23edf: Difference between revisions

Revision as of 17:23, 12 June 2015

IMPORTED REVISION FROM WIKISPACES

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This revision was by author toddiharrop and made on 2015-06-12 17:23:21 UTC.

The original revision id was 553792278.

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:

Twenty-three equal divisions of the perfect fifth (23ed3/2)

Rank 1 scale with step size of 30.52 cents.
Close to 39ed2 and/or 62ed3, however, the respective 
octave and/or twelfth would need to be nearly 10 cents flat.
A proponent of this scale is Petr Pařízek.

Some intervals in table below, selected on the basis of
single-use of primes (for most cases):
|| **Step** || **Size (cents)** || **Approx. ratio** || **Error from ratio (cents)** ||
|| 19 || 579.9 || 7/5 || –2.6¢ ||
|| 23 || 702 || 3/2 ||   ||
|| 24 || 732.5 || 29/19 || +0.4¢ ||
|| 29 || 885.1 || 5/3 || +0.7¢ ||
|| 31 || 946.1 || 19/11 || –0.1¢ ||
|| 35 || 1068 || 13/7 || –3.5¢ ||
|| 46 || 1404 || 9/4 ||   ||
|| 48 || 1465 || 7/3 || –1.9¢ ||
|| 52 || 1587 || 5/2 || +0.7¢ ||
|| 55 || 1679 || 29/11 || +0.3¢ ||
|| 58 || 1770 || 25/9 || +1.4¢ ||
|| 71 || 2167 || 7/2 || –1.9¢ ||
||   ||   ||   ||   ||
–Todd Harrop

Original HTML content:

<html><head><title>23edf</title></head><body>Twenty-three equal divisions of the perfect fifth (23ed3/2)<br />
<br />
Rank 1 scale with step size of 30.52 cents.<br />
Close to 39ed2 and/or 62ed3, however, the respective <br />
octave and/or twelfth would need to be nearly 10 cents flat.<br />
A proponent of this scale is Petr Pařízek.<br />
<br />
Some intervals in table below, selected on the basis of<br />
single-use of primes (for most cases):<br />


<table class="wiki_table">
    <tr>
        <td><strong>Step</strong><br />
</td>
        <td><strong>Size (cents)</strong><br />
</td>
        <td><strong>Approx. ratio</strong><br />
</td>
        <td><strong>Error from ratio (cents)</strong><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>579.9<br />
</td>
        <td>7/5<br />
</td>
        <td>–2.6¢<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>702<br />
</td>
        <td>3/2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>732.5<br />
</td>
        <td>29/19<br />
</td>
        <td>+0.4¢<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>885.1<br />
</td>
        <td>5/3<br />
</td>
        <td>+0.7¢<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>946.1<br />
</td>
        <td>19/11<br />
</td>
        <td>–0.1¢<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>1068<br />
</td>
        <td>13/7<br />
</td>
        <td>–3.5¢<br />
</td>
    </tr>
    <tr>
        <td>46<br />
</td>
        <td>1404<br />
</td>
        <td>9/4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td>1465<br />
</td>
        <td>7/3<br />
</td>
        <td>–1.9¢<br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td>1587<br />
</td>
        <td>5/2<br />
</td>
        <td>+0.7¢<br />
</td>
    </tr>
    <tr>
        <td>55<br />
</td>
        <td>1679<br />
</td>
        <td>29/11<br />
</td>
        <td>+0.3¢<br />
</td>
    </tr>
    <tr>
        <td>58<br />
</td>
        <td>1770<br />
</td>
        <td>25/9<br />
</td>
        <td>+1.4¢<br />
</td>
    </tr>
    <tr>
        <td>71<br />
</td>
        <td>2167<br />
</td>
        <td>7/2<br />
</td>
        <td>–1.9¢<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

