23edf: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

: This revision was by author [[User:toddiharrop|toddiharrop]] and made on <tt>2015-06-~~12 17~~:23:21 UTC</tt>.

: This revision was by author [[User:toddiharrop|toddiharrop]] and made on <tt>2015-06-13 05:23:10 UTC</tt>.

: The original revision id was <tt>~~553792278~~</tt>.

: The original revision id was <tt>553808036</tt>.

: The revision comment was: <tt></tt>

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

Line 9:

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.

octave and 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)** ||

||= **Step** ||= **Size**

|| 19 || 579.9 || 7/5 || –2.6¢ ||

**(cents)** ||= **Approx.**

|| 23 || 702 || 3/2 || ||

**(JI) ratio** ||= **Error from**

|| 24 || 732.5 || 29/19 || +0.4¢ ||

**ratio (cents)** ||

|| 29 || 885.1 || 5/3 || +0.7¢ ||

||= 19 ||= 579.9 ||= 7/5 ||= –2.6¢ ||

|| 31 || 946.1 || 19/11 || –0.1¢ ||

||= 23 ||= 702 ||= 3/2 ||= ||

|| 35 || 1068 || 13/7 || –3.5¢ ||

||= 24 ||= 732.5 ||= 29/19 ||= +0.4¢ ||

|| 46 || 1404 || 9/4 || ||

||= 29 ||= 885.1 ||= 5/3 ||= +0.7¢ ||

|| 48 || 1465 || 7/3 || –1.9¢ ||

||= 31 ||= 946.1 ||= 19/11 ||= –0.1¢ ||

|| 52 || 1587 || 5/2 || +0.7¢ ||

||= 35 ||= 1068 ||= 13/7 ||= –3.5¢ ||

|| 55 || 1679 || 29/11 || +0.3¢ ||

||= 46 ||= 1404 ||= 9/4 ||= ||

|| 58 || 1770 || 25/9 || +1.4¢ ||

||= 48 ||= 1465 ||= 7/3 ||= –1.9¢ ||

|| 71 || 2167 || 7/2 || –1.9¢ ||

||= 52 ||= 1587 ||= 5/2 ||= +0.7¢ ||

|| || || || ||

||= 55 ||= 1679 ||= 29/11 ||= +0.3¢ ||

–Todd Harrop</pre></div>

||= 58 ||= 1770 ||= 25/9 ||= +1.4¢ ||

||= 71 ||= 2167 ||= 7/2 ||= –1.9¢ ||

||= ||= ||= ||= ||

–Todd Harrop (June 2015)</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"><html><head><title>23edf</title></head><body>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

Close to 39ed2 and/or 62ed3, however, the respective

octave and~~/or~~ twelfth would need to be nearly 10 cents flat.

octave and twelfth would need to be nearly 10 cents flat.

A proponent of this scale is Petr Pařízek.

Line 44:

Line 47:

<tr>

<td>Step

<td style="text-align: center;">Step

</td>

<td>Size (cents)

<td style="text-align: center;">Size

(cents)

</td>

<td>Approx. ratio

<td style="text-align: center;">Approx.

(JI) ratio

</td>

<td>Error from ratio (cents)

<td style="text-align: center;">Error from

ratio (cents)

