34edo: Difference between revisions

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= = 

34edo divides the octave into 34 equal steps of approximately 35.29412 [[cent]]s. 34edo contains two [[xenharmonic/17edo|17edo]]'s and the half-octave tritone of 600 cents.

===Approximations to Just Intonation=== 
Like [[xenharmonic/17edo|17edo]], 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 17/18, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a [[xenharmonic/meantone|meantone ]]system.

//Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.// ([[http://en.wikipedia.org/wiki/34_equal_temperament|Wikipedia]])

===34edo and phi=== 
As a Fibonacci number, 34edo contains a fraction of an octave which is close approximation to the irrational interval phi -- 21 degrees of 34edo, approximately 741.2 cents. Repeated iterations of this interval generates [[xenharmonic/MOSScales|Moment of Symmetry]] scales with near-phi relationships between the step sizes. As a 2.3.5.13 temperament, the 21\34 generator is an approximate 20/13, and the temperament tempers out 512/507 and 140625/140608. From the tempering of 512/507, two 16/13 neutral thirds are an approximate 3/2, defining an essentially tempered neutral triad with a sharp rather than a flat fifth.

===Linear temperaments=== 
[[List of 34et rank two temperaments by badness]]
||~ Periods
per octave ||~ Generator ||~ Cents ||~ Linear temperaments ||
|| 1 || 1\34 || 35.294 ||   ||
||   || 3\34 || 105.882 ||   ||
||   || 5\34 || 176.471 || [[xenharmonic/Tetracot|Tetracot]]/[[xenharmonic/Bunya|Bunya]]/[[xenharmonic/Monkey|Monkey]] ||
||   || 7\34 || 247.059 || [[xenharmonic/Immunity|Immunity]] ||
||   || 9\34 || 317.647 || [[xenharmonic/Hanson|Hanson]]/[[xenharmonic/Keemun|Keemun]] ||
||   || 11\34 || 388.235 || [[xenharmonic/Wuerschmidt|Wuerschmidt]]/[[xenharmonic/Worschmidt|Worschmidt]] ||
||   || 13\34 || 458.824 ||   ||
||   || 15\34 || 529.412 ||   ||
|| 2 || 1\34 || 35.294 ||   ||
||   || 2\34 || 70.588 || [[xenharmonic/Vishnu|Vishnu]] ||
||   || 3\34 || 105.882 || [[xenharmonic/Srutal|Srutal]]/[[xenharmonic/Pajara|Pajara]]/[[xenharmonic/Diaschismic|Diaschismic]] ||
||   || 4\34 || 141.176 || [[xenharmonic/Fifive|Fifive]] ||
||   || 5\34 || 176.471 ||   ||
||   || 6\34 || 211.765 ||   ||
||   || 7\34 || 247.059 ||   ||
||   || 8\34 || 282.353 ||   ||
|| 17 || 1\34 || 35.294 ||   ||
===Intervals:=== 
|| degrees of 34edo || cents || approx. ratios of
2.3.5.13.17 [[xenharmonic/subgroup|subgroup]] || additional ratios
of the full [[xenharmonic/17-limit|17-limit]] ||
|| 0 || 0.0 || 1/1 ||   ||
|| 1 || 35.294 ||   ||   ||
|| 2 || 70.588 ||   ||   ||
|| 3 || 105.882 || 17/16, 18/17, 16/15 || 15/14 ||
|| 4 || 141.176 || 13/12 || 14/13, 12/11 ||
|| 5 || 176.471 || 10/9 || 11/10 ||
|| 6 || 211.765 || 9/8, 17/15 || 8/7 ||
|| 7 || 247.059 || 15/13 ||   ||
|| 8 || 282.353 || 20/17 || 7/6, 13/11 ||
|| 9 || 317.647 || 6/5 || 17/14 ||
|| 10 || 352.941 || 16/13 || 11/9 ||
|| 11 || 388.235 || 5/4 ||   ||
|| 12 || 423.529 ||   || 9/7 ||
|| 13 || 458.823 || 13/10, 17/13 || 22/17 ||
|| 14 || 494.118 || 4/3 ||   ||
|| 15 || 529.412 ||   || 15/11 ||
|| 16 || 564.706 || 18/13 || 11/8 ||
|| 17 || 600 || 17/12, 24/17 || 7/5, 10/7 ||
|| 18 || 635.294 || 13/9 || 16/11 ||
|| 19 || 670.588 ||   || 22/15 ||
|| 20 || 705.882 || 3/2 ||   ||
|| 21 || 741.176 || 20/13, 26/17 || 17/11 ||
|| 22 || 776.471 ||   || 14/9 ||
|| 23 || 811.765 || 8/5 ||   ||
|| 24 || 847.059 || 13/8 || 18/11 ||
|| 25 || 882.353 || 5/3 || 28/17 ||
|| 26 || 917.647 || 17/10 || 12/7, 22/13 ||
|| 27 || 952.941 || 26/15 ||   ||
|| 28 || 988.235 || 16/9, 30/17 || 7/4 ||
|| 29 || 1023.529 || 9/5 || 20/11 ||
|| 30 || 1058.823 || 24/13 || 13/7, 11/6 ||
|| 31 || 1094.118 || 32/17, 17/9, 15/8 || 28/15 ||
|| 32 || 1129.412 ||   ||   ||
|| 33 || 1164.706 ||   ||   ||

