28edo: Difference between revisions

Revision as of 19:08, 17 September 2010

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author JinowKeatiuku and made on 2010-09-17 19:08:00 UTC.

The original revision id was 163549865.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, most of which are also found in 14edo.

The following table compares it to potentially useful nearby just intervals.

|| Step # ||   ||   ||   || ET Cents ||   || Just Interval || Just Cents || Difference (ET minus Just) ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| 1 ||   ||   ||   || 42.86 ||   ||   ||   ||   ||   ||
|| 2 ||   ||   ||   || 85.71 ||   || 21:20 || 84.47 || 1.24 ||   ||
|| 3 ||   ||   ||   || 128.57 ||   || 14:13 || 128.30 || 0.27 ||   ||
|| 4 ||   ||   ||   || 171.43 ||   || 11:10 || 165.00 || 6.43 ||   ||
|| 5 ||   ||   ||   || 214.29 ||   || 17:15 || 216.69 || -2.40 ||   ||
|| 6 ||   ||   ||   || 257.14 ||   || 7:6 || 266.87 || -9.73 ||   ||
|| 7 ||   ||   ||   || 300 ||   || 6:5 || 315.64 || -15.64 ||   ||
|| 8 ||   ||   ||   || 342.86 ||   || 11:9 || 347.41 || -4.55 ||   ||
|| 9 ||   ||   ||   || 385.71 ||   || 5:4 || 386.31 || -0.60 ||   ||
|| 10 ||   ||   ||   || 428.57 ||   || 9:7 || 435.08 || -6.51 ||   ||
|| 11 ||   ||   ||   || 471.43 ||   ||   ||   ||   ||   ||
|| 12 ||   ||   ||   || 514.29 ||   || 4:3 || 498.04 || 16.25 ||   ||
|| 13 ||   ||   ||   || 557.14 ||   ||   ||   ||   ||   ||
|| 14 ||   ||   ||   || 600 ||   || 7:5 || 582.51 || 17.49 ||   ||
|| 15 ||   ||   ||   || 642.86 ||   ||   ||   ||   ||   ||
|| 16 ||   ||   ||   || 685.71 ||   || 3:2 || 701.96 || -16.25 ||   ||
|| 17 ||   ||   ||   || 728.57 ||   ||   ||   ||   ||   ||
|| 18 ||   ||   ||   || 771.43 ||   || 14:9 || 764.92 || 6.51 ||   ||
|| 19 ||   ||   ||   || 814.29 ||   || 5:8 || 813.68 || 0.61 ||   ||
|| 20 ||   ||   ||   || 857.14 ||   || 18:11 || 852.59 || 4.55 ||   ||
|| 21 ||   ||   ||   || 900 ||   || 5:3 || 884.36 || 15.64 ||   ||
|| 22 ||   ||   ||   || 942.86 ||   || 12:7 || 933.13 || 9.73 ||   ||
|| 23 ||   ||   ||   || 985.71 ||   || 30:17 || 983.31 || 2.40 ||   ||
|| 24 ||   ||   ||   || 1028.57 ||   || 9:5 || 1035.00 || -6.43 ||   ||
|| 25 ||   ||   ||   || 1071.42 ||   || 13:7 || 1071.70 || -0.27 ||   ||
|| 26 ||   ||   ||   || 1114.29 ||   || 40:21 || 1115.53 || -1.24 ||   ||
|| 27 ||   ||   ||   || 1157.14 ||   ||   ||   ||   ||   ||
|| 28 ||   ||   ||   || 1200 ||   || 2:1 || 1200 || 0 ||   ||

Original HTML content:

<html><head><title>28edo</title></head><body>28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, most of which are also found in 14edo.<br />
<br />
The following table compares it to potentially useful nearby just intervals.<br />
<br />


