99edo: Difference between revisions

Revision as of 21:46, 15 January 2013

IMPORTED REVISION FROM WIKISPACES

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This revision was by author Andrew_Heathwaite and made on 2013-01-15 21:46:38 UTC.

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Original Wikitext content:

The //99 equal temperament//, often abbreviated 99-tET, 99-EDO, or 99-ET, is the scale derived by dividing the octave into 99 equally-sized steps, where each step represents a frequency ratio of 12.1212 cents. It is a very strong 7-limit (and 9 odd limit) temperament, but extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far of the mark. It tempers out 3136/3125, 5120/5103, 6144/6125, 2401/2400 and 4375/4374, and supports hemififths, amity, parakleismic, hemiwürschmidt and ennealimmal temperaments, and is pretty well a perfect tuning for hendecatonic temperament. It has a sound defined by the slight sharpness (1.075, 1.565, 0.871 cents) of its 3, 5, and 7.

Using the [[patent val]], <99 157 230 278 342|, 99 is the [[optimal patent val]] for the rank four temperament tempering out 121/120; zeus, the rank three temperament tempering out 121/120 and 176/175; hemiwur, one of the rank two 11-limit extensions of hemiwürschmidt; and hitchcock (11-limit amity), the rank two temperament which also tempers out 2200/2187. Using the <99 157 230 278 343| ("99e") val, 99 tempers out 896/891, 243/242, 441/440 and 540/539, and is an excellent tuning for the 11-limit version of [[Breedsmic temperaments|hemififths temperament]]. Hence 99, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way.

=Scales= 
[[tutone6]]
[[tutone7]]
[[tutone13]]

=Music in 99edo= 
[[http://www.archive.org/details/NonagintaEtNovem|Nonaginta et Novem]] //[[http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/Nonaginta%20et%20Novem.mp3|play]]// by [[Gene Ward Smith]]

=Intervals= 
||~ Degrees ||~ Cents Value ||
|| 1 || 12.121 ||
|| 2 || 24.242 ||
|| 3 || 36.364 ||
|| 4 || 48.485 ||
|| 5 || 60.606 ||
|| 6 || 72.727 ||
|| 7 || 84.848 ||
|| 8 || 96.97 ||
|| 9 || 109.091 ||
|| 10 || 121.212 ||
|| 11 || 133.333 ||
|| 12 || 145.455 ||
|| 13 || 157.576 ||
|| 14 || 169.697 ||
|| 15 || 181.818 ||
|| 16 || 193.939 ||
|| 17 || 206.061 ||
|| 18 || 218.182 ||
|| 19 || 230.303 ||
|| 20 || 242.424 ||
|| 21 || 254.545 ||
|| 22 || 266.667 ||
|| 23 || 278.788 ||
|| 24 || 290.909 ||
|| 25 || 303.03 ||
|| 26 || 315.152 ||
|| 27 || 327.273 ||
|| 28 || 339.394 ||
|| 29 || 351.515 ||
|| 30 || 363.636 ||
|| 31 || 375.758 ||
|| 32 || 387.879 ||
|| 33 || 400 ||
|| 34 || 412.121 ||
|| 35 || 424.242 ||
|| 36 || 436.364 ||
|| 37 || 448.485 ||
|| 38 || 460.606 ||
|| 39 || 472.727 ||
|| 40 || 484.848 ||
|| 41 || 496.97 ||
|| 42 || 509.091 ||
|| 43 || 521.212 ||
|| 44 || 533.333 ||
|| 45 || 545.455 ||
|| 46 || 557.576 ||
|| 47 || 569.697 ||
|| 48 || 581.818 ||
|| 49 || 593.939 ||
|| 50 || 606.061 ||
|| 51 || 618.182 ||
|| 52 || 630.303 ||
|| 53 || 642.424 ||
|| 54 || 654.545 ||
|| 55 || 666.667 ||
|| 56 || 678.788 ||
|| 57 || 690.909 ||
|| 58 || 703.03 ||
|| 59 || 715.152 ||
|| 60 || 727.273 ||
|| 61 || 739.394 ||
|| 62 || 751.515 ||
|| 63 || 763.636 ||
|| 64 || 775.758 ||
|| 65 || 787.879 ||
|| 66 || 800 ||
|| 67 || 812.121 ||
|| 68 || 824.242 ||
|| 69 || 836.364 ||
|| 70 || 848.485 ||
|| 71 || 860.606 ||
|| 72 || 872.727 ||
|| 73 || 884.848 ||
|| 74 || 896.97 ||
|| 75 || 909.091 ||
|| 76 || 921.212 ||
|| 77 || 933.333 ||
|| 78 || 945.455 ||
|| 79 || 957.576 ||
|| 80 || 969.697 ||
|| 81 || 981.818 ||
|| 82 || 993.939 ||
|| 83 || 1006.061 ||
|| 84 || 1018.182 ||
|| 85 || 1030.303 ||
|| 86 || 1042.424 ||
|| 87 || 1054.545 ||
|| 88 || 1066.667 ||
|| 89 || 1078.788 ||
|| 90 || 1090.909 ||
|| 91 || 1103.03 ||
|| 92 || 1115.152 ||
|| 93 || 1127.273 ||
|| 94 || 1139.394 ||
|| 95 || 1151.515 ||
|| 96 || 1163.636 ||
|| 97 || 1175.758 ||
|| 98 || 1187.879 ||
|| 99 || 1200 ||