==<span style="background-color: #ffffff;">Commas</span>== 
<span style="background-color: #ffffff;">34-EDO [[xenharmonic/tempering out|tempers out]] the following [[xenharmonic/comma|comma]]s. (Note: This assumes the [[xenharmonic/val|val]] < 34 54 79 95 118 126 |.)</span>

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||= <span style="background-color: #ffffff; display: block; text-align: center;">134217728/129140163</span> ||< | 27 -17 > ||> 66.765 ||= 17-comma ||=   ||=   ||
||= 20000/19683 || <span style="background-color: #ffffff; display: block; text-align: left;">| 5 -9 4 ></span> ||> <span style="background-color: #ffffff; display: block; text-align: right;">27.660</span> ||= Minimal Diesis ||= Tetracot Comma ||   ||
||= <span style="background-color: #ffffff; display: block; text-align: center;">2048/2025</span> ||< | 11 -4 -2 > ||> 19.553 ||= Diaschisma ||= <span style="background-color: #ffffff; display: block; text-align: center;">Semicomma Majeur</span> ||=   ||
||= <span style="background-color: #ffffff; display: block; text-align: center;">393216/390625</span> || |
<span style="display: block; text-align: left;">17 1 -8 ></span> ||> <span style="background-color: #ffffff; display: block; text-align: right;">11.445</span> ||= Würschmidt comma ||=   ||   ||
||= <span style="background-color: #ffffff; display: block; text-align: center;">15625/15552</span> || <span style="display: block; text-align: left;">| -6 -5 6 ></span> ||> <span style="display: block; text-align: right;">8.1073</span> ||= <span style="display: block; text-align: center;">Kleisma</span> ||= <span style="display: block; text-align: center;">Semicomma Majeur</span> ||   ||
||= <span style="background-color: #ffffff; display: block; text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">1212717/1210381</span></span> ||< <span style="background-color: #ffffff;">| 23 6 -14 ></span> ||> 3.338 ||= <span style="background-color: #ffffff; display: block; text-align: center;">Vishnuzma</span> ||= Semisuper ||=   ||
||= 1029/1000 ||< | -3 1 -3 3 > ||> 49.492 ||= <span style="background-color: #ffffff;">Keega</span> ||=   ||=   ||
||= [[xenharmonic/49_48|49/48]] ||< | -4 -1 0 2 > ||> 35.697 ||= Slendro Diesis ||=   ||=   ||
||= 875/864 ||< | -5 -3 3 1 > ||> 21.902 ||= Keema ||=   ||=   ||
||= 126/125 ||< | 1 2 -3 1 > ||> 13.795 ||= Starling comma ||= Septimal semicomma ||=   ||
||= 100/99 ||< | 2 -2 2 0 -1> ||> 17.399 ||= Ptolemisma ||= Ptolemy's comma ||=   ||
||= 243/242 ||< <span style="background-color: #ffffff; display: block; text-align: left;">| -1 5 0 0 -2 ></span> ||> <span style="background-color: #ffffff; display: block; text-align: right;">7.1391</span> ||= Rastma ||= Neutral third comma ||=   ||
||= 385/384 ||< <span style="background-color: #ffffff; display: block; text-align: left;">| -7 -1 1 1 1 ></span> ||> <span style="background-color: #ffffff; display: block; text-align: right;">4.5026</span> ||= Keenanisma ||=   ||=   ||
||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.120 ||= Superleap ||=   ||=   ||