<table class="wiki_table">
    <tr>
        <td>Step #<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>ET Cents<br />
</td>
        <td><br />
</td>
        <td>Just Interval<br />
</td>
        <td>Just Cents<br />
</td>
        <td>Difference (ET minus Just)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>42.86<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>85.71<br />
</td>
        <td><br />
</td>
        <td>21:20<br />
</td>
        <td>84.47<br />
</td>
        <td>1.24<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>128.57<br />
</td>
        <td><br />
</td>
        <td>14:13<br />
</td>
        <td>128.30<br />
</td>
        <td>0.27<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>171.43<br />
</td>
        <td><br />
</td>
        <td>11:10<br />
</td>
        <td>165.00<br />
</td>
        <td>6.43<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>214.29<br />
</td>
        <td><br />
</td>
        <td>17:15<br />
</td>
        <td>216.69<br />
</td>
        <td>-2.40<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>257.14<br />
</td>
        <td><br />
</td>
        <td>7:6<br />
</td>
        <td>266.87<br />
</td>
        <td>-9.73<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>300<br />
</td>
        <td><br />
</td>
        <td>6:5<br />
</td>
        <td>315.64<br />
</td>
        <td>-15.64<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>342.86<br />
</td>
        <td><br />
</td>
        <td>11:9<br />
</td>
        <td>347.41<br />
</td>
        <td>-4.55<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>385.71<br />
</td>
        <td><br />
</td>
        <td>5:4<br />
</td>
        <td>386.31<br />
</td>
        <td>-0.60<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>428.57<br />
</td>
        <td><br />
</td>
        <td>9:7<br />
</td>
        <td>435.08<br />
</td>
        <td>-6.51<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>471.43<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>514.29<br />
</td>
        <td><br />
</td>
        <td>4:3<br />
</td>
        <td>498.04<br />
</td>
        <td>16.25<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>557.14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>600<br />
</td>
        <td><br />
</td>
        <td>7:5<br />
</td>
        <td>582.51<br />
</td>
        <td>17.49<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>642.86<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>685.71<br />
</td>
        <td><br />
</td>
        <td>3:2<br />
</td>
        <td>701.96<br />
</td>
        <td>-16.25<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>728.57<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>771.43<br />
</td>
        <td><br />
</td>
        <td>14:9<br />
</td>
        <td>764.92<br />
</td>
        <td>6.51<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>814.29<br />
</td>
        <td><br />
</td>
        <td>5:8<br />
</td>
        <td>813.68<br />
</td>
        <td>0.61<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>857.14<br />
</td>
        <td><br />
</td>
        <td>18:11<br />
</td>
        <td>852.59<br />
</td>
        <td>4.55<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>900<br />
</td>
        <td><br />
</td>
        <td>5:3<br />
</td>
        <td>884.36<br />
</td>
        <td>15.64<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>942.86<br />
</td>
        <td><br />
</td>
        <td>12:7<br />
</td>
        <td>933.13<br />
</td>
        <td>9.73<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>985.71<br />
</td>
        <td><br />
</td>
        <td>30:17<br />
</td>
        <td>983.31<br />
</td>
        <td>2.40<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1028.57<br />
</td>
        <td><br />
</td>
        <td>9:5<br />
</td>
        <td>1035.00<br />
</td>
        <td>-6.43<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1071.42<br />
</td>
        <td><br />
</td>
        <td>13:7<br />
</td>
        <td>1071.70<br />
</td>
        <td>-0.27<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1114.29<br />
</td>
        <td><br />
</td>
        <td>40:21<br />
</td>
        <td>1115.53<br />
</td>
        <td>-1.24<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1157.14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200<br />
</td>
        <td><br />
</td>
        <td>2:1<br />
</td>
        <td>1200<br />
</td>
        <td>0<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</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:JinowKeatiuku|JinowKeatiuku]] and made on <tt>2010-09-16 21:33:03 UTC</tt>.<br>
+: This revision was by author [[User:JinowKeatiuku|JinowKeatiuku]] and made on <tt>2010-09-17 19:08:00 UTC</tt>.<br>
-: The original revision id was <tt>163324345</tt>.<br>
+: The original revision id was <tt>163549865</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>
 <h4>Original Wikitext content:</h4>
-<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">28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It does not have good perfect fifths or perfect fourths, so although it has some familiar intervals, it may sound disorienting. It also has decent approximations of several septimal intervals.
+<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">28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, most of which are also found in 14edo.
 The following table compares it to potentially useful nearby just intervals.
@@ Line 41: / Line 41: @@
 || 28 ||   ||   ||   || 1200 ||   || 2:1 || 1200 || 0 ||   ||</pre></div>
 <h4>Original HTML content:</h4>
-<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;28edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It does not have good perfect fifths or perfect fourths, so although it has some familiar intervals, it may sound disorienting. It also has decent approximations of several septimal intervals.&lt;br /&gt;
+<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;28edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, most of which are also found in 14edo.&lt;br /&gt;
 &lt;br /&gt;
 The following table compares it to potentially useful nearby just intervals.&lt;br /&gt;

28edo: Difference between revisions

Revision as of 19:08, 17 September 2010

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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