&gt;
@@ Line 128: / Line 130: @@
 &lt;/td&gt;
          &lt;td&gt;1/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;(see comma table)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 144: / Line 148: @@
 &lt;/td&gt;
          &lt;td&gt;36/35&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;25/24&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;81/80&lt;br /&gt;
@@ Line 158: / Line 164: @@
 &lt;/td&gt;
          &lt;td&gt;25/24&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 172: / Line 180: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16/15&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;18/17&lt;br /&gt;
@@ Line 185: / Line 195: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;12/11&lt;br /&gt;
+         &lt;td&gt;12/11, 16/15&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 200: / Line 212: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;10/9&lt;br /&gt;
@@ Line 210: / Line 224: @@
 &lt;/td&gt;
          &lt;td&gt;205.71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 228: / Line 244: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7/6&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 242: / Line 260: @@
 &lt;/td&gt;
          &lt;td&gt;7/6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 256: / Line 276: @@
 &lt;/td&gt;
          &lt;td&gt;6/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 270: / Line 292: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6/5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;11/9&lt;br /&gt;
@@ Line 282: / Line 306: @@
 &lt;/td&gt;
          &lt;td&gt;5/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 299: / Line 325: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;14/11&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 310: / Line 338: @@
 &lt;/td&gt;
          &lt;td&gt;22/17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 326: / Line 356: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4/3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 333: / Line 365: @@
          &lt;td&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;fa&lt;br /&gt;
+         &lt;td&gt;fa(h)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;514.29&lt;br /&gt;
@@ Line 340: / Line 372: @@
 &lt;/td&gt;
          &lt;td&gt;4/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 352: / Line 386: @@
 &lt;/td&gt;
          &lt;td&gt;11/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 368: / Line 404: @@
 &lt;/td&gt;
          &lt;td&gt;24/17&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17/12&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 382: / Line 420: @@
 &lt;/td&gt;
          &lt;td&gt;17/12&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;24/17&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 394: / Line 434: @@
 &lt;/td&gt;
          &lt;td&gt;16/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 410: / Line 452: @@
 &lt;/td&gt;
          &lt;td&gt;3/2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 417: / Line 461: @@
          &lt;td&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;so&lt;br /&gt;
+         &lt;td&gt;so(h)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;720&lt;br /&gt;
@@ Line 424: / Line 468: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 435: / Line 481: @@
          &lt;td&gt;754.29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17/11&lt;br /&gt;
+         &lt;td&gt;17/11, 25/16&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;25/24&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;14/9&lt;br /&gt;
@@ Line 450: / Line 498: @@
 &lt;/td&gt;
          &lt;td&gt;11/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 464: / Line 514: @@
 &lt;/td&gt;
          &lt;td&gt;8/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 480: / Line 532: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5/3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;18/11&lt;br /&gt;
@@ Line 494: / Line 548: @@
 &lt;/td&gt;
          &lt;td&gt;5/3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 508: / Line 564: @@
 &lt;/td&gt;
          &lt;td&gt;12/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 520: / Line 578: @@
 &lt;/td&gt;
          &lt;td&gt;7/4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 532: / Line 592: @@
 &lt;/td&gt;
          &lt;td&gt;994.29&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 548: / Line 610: @@
 &lt;/td&gt;
          &lt;td&gt;20/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 563: / Line 627: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;11/6&lt;br /&gt;
+         &lt;td&gt;11/6, 15/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 578: / Line 644: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15/8&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;17/9&lt;br /&gt;
@@ Line 588: / Line 656: @@
 &lt;/td&gt;
          &lt;td&gt;1131.43&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 602: / Line 672: @@
 &lt;/td&gt;
          &lt;td&gt;1165.71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;

35edo: Difference between revisions

Revision as of 08:33, 6 May 2012

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