==Listen== 
* [[@http://www.archive.org/details/Ascension_105|Ascension]]
Drums Bass and 34-tone guitar

==Links== 
* [[http://www.microstick.net/34guitararticle.htm|34 Equal Guitar]] by [[xenharmonic/Larry Hanson|Larry Hanson]]

Original HTML content:

<html><head><title>34edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><!-- ws:end:WikiTextHeadingRule:0 --> </h1>
 <br />
34edo divides the octave into 34 equal steps of approximately 35.29412 <a class="wiki_link" href="/cent">cent</a>s. 34edo contains two <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a>'s and the half-octave tritone of 600 cents.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Approximations to Just Intonation"></a><!-- ws:end:WikiTextHeadingRule:2 -->Approximations to Just Intonation</h3>
 Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a>, 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 17/18, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone">meantone </a>system.<br />
<br />
<em>Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.</em> (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/34_equal_temperament" rel="nofollow">Wikipedia</a>)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x--34edo and phi"></a><!-- ws:end:WikiTextHeadingRule:4 -->34edo and phi</h3>
 As a Fibonacci number, 34edo contains a fraction of an octave which is close approximation to the irrational interval phi -- 21 degrees of 34edo, approximately 741.2 cents. Repeated iterations of this interval generates <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">Moment of Symmetry</a> scales with near-phi relationships between the step sizes. As a 2.3.5.13 temperament, the 21\34 generator is an approximate 20/13, and the temperament tempers out 512/507 and 140625/140608. From the tempering of 512/507, two 16/13 neutral thirds are an approximate 3/2, defining an essentially tempered neutral triad with a sharp rather than a flat fifth.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x--Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Linear temperaments</h3>
 <a class="wiki_link" href="/List%20of%2034et%20rank%20two%20temperaments%20by%20badness">List of 34et rank two temperaments by badness</a><br />


<table class="wiki_table">
    <tr>
        <th>Periods<br />
per octave<br />
</th>
        <th>Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Linear temperaments<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>1\34<br />
</td>
        <td>35.294<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3\34<br />
</td>
        <td>105.882<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5\34<br />
</td>
        <td>176.471<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tetracot">Tetracot</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Bunya">Bunya</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Monkey">Monkey</a><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>7\34<br />
</td>
        <td>247.059<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Immunity">Immunity</a><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>9\34<br />
</td>
        <td>317.647<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hanson">Hanson</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Keemun">Keemun</a><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>11\34<br />
</td>
        <td>388.235<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Wuerschmidt">Wuerschmidt</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Worschmidt">Worschmidt</a><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>13\34<br />
</td>
        <td>458.824<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>15\34<br />
</td>
        <td>529.412<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>1\34<br />
</td>
        <td>35.294<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>2\34<br />
</td>
        <td>70.588<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vishnu">Vishnu</a><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3\34<br />
</td>
        <td>105.882<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Srutal">Srutal</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Pajara">Pajara</a>/<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Diaschismic">Diaschismic</a><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>4\34<br />
</td>
        <td>141.176<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Fifive">Fifive</a><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5\34<br />
</td>
        <td>176.471<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>6\34<br />
</td>
        <td>211.765<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>7\34<br />
</td>
        <td>247.059<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>8\34<br />
</td>
        <td>282.353<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>1\34<br />
</td>
        <td>35.294<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x--Intervals:"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals:</h3>
 