Original HTML content:

<html><head><title>99edo</title></head><body>The <em>99 equal temperament</em>, often abbreviated 99-tET, 99-EDO, or 99-ET, is the scale derived by dividing the octave into 99 equally-sized steps, where each step represents a frequency ratio of 12.1212 cents. It is a very strong 7-limit (and 9 odd limit) temperament, but extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far of the mark. It tempers out 3136/3125, 5120/5103, 6144/6125, 2401/2400 and 4375/4374, and supports hemififths, amity, parakleismic, hemiwürschmidt and ennealimmal temperaments, and is pretty well a perfect tuning for hendecatonic temperament. It has a sound defined by the slight sharpness (1.075, 1.565, 0.871 cents) of its 3, 5, and 7.<br />
<br />
Using the <a class="wiki_link" href="/patent%20val">patent val</a>, &lt;99 157 230 278 342|, 99 is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank four temperament tempering out 121/120; zeus, the rank three temperament tempering out 121/120 and 176/175; hemiwur, one of the rank two 11-limit extensions of hemiwürschmidt; and hitchcock (11-limit amity), the rank two temperament which also tempers out 2200/2187. Using the &lt;99 157 230 278 343| (&quot;99e&quot;) val, 99 tempers out 896/891, 243/242, 441/440 and 540/539, and is an excellent tuning for the 11-limit version of <a class="wiki_link" href="/Breedsmic%20temperaments">hemififths temperament</a>. Hence 99, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1>
 <a class="wiki_link" href="/tutone6">tutone6</a><br />
<a class="wiki_link" href="/tutone7">tutone7</a><br />
<a class="wiki_link" href="/tutone13">tutone13</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Music in 99edo"></a><!-- ws:end:WikiTextHeadingRule:2 -->Music in 99edo</h1>
 <a class="wiki_link_ext" href="http://www.archive.org/details/NonagintaEtNovem" rel="nofollow">Nonaginta et Novem</a> <em><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/mine/Nonaginta%20et%20Novem.mp3" rel="nofollow">play</a></em> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <th>Degrees<br />
</th>
        <th>Cents Value<br />
</th>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>12.121<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>24.242<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>36.364<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>48.485<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>60.606<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>72.727<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>84.848<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>96.97<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>109.091<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>121.212<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>133.333<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>145.455<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>157.576<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>169.697<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>181.818<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>193.939<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>206.061<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>218.182<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>230.303<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>242.424<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>254.545<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>266.667<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>278.788<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>290.909<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>303.03<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>315.152<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>327.273<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>339.394<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>351.515<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>363.636<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>375.758<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>387.879<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>400<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>412.121<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>424.242<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>436.364<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>448.485<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>460.606<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>472.727<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>484.848