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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | '''23EDF''' is the [[EDF|equal division of the just perfect fifth]] into 23 parts of 30.5198 [[cents]] each, corresponding to 39.3188 [[edo]] (similar to every third step of [[118edo]]). |
| : 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>553792278</tt>.<br>
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| : 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">Twenty-three equal divisions of the perfect fifth (23ed3/2)
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|
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| Rank 1 scale with step size of 30.52 cents.
| | ==History== |
| Close to 39ed2 and/or 62ed3, however, the respective
| | A proponent of 23edf is [[Petr Pařízek]]. The first to write about 23edf on this wiki was [[Todd Harrop]] in 2015. |
| 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
| | ==Theory== |
| single-use of primes (for most cases):
| | 23edf is close to [[39edo]] and/or [[62edt]], however, the respective [[octave]] and [[tritave|twelfth]] would need to be nearly 10 cents flat. |
| || **Step** || **Size (cents)** || **Approx. ratio** || **Error from ratio (cents)** ||
| |
| || 19 || 579.9 || 7/5 || –2.6¢ ||
| |
| || 23 || 702 || 3/2 || ||
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| || 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¢ ||
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| || 46 || 1404 || 9/4 || ||
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| || 48 || 1465 || 7/3 || –1.9¢ ||
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| || 52 || 1587 || 5/2 || +0.7¢ ||
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| || 55 || 1679 || 29/11 || +0.3¢ ||
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| || 58 || 1770 || 25/9 || +1.4¢ ||
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| || 71 || 2167 || 7/2 || –1.9¢ ||
| |
| || || || || ||
| |
| –Todd Harrop</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)<br />
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| <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 />
| |
|
| |
|
| | Some intervals in table below, selected on the basis of single-use of [[prime]]s (for most cases): |
|
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|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <td><strong>Step</strong><br />
| | | style="text-align:center;" | '''Step''' |
| </td>
| | | style="text-align:center;" | '''Size''' |
| <td><strong>Size (cents)</strong><br />
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| </td>
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| <td><strong>Approx. ratio</strong><br />
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| </td>
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| <td><strong>Error from ratio (cents)</strong><br />
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| </td>
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| </tr>
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| <tr>
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| <td>19<br />
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| </td>
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| <td>579.9<br />
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| </td>
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| <td>7/5<br />
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| </td>
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| <td>–2.6¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>23<br />
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| </td>
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| <td>702<br />
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| </td>
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| <td>3/2<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td>24<br />
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| </td>
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| <td>732.5<br />
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| </td>
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| <td>29/19<br />
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| </td>
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| <td>+0.4¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>29<br />
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| </td>
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| <td>885.1<br />
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| </td>
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| <td>5/3<br />
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| </td>
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| <td>+0.7¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>31<br />
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| </td>
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| <td>946.1<br />
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| </td>
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| <td>19/11<br />
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| </td>
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| <td>–0.1¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>35<br />
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| </td>
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| <td>1068<br />
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| </td>
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| <td>13/7<br />
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| </td>
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| <td>–3.5¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>46<br />
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| </td>
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| <td>1404<br />
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| </td>
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| <td>9/4<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td>48<br />
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| </td>
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| <td>1465<br />
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| </td>
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| <td>7/3<br />
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| </td>
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| <td>–1.9¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>52<br />
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| </td>