<table class="wiki_table">
    <tr>
        <td>degrees of 34edo<br />
</td>
        <td>cents<br />
</td>
        <td>approx. ratios of<br />
2.3.5.13.17 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/subgroup">subgroup</a><br />
</td>
        <td>additional ratios<br />
of the full <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit">17-limit</a><br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0.0<br />
</td>
        <td>1/1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>35.294<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>70.588<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>105.882<br />
</td>
        <td>17/16, 18/17, 16/15<br />
</td>
        <td>15/14<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>141.176<br />
</td>
        <td>13/12<br />
</td>
        <td>14/13, 12/11<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>176.471<br />
</td>
        <td>10/9<br />
</td>
        <td>11/10<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>211.765<br />
</td>
        <td>9/8, 17/15<br />
</td>
        <td>8/7<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>247.059<br />
</td>
        <td>15/13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>282.353<br />
</td>
        <td>20/17<br />
</td>
        <td>7/6, 13/11<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>317.647<br />
</td>
        <td>6/5<br />
</td>
        <td>17/14<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>352.941<br />
</td>
        <td>16/13<br />
</td>
        <td>11/9<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>388.235<br />
</td>
        <td>5/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>423.529<br />
</td>
        <td><br />
</td>
        <td>9/7<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>458.823<br />
</td>
        <td>13/10, 17/13<br />
</td>
        <td>22/17<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>494.118<br />
</td>
        <td>4/3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>529.412<br />
</td>
        <td><br />
</td>
        <td>15/11<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>564.706<br />
</td>
        <td>18/13<br />
</td>
        <td>11/8<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>600<br />
</td>
        <td>17/12, 24/17<br />
</td>
        <td>7/5, 10/7<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>635.294<br />
</td>
        <td>13/9<br />
</td>
        <td>16/11<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>670.588<br />
</td>
        <td><br />
</td>
        <td>22/15<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>705.882<br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>741.176<br />
</td>
        <td>20/13, 26/17<br />
</td>
        <td>17/11<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>776.471<br />
</td>
        <td><br />
</td>
        <td>14/9<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>811.765<br />
</td>
        <td>8/5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>847.059<br />
</td>
        <td>13/8<br />
</td>
        <td>18/11<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>882.353<br />
</td>
        <td>5/3<br />
</td>
        <td>28/17<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>917.647<br />
</td>
        <td>17/10<br />
</td>
        <td>12/7, 22/13<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>952.941<br />
</td>
        <td>26/15<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>988.235<br />
</td>
        <td>16/9, 30/17<br />
</td>
        <td>7/4<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>1023.529<br />
</td>
        <td>9/5<br />
</td>
        <td>20/11<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>1058.823<br />
</td>
        <td>24/13<br />
</td>
        <td>13/7, 11/6<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>1094.118<br />
</td>
        <td>32/17, 17/9, 15/8<br />
</td>
        <td>28/15<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>1129.412<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>1164.706<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Commas"></a><!-- ws:end:WikiTextHeadingRule:10 --><span style="background-color: #ffffff;">Commas</span></h2>
 <span style="background-color: #ffffff;">34-EDO <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> the following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/val">val</a> &lt; 34 54 79 95 118 126 |.)</span><br />
<br />