–Todd Harrop</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:toddiharrop|toddiharrop]] and made on <tt>2015-06-12 16:22:40 UTC</tt>.<br>
+: This revision was by author [[User:toddiharrop|toddiharrop]] and made on <tt>2015-06-12 17:23:21 UTC</tt>.<br>
-: The original revision id was <tt>553789738</tt>.<br>
+: The original revision id was <tt>553792278</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">Twenty-three equal divisions of the perfect fifth (23ed3/2)
 Rank 1 scale with step size of 30.52 cents.
-Close to 39ed2 and/or 62ed3, however, the respective octave and/or twelfth would need to be nearly 10 cents flat.
+Close to 39ed2 and/or 62ed3, however, the respective
+octave and/or twelfth would need to be nearly 10 cents flat.
 A proponent of this scale is Petr Pařízek.
-Selected intervals in table below, showing near-perfect frequency ratios:
+Some intervals in table below, selected on the basis of
+single-use of primes (for most cases):
 || **Step** || **Size (cents)** || **Approx. ratio** || **Error from ratio (cents)** ||
-|| 19 || 582.5 || 7/5 || –2.6¢ ||
+|| 19 || 579.9 || 7/5 || –2.6¢ ||
 || 23 || 702 || 3/2 ||   ||
-|| 24 || 732.1 || 29/19 || +0.4¢ ||
+|| 24 || 732.5 || 29/19 || +0.4¢ ||
-|| 29 || 884.4 || 5/3 || +0.7¢ ||
+|| 29 || 885.1 || 5/3 || +0.7¢ ||
-|| 31 || 946.2 || 19/11 || –0.1¢ ||
+|| 31 || 946.1 || 19/11 || –0.1¢ ||
-|| 35 || 1072 || 13/7 || –3.5¢ ||
+|| 35 || 1068 || 13/7 || –3.5¢ ||
 || 46 || 1404 || 9/4 ||   ||
-|| 48 || 1467 || 7/3 || –1.9¢ ||
+|| 48 || 1465 || 7/3 || –1.9¢ ||
-|| 52 || 1586 || 5/2 || +0.7¢ ||
+|| 52 || 1587 || 5/2 || +0.7¢ ||
-|| 55 || 1678 || 29/11 || +0.3¢ ||
+|| 55 || 1679 || 29/11 || +0.3¢ ||
-|| 58 || 1769 || 25/9 || +1.4¢ ||
+|| 58 || 1770 || 25/9 || +1.4¢ ||
-|| 71 || 2169 || 7/2 || –1.9¢ ||
+|| 71 || 2167 || 7/2 || –1.9¢ ||
 ||   ||   ||   ||   ||
 –Todd Harrop</pre></div>
@@ Line 31: / Line 33: @@
 <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;23edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Twenty-three equal divisions of the perfect fifth (23ed3/2)&lt;br /&gt;
 &lt;br /&gt;
-Rank 1 scale with step size of 30.52 cents. &lt;br /&gt;
+Rank 1 scale with step size of 30.52 cents.&lt;br /&gt;
-Close to 39ed2 and/or 62ed3, however, the respective octave and/or twelfth would need to be nearly 10 cents flat. &lt;br /&gt;
+Close to 39ed2 and/or 62ed3, however, the respective &lt;br /&gt;
+octave and/or twelfth would need to be nearly 10 cents flat.&lt;br /&gt;
 A proponent of this scale is Petr Pařízek.&lt;br /&gt;
 &lt;br /&gt;
-Selected intervals in table below, showing near-perfect frequency ratios:&lt;br /&gt;
+Some intervals in table below, selected on the basis of&lt;br /&gt;
+single-use of primes (for most cases):&lt;br /&gt;
@@ Line 52: / Line 56: @@
          &lt;td&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;582.5&lt;br /&gt;
+         &lt;td&gt;579.9&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/5&lt;br /&gt;
@@ Line 72: / Line 76: @@
          &lt;td&gt;24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;732.1&lt;br /&gt;
+         &lt;td&gt;732.5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;29/19&lt;br /&gt;
@@ Line 82: / Line 86: @@
          &lt;td&gt;29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;884.4&lt;br /&gt;
+         &lt;td&gt;885.1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/3&lt;br /&gt;
@@ Line 92: / Line 96: @@
          &lt;td&gt;31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;946.2&lt;br /&gt;
+         &lt;td&gt;946.1&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;19/11&lt;br /&gt;
@@ Line 102: / Line 106: @@
          &lt;td&gt;35&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1072&lt;br /&gt;
+         &lt;td&gt;1068&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;13/7&lt;br /&gt;
@@ Line 122: / Line 126: @@
          &lt;td&gt;48&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1467&lt;br /&gt;
+         &lt;td&gt;1465&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/3&lt;br /&gt;
@@ Line 132: / Line 136: @@
          &lt;td&gt;52&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1586&lt;br /&gt;
+         &lt;td&gt;1587&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/2&lt;br /&gt;
@@ Line 142: / Line 146: @@
          &lt;td&gt;55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1678&lt;br /&gt;
+         &lt;td&gt;1679&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;29/11&lt;br /&gt;
@@ Line 152: / Line 156: @@
          &lt;td&gt;58&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1769&lt;br /&gt;
+         &lt;td&gt;1770&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;25/9&lt;br /&gt;
@@ Line 162: / Line 166: @@
          &lt;td&gt;71&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2169&lt;br /&gt;
+         &lt;td&gt;2167&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/2&lt;br /&gt;

23edf: Difference between revisions

Revision as of 17:23, 12 June 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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