</td>

</tr>

<tr>

<td>19

<td style="text-align: center;">19

</td>

<td>579.9

<td style="text-align: center;">579.9

</td>

<td>7/5

<td style="text-align: center;">7/5

</td>

<td>–2.6¢

<td style="text-align: center;">–2.6¢

</td>

</tr>

<tr>

<td>23

<td style="text-align: center;">23

</td>

<td>702

<td style="text-align: center;">702

</td>

<td>3/2

<td style="text-align: center;">3/2

</td>

<td>

</td>

</tr>

<tr>

<td>24

<td style="text-align: center;">24

</td>

<td>732.5

<td style="text-align: center;">732.5

</td>

<td>29/19

<td style="text-align: center;">29/19

</td>

<td>+0.4¢

<td style="text-align: center;">+0.4¢

</td>

</tr>

<tr>

<td>29

<td style="text-align: center;">29

</td>

<td>885.1

<td style="text-align: center;">885.1

</td>

<td>5/3

<td style="text-align: center;">5/3

</td>

<td>+0.7¢

<td style="text-align: center;">+0.7¢

</td>

</tr>

<tr>

<td>31

<td style="text-align: center;">31

</td>

<td>946.1

<td style="text-align: center;">946.1

</td>

<td>19/11

<td style="text-align: center;">19/11

</td>

<td>–0.1¢

<td style="text-align: center;">–0.1¢

</td>

</tr>

<tr>

<td>35

<td style="text-align: center;">35

</td>

<td>1068

<td style="text-align: center;">1068

</td>

<td>13/7

<td style="text-align: center;">13/7

</td>

<td>–3.5¢

<td style="text-align: center;">–3.5¢

</td>

</tr>

<tr>

<td>46

<td style="text-align: center;">46

</td>

<td>1404

<td style="text-align: center;">1404

</td>

<td>9/4

<td style="text-align: center;">9/4

</td>

<td>

</td>

</tr>

<tr>

<td>48

<td style="text-align: center;">48

</td>

<td>1465

<td style="text-align: center;">1465

</td>

<td>7/3

<td style="text-align: center;">7/3

</td>

<td>–1.9¢

<td style="text-align: center;">–1.9¢

</td>

</tr>

<tr>

<td>52

<td style="text-align: center;">52

</td>

<td>1587

<td style="text-align: center;">1587

</td>

<td>5/2

<td style="text-align: center;">5/2

</td>

<td>+0.7¢

<td style="text-align: center;">+0.7¢

</td>

</tr>

<tr>

<td>55

<td style="text-align: center;">55

</td>

<td>1679

<td style="text-align: center;">1679

</td>

<td>29/11

<td style="text-align: center;">29/11

</td>

<td>+0.3¢

<td style="text-align: center;">+0.3¢

</td>

</tr>

<tr>

<td>58

<td style="text-align: center;">58

</td>

<td>1770

<td style="text-align: center;">1770

</td>

<td>25/9

<td style="text-align: center;">25/9

</td>

<td>+1.4¢

<td style="text-align: center;">+1.4¢

</td>

</tr>

<tr>

<td>71

<td style="text-align: center;">71

</td>

<td>2167

<td style="text-align: center;">2167

</td>

<td>7/2

<td style="text-align: center;">7/2

</td>

<td>–1.9¢

<td style="text-align: center;">–1.9¢

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

</tr>

</table>

–Todd Harrop</body></html></pre></div>

–Todd Harrop (June 2015)</body></html></pre></div>

@@ 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 17:23:21 UTC</tt>.<br>
+: This revision was by author [[User:toddiharrop|toddiharrop]] and made on <tt>2015-06-13 05:23:10 UTC</tt>.<br>
-: The original revision id was <tt>553792278</tt>.<br>
+: The original revision id was <tt>553808036</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 9: / Line 9: @@
 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.
+octave and 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)** ||
+||= **Step** ||= **Size**
-|| 19 || 579.9 || 7/5 || –2.6¢ ||
+**(cents)** ||= **Approx.**
-|| 23 || 702 || 3/2 ||   ||
+**(JI) ratio** ||= **Error from**
-|| 24 || 732.5 || 29/19 || +0.4¢ ||
+**ratio (cents)** ||
-|| 29 || 885.1 || 5/3 || +0.7¢ ||
+||= 19 ||= 579.9 ||= 7/5 ||= –2.6¢ ||
-|| 31 || 946.1 || 19/11 || –0.1¢ ||
+||= 23 ||= 702 ||= 3/2 ||=   ||
-|| 35 || 1068 || 13/7 || –3.5¢ ||
+||= 24 ||= 732.5 ||= 29/19 ||= +0.4¢ ||
-|| 46 || 1404 || 9/4 ||   ||
+||= 29 ||= 885.1 ||= 5/3 ||= +0.7¢ ||
-|| 48 || 1465 || 7/3 || –1.9¢ ||
+||= 31 ||= 946.1 ||= 19/11 ||= –0.1¢ ||
-|| 52 || 1587 || 5/2 || +0.7¢ ||
+||= 35 ||= 1068 ||= 13/7 ||= –3.5¢ ||
-|| 55 || 1679 || 29/11 || +0.3¢ ||
+||= 46 ||= 1404 ||= 9/4 ||=   ||
-|| 58 || 1770 || 25/9 || +1.4¢ ||
+||= 48 ||= 1465 ||= 7/3 ||= –1.9¢ ||
-|| 71 || 2167 || 7/2 || –1.9¢ ||
+||= 52 ||= 1587 ||= 5/2 ||= +0.7¢ ||
-||   ||   ||   ||   ||
+||= 55 ||= 1679 ||= 29/11 ||= +0.3¢ ||
-–Todd Harrop</pre></div>
+||= 58 ||= 1770 ||= 25/9 ||= +1.4¢ ||
+||= 71 ||= 2167 ||= 7/2 ||= –1.9¢ ||
+||=   ||=   ||=   ||=   ||
+–Todd Harrop (June 2015)</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;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;
-Close to 39ed2 and/or 62ed3, however, the respective &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;
+octave and 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;
@@ Line 44: / Line 47: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;strong&gt;Step&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Step&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;Size (cents)&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Size&lt;/strong&gt; &lt;br /&gt;
+&lt;strong&gt;(cents)&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;Approx. ratio&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approx.&lt;/strong&gt; &lt;br /&gt;
+&lt;strong&gt;(JI) ratio&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;Error from ratio (cents)&lt;/strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;strong&gt;Error from&lt;/strong&gt; &lt;br /&gt;
+&lt;strong&gt;ratio (cents)&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;579.9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;579.9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7/5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;–2.6¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;–2.6¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;23&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;702&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;702&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;3/2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;24&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;732.5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;732.5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;29/19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;29/19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.4¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;+0.4¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;29&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;885.1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;885.1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5/3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.7¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;+0.7¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;31&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;946.1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;946.1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;19/11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;–0.1¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;–0.1¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;35&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1068&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1068&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;13/7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13/7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;–3.5¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;–3.5¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1404&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1404&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;9/4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9/4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;48&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;48&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1465&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1465&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7/3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;–1.9¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;–1.9¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;52&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;52&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1587&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1587&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;5/2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5/2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.7¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;+0.7¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;55&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1679&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1679&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;29/11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;29/11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+0.3¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;+0.3¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;58&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;58&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1770&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1770&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;25/9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25/9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;+1.4¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;+1.4¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;71&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;71&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;2167&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2167&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;7/2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7/2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;–1.9¢&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;–1.9¢&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
 &lt;/table&gt;
-–Todd Harrop&lt;/body&gt;&lt;/html&gt;</pre></div>
+–Todd Harrop (June 2015)&lt;/body&gt;&lt;/html&gt;</pre></div>