<table class="wiki_table">
    <tr>
        <th>Comma<br />
</th>
        <th>Monzo<br />
</th>
        <th>Value (Cents)<br />
</th>
        <th>Name 1<br />
</th>
        <th>Name 2<br />
</th>
        <th>Name 3<br />
</th>
    </tr>
    <tr>
        <td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">134217728/129140163</span><br />
</td>
        <td style="text-align: left;">| 27 -17 &gt;<br />
</td>
        <td style="text-align: right;">66.765<br />
</td>
        <td style="text-align: center;">17-comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">20000/19683<br />
</td>
        <td><span style="background-color: #ffffff; display: block; text-align: left;">| 5 -9 4 &gt;</span><br />
</td>
        <td style="text-align: right;"><span style="background-color: #ffffff; display: block; text-align: right;">27.660</span><br />
</td>
        <td style="text-align: center;">Minimal Diesis<br />
</td>
        <td style="text-align: center;">Tetracot Comma<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">2048/2025</span><br />
</td>
        <td style="text-align: left;">| 11 -4 -2 &gt;<br />
</td>
        <td style="text-align: right;">19.553<br />
</td>
        <td style="text-align: center;">Diaschisma<br />
</td>
        <td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">Semicomma Majeur</span><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">393216/390625</span><br />
</td>
        <td>|<br />
<span style="display: block; text-align: left;">17 1 -8 &gt;</span><br />
</td>
        <td style="text-align: right;"><span style="background-color: #ffffff; display: block; text-align: right;">11.445</span><br />
</td>
        <td style="text-align: center;">Würschmidt comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">15625/15552</span><br />
</td>
        <td><span style="display: block; text-align: left;">| -6 -5 6 &gt;</span><br />
</td>
        <td style="text-align: right;"><span style="display: block; text-align: right;">8.1073</span><br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">Kleisma</span><br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">Semicomma Majeur</span><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">1212717/1210381</span></span><br />
</td>
        <td style="text-align: left;"><span style="background-color: #ffffff;">| 23 6 -14 &gt;</span><br />
</td>
        <td style="text-align: right;">3.338<br />
</td>
        <td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">Vishnuzma</span><br />
</td>
        <td style="text-align: center;">Semisuper<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1029/1000<br />
</td>
        <td style="text-align: left;">| -3 1 -3 3 &gt;<br />
</td>
        <td style="text-align: right;">49.492<br />
</td>
        <td style="text-align: center;"><span style="background-color: #ffffff;">Keega</span><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/49_48">49/48</a><br />
</td>
        <td style="text-align: left;">| -4 -1 0 2 &gt;<br />
</td>
        <td style="text-align: right;">35.697<br />
</td>
        <td style="text-align: center;">Slendro Diesis<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">875/864<br />
</td>
        <td style="text-align: left;">| -5 -3 3 1 &gt;<br />
</td>
        <td style="text-align: right;">21.902<br />
</td>
        <td style="text-align: center;">Keema<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">126/125<br />
</td>
        <td style="text-align: left;">| 1 2 -3 1 &gt;<br />
</td>
        <td style="text-align: right;">13.795<br />
</td>
        <td style="text-align: center;">Starling comma<br />
</td>
        <td style="text-align: center;">Septimal semicomma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">100/99<br />
</td>
        <td style="text-align: left;">| 2 -2 2 0 -1&gt;<br />
</td>
        <td style="text-align: right;">17.399<br />
</td>
        <td style="text-align: center;">Ptolemisma<br />
</td>
        <td style="text-align: center;">Ptolemy's comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">243/242<br />
</td>
        <td style="text-align: left;"><span style="background-color: #ffffff; display: block; text-align: left;">| -1 5 0 0 -2 &gt;</span><br />
</td>
        <td style="text-align: right;"><span style="background-color: #ffffff; display: block; text-align: right;">7.1391</span><br />
</td>
        <td style="text-align: center;">Rastma<br />
</td>
        <td style="text-align: center;">Neutral third comma<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">385/384<br />
</td>
        <td style="text-align: left;"><span style="background-color: #ffffff; display: block; text-align: left;">| -7 -1 1 1 1 &gt;</span><br />
</td>
        <td style="text-align: right;"><span style="background-color: #ffffff; display: block; text-align: right;">4.5026</span><br />
</td>
        <td style="text-align: center;">Keenanisma<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">91/90<br />