<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>496.97<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>509.091<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>521.212<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>533.333<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>545.455<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>557.576<br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td>569.697<br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>581.818<br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td>593.939<br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td>606.061<br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td>618.182<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>630.303<br />
</td>
    </tr>
    <tr>
        <td>53<br />
</td>
        <td>642.424<br />
</td>
    </tr>
    <tr>
        <td>54<br />
</td>
        <td>654.545<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>666.667<br />
</td>
    </tr>
    <tr>
        <td>56<br />
</td>
        <td>678.788<br />
</td>
    </tr>
    <tr>
        <td>57<br />
</td>
        <td>690.909<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>703.03<br />
</td>
    </tr>
    <tr>
        <td>59<br />
</td>
        <td>715.152<br />
</td>
    </tr>
    <tr>
        <td>60<br />
</td>
        <td>727.273<br />
</td>
    </tr>
    <tr>
        <td>61<br />
</td>
        <td>739.394<br />
</td>
    </tr>
    <tr>
        <td>62<br />
</td>
        <td>751.515<br />
</td>
    </tr>
    <tr>
        <td>63<br />
</td>
        <td>763.636<br />
</td>
    </tr>
    <tr>
        <td>64<br />
</td>
        <td>775.758<br />
</td>
    </tr>
    <tr>
        <td>65<br />
</td>
        <td>787.879<br />
</td>
    </tr>
    <tr>
        <td>66<br />
</td>
        <td>800<br />
</td>
    </tr>
    <tr>
        <td>67<br />
</td>
        <td>812.121<br />
</td>
    </tr>
    <tr>
        <td>68<br />
</td>
        <td>824.242<br />
</td>
    </tr>
    <tr>
        <td>69<br />
</td>
        <td>836.364<br />
</td>
    </tr>
    <tr>
        <td>70<br />
</td>
        <td>848.485<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>860.606<br />
</td>
    </tr>
    <tr>
        <td>72<br />
</td>
        <td>872.727<br />
</td>
    </tr>
    <tr>
        <td>73<br />
</td>
        <td>884.848<br />
</td>
    </tr>
    <tr>
        <td>74<br />
</td>
        <td>896.97<br />
</td>
    </tr>
    <tr>
        <td>75<br />
</td>
        <td>909.091<br />
</td>
    </tr>
    <tr>
        <td>76<br />
</td>
        <td>921.212<br />
</td>
    </tr>
    <tr>
        <td>77<br />
</td>
        <td>933.333<br />
</td>
    </tr>
    <tr>
        <td>78<br />
</td>
        <td>945.455<br />
</td>
    </tr>
    <tr>
        <td>79<br />
</td>
        <td>957.576<br />
</td>
    </tr>
    <tr>
        <td>80<br />
</td>
        <td>969.697<br />
</td>
    </tr>
    <tr>
        <td>81<br />
</td>
        <td>981.818<br />
</td>
    </tr>
    <tr>
        <td>82<br />
</td>
        <td>993.939<br />
</td>
    </tr>
    <tr>
        <td>83<br />
</td>
        <td>1006.061<br />
</td>
    </tr>
    <tr>
        <td>84<br />
</td>
        <td>1018.182<br />
</td>
    </tr>
    <tr>
        <td>85<br />
</td>
        <td>1030.303<br />
</td>
    </tr>
    <tr>
        <td>86<br />
</td>
        <td>1042.424<br />
</td>
    </tr>
    <tr>
        <td>87<br />
</td>
        <td>1054.545<br />
</td>
    </tr>
    <tr>
        <td>88<br />
</td>
        <td>1066.667<br />
</td>
    </tr>
    <tr>
        <td>89<br />
</td>
        <td>1078.788<br />
</td>
    </tr>
    <tr>
        <td>90<br />
</td>
        <td>1090.909<br />
</td>
    </tr>
    <tr>
        <td>91<br />
</td>
        <td>1103.03<br />
</td>
    </tr>
    <tr>
        <td>92<br />
</td>
        <td>1115.152<br />
</td>
    </tr>
    <tr>
        <td>93<br />
</td>
        <td>1127.273<br />
</td>
    </tr>
    <tr>
        <td>94<br />
</td>
        <td>1139.394<br />
</td>
    </tr>
    <tr>
        <td>95<br />
</td>
        <td>1151.515<br />
</td>
    </tr>
    <tr>
        <td>96<br />
</td>
        <td>1163.636<br />
</td>
    </tr>
    <tr>
        <td>97<br />
</td>
        <td>1175.758<br />
</td>
    </tr>
    <tr>
        <td>98<br />
</td>
        <td>1187.879<br />
</td>
    </tr>
    <tr>
        <td>99<br />
</td>
        <td>1200<br />
</td>
    </tr>
</table>

</body></html>

99edo: Difference between revisions

Revision as of 21:46, 15 January 2013

IMPORTED REVISION FROM WIKISPACES

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