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| <td>1587<br />
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| </td>
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| <td>5/2<br />
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| </td>
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| <td>+0.7¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>55<br />
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| </td>
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| <td>1679<br />
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| </td>
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| <td>29/11<br />
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| </td>
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| <td>+0.3¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>58<br />
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| </td>
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| <td>1770<br />
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| </td>
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| <td>25/9<br />
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| </td>
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| <td>+1.4¢<br />
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| </td>
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| </tr>
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| <tr>
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| <td>71<br />
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| </td>
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| <td>2167<br />
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| </td>
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| <td>7/2<br />
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| </td>
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| <td>–1.9¢<br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| </table>
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|
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|
| –Todd Harrop</body></html></pre></div>
| | '''(cents)''' |
| | | style="text-align:center;" | '''Approx.''' |
| | |
| | '''(JI) ratio''' |
| | | style="text-align:center;" | '''Error from''' |
| | |
| | '''ratio (cents)''' |
| | |- |
| | | style="text-align:center;" | 19 |
| | | style="text-align:center;" | 579.9 |
| | | style="text-align:center;" | 7/5 |
| | | style="text-align:center;" | –2.6¢ |
| | |- |
| | | style="text-align:center;" | 23 |
| | | style="text-align:center;" | 702 |
| | | style="text-align:center;" | 3/2 |
| | | style="text-align:center;" | |
| | |- |
| | | style="text-align:center;" | 24 |
| | | style="text-align:center;" | 732.5 |
| | | style="text-align:center;" | 29/19 |
| | | style="text-align:center;" | +0.4¢ |
| | |- |
| | | style="text-align:center;" | 29 |
| | | style="text-align:center;" | 885.1 |
| | | style="text-align:center;" | 5/3 |
| | | style="text-align:center;" | +0.7¢ |
| | |- |
| | | style="text-align:center;" | 31 |
| | | style="text-align:center;" | 946.1 |
| | | style="text-align:center;" | 19/11 |
| | | style="text-align:center;" | –0.1¢ |
| | |- |
| | | style="text-align:center;" | 35 |
| | | style="text-align:center;" | 1068 |
| | | style="text-align:center;" | 13/7 |
| | | style="text-align:center;" | –3.5¢ |
| | |- |
| | | style="text-align:center;" | 46 |
| | | style="text-align:center;" | 1404 |
| | | style="text-align:center;" | 9/4 |
| | | style="text-align:center;" | |
| | |- |
| | | style="text-align:center;" | 48 |
| | | style="text-align:center;" | 1465 |
| | | style="text-align:center;" | 7/3 |
| | | style="text-align:center;" | –1.9¢ |
| | |- |
| | | style="text-align:center;" | 52 |
| | | style="text-align:center;" | 1587 |
| | | style="text-align:center;" | 5/2 |
| | | style="text-align:center;" | +0.7¢ |
| | |- |
| | | style="text-align:center;" | 55 |
| | | style="text-align:center;" | 1679 |
| | | style="text-align:center;" | 29/11 |
| | | style="text-align:center;" | +0.3¢ |
| | |- |
| | | style="text-align:center;" | 58 |
| | | style="text-align:center;" | 1770 |
| | | style="text-align:center;" | 25/9 |
| | | style="text-align:center;" | +1.4¢ |
| | |- |
| | | style="text-align:center;" | 71 |
| | | style="text-align:center;" | 2167 |
| | | style="text-align:center;" | 7/2 |
| | | style="text-align:center;" | –1.9¢ |
| | |} |
| | |
| | === Harmonics === |
| | {{Harmonics in equal|23|3|2}} |
| | {{Harmonics in equal|23|3|2|start=12|collapsed=1}} |
| | |
| | == Intervals == |
| | {| class="wikitable mw-collapsible" |
| | |+ Intervals of 23edf |
| | |- |
| | !Step number |
| | !Size (cents) |
| | |- |
| | |1 |
| | |30.5198 |
| | |- |
| | |2 |
| | |61.0296 |
| | |- |
| | |3 |
| | |91.55935 |
| | |- |
| | |4 |
| | |122.0791 |
| | |- |
| | |5 |
| | |152.5989 |
| | |- |
| | |6 |
| | |183.1187 |
| | |- |
| | |7 |
| | |213.6385 |
| | |- |
| | |8 |
| | |244.1583 |
| | |- |
| | |9 |
| | |274.678 |
| | |- |
| | |10 |
| | |305.1978 |
| | |- |
| | |11 |
| | |335.7176 |
| | |- |
| | |12 |
| | |366.2374 |
| | |- |
| | |13 |
| | |396.7572 |
| | |- |
| | |14 |
| | |427.277 |
| | |- |
| | |15 |
| | |457.7967 |
| | |- |
| | |16 |
| | |488.3165 |
| | |- |
| | |17 |
| | |518.8363 |
| | |- |
| | |18 |
| | |549.3561 |
| | |- |
| | |19 |
| | |579.8759 |
| | |- |
| | |20 |
| | |610.39565 |
| | |- |
| | |21 |
| | |640.9154 |
| | |- |
| | |22 |
| | |671.4352 |
| | |- |
| | |23 |
| | |701.955 |
| | |- |
| | |24 |
| | |732.4748 |
| | |- |
| | |25 |
| | |762.9946 |
| | |- |
| | |26 |
| | |793.51435 |
| | |- |
| | |27 |
| | |824.0341 |
| | |- |
| | |28 |
| | |854.5539 |
| | |- |
| | |29 |
| | |885.0737 |
| | |- |
| | |30 |
| | |915.5935 |
| | |- |
| | |31 |
| | |946.1133 |
| | |- |
| | |32 |
| | |976.633 |
| | |- |
| | |33 |
| | |1007.1529 |
| | |- |
| | |34 |
| | |1037.6726 |
| | |- |
| | |35 |
| | |1068.1924 |
| | |- |
| | |36 |
| | |1098.7122 |
| | |- |
| | |37 |
| | |1129.232 |
| | |- |
| | |38 |
| | |1159.7517 |
| | |- |
| | |39 |
| | |1190.2715 |
| | |- |
| | |40 |
| | |1220.7913 |
| | |- |
| | |41 |
| | |1251.3111 |
| | |- |
| | |42 |
| | |1281.8309 |
| | |- |
| | |43 |
| | |1312.35065 |
| | |- |
| | |44 |
| | |1342.8704 |
| | |- |
| | |45 |
| | |1373.3902 |
| | |- |
| | |46 |
| | |1403.91 |
| | |} |
| | {{todo|inline=1|complete table|text=Add at least one more column, showing what the notes are named, what JI they approximate, or anything else interesting about them individually.}} |
| | |
| | |
| | {{todo|expand}} |
| | [[Category:nonoctave]] |