</td>
        <td style="text-align: left;">| -1 -2 -1 1 0 1 &gt;<br />
</td>
        <td style="text-align: right;">19.120<br />
</td>
        <td style="text-align: center;">Superleap<br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Listen"></a><!-- ws:end:WikiTextHeadingRule:12 -->Listen</h2>
 <ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank">Ascension</a></li></ul>Drums Bass and 34-tone guitar<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Links"></a><!-- ws:end:WikiTextHeadingRule:14 -->Links</h2>
 <ul><li><a class="wiki_link_ext" href="http://www.microstick.net/34guitararticle.htm" rel="nofollow">34 Equal Guitar</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Larry%20Hanson">Larry Hanson</a></li></ul></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>2012-04-18 21:34:55 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2012-04-19 03:32:38 UTC</tt>.<br>
-: The original revision id was <tt>322400186</tt>.<br>
+: The original revision id was <tt>322497592</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">= =
-edo divides the octave into 34 equal steps of approximately 35.29412 cents. 34edo contains two [[xenharmonic/17edo|17edo]]'s and the half-octave tritone of 600 cents.
+edo divides the octave into 34 equal steps of approximately 35.29412 [[cent]]s. 34edo contains two [[xenharmonic/17edo|17edo]]'s and the half-octave tritone of 600 cents.
 ===Approximations to Just Intonation===
@@ Line 85: / Line 85: @@
 ||= 20000/19683 || &lt;span style="background-color: #ffffff; display: block; text-align: left;"&gt;| 5 -9 4 &gt;&lt;/span&gt; ||&gt; &lt;span style="background-color: #ffffff; display: block; text-align: right;"&gt;27.660&lt;/span&gt; ||= Minimal Diesis ||= Tetracot Comma ||   ||
 ||= &lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;2048/2025&lt;/span&gt; ||&lt; | 11 -4 -2 &gt; ||&gt; 19.553 ||= Diaschisma ||= &lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;Semicomma Majeur&lt;/span&gt; ||=   ||
-||= &lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;393216/390625&lt;/span&gt; || |&lt;span style="text-align: left;"&gt;17 1 -8 &gt;&lt;/span&gt; ||&gt; &lt;span style="background-color: #ffffff; display: block; text-align: right;"&gt;11.445&lt;/span&gt; ||= Würschmidt comma ||=   ||   ||
+||= &lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;393216/390625&lt;/span&gt; || |
+&lt;span style="display: block; text-align: left;"&gt;17 1 -8 &gt;&lt;/span&gt; ||&gt; &lt;span style="background-color: #ffffff; display: block; text-align: right;"&gt;11.445&lt;/span&gt; ||= Würschmidt comma ||=   ||   ||
 ||= &lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;15625/15552&lt;/span&gt; || &lt;span style="display: block; text-align: left;"&gt;| -6 -5 6 &gt;&lt;/span&gt; ||&gt; &lt;span style="display: block; text-align: right;"&gt;8.1073&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;Kleisma&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;Semicomma Majeur&lt;/span&gt; ||   ||
 ||= &lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;&lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;1212717/1210381&lt;/span&gt;&lt;/span&gt; ||&lt; &lt;span style="background-color: #ffffff;"&gt;| 23 6 -14 &gt;&lt;/span&gt; ||&gt; 3.338 ||= &lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;Vishnuzma&lt;/span&gt; ||= Semisuper ||=   ||
@@ Line 107: / Line 108: @@
 <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;34edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; &lt;/h1&gt;
   &lt;br /&gt;
-edo divides the octave into 34 equal steps of approximately 35.29412 cents. 34edo contains two &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo"&gt;17edo&lt;/a&gt;'s and the half-octave tritone of 600 cents.&lt;br /&gt;
+edo divides the octave into 34 equal steps of approximately 35.29412 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s. 34edo contains two &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo"&gt;17edo&lt;/a&gt;'s and the half-octave tritone of 600 cents.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Approximations to Just Intonation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Approximations to Just Intonation&lt;/h3&gt;
@@ Line 729: / Line 730: @@
          &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff; display: block; text-align: center;"&gt;393216/390625&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;|&lt;span style="text-align: left;"&gt;17 1 -8 &amp;gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;|&lt;br /&gt;
+&lt;span style="display: block; text-align: left;"&gt;17 1 -8 &amp;gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: right;"&gt;&lt;span style="background-color: #ffffff; display: block; text-align: right;"&gt;11.445&lt;/span&gt;&lt;br /&gt;

34edo: Difference between revisions

Revision as of 03:32, 19 April 2012

IMPORTED REVISION FROM WIKISPACES

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