|
|
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | Twenty-three equal divisions of the perfect fifth (23ed3/2) |
| 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>2015-06-13 05:23:10 UTC</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>
| |
| <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)
| |
|
| |
|
| Rank 1 scale with step size of 30.52 cents. | | 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 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. | | A proponent of this scale is Petr Pařízek. |
|
| |
|
| Some intervals in table below, selected on the basis of | | Some intervals in table below, selected on the basis of |
| | |
| single-use of primes (for most cases): | | single-use of primes (for most cases): |
| ||= **Step** ||= **Size**
| |
| **(cents)** ||= **Approx.**
| |
| **(JI) 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 (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)<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 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 />
| |
|
| |
|
| | {| class="wikitable" |
| | |- |
| | | style="text-align:center;" | '''Step''' |
| | | style="text-align:center;" | '''Size''' |
| | |
| | '''(cents)''' |
| | | style="text-align:center;" | '''Approx.''' |
|
| |
|
| <table class="wiki_table">
| | '''(JI) ratio''' |
| <tr>
| | | style="text-align:center;" | '''Error from''' |
| <td style="text-align: center;"><strong>Step</strong><br />
| |
| </td>
| |
| <td style="text-align: center;"><strong>Size</strong> <br />
| |
| <strong>(cents)</strong><br />
| |
| </td>
| |
| <td style="text-align: center;"><strong>Approx.</strong> <br />
| |
| <strong>(JI) ratio</strong><br />
| |
| </td>
| |
| <td style="text-align: center;"><strong>Error from</strong> <br />
| |
| <strong>ratio (cents)</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">19<br />
| |
| </td>
| |
| <td style="text-align: center;">579.9<br />
| |
| </td>
| |
| <td style="text-align: center;">7/5<br />
| |
| </td>
| |
| <td style="text-align: center;">–2.6¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">23<br />
| |
| </td>
| |
| <td style="text-align: center;">702<br />
| |
| </td>
| |
| <td style="text-align: center;">3/2<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">24<br />
| |
| </td>
| |
| <td style="text-align: center;">732.5<br />
| |
| </td>
| |
| <td style="text-align: center;">29/19<br />
| |
| </td>
| |
| <td style="text-align: center;">+0.4¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">29<br />
| |
| </td>
| |
| <td style="text-align: center;">885.1<br />
| |
| </td>
| |
| <td style="text-align: center;">5/3<br />
| |
| </td>
| |
| <td style="text-align: center;">+0.7¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">31<br />
| |
| </td>
| |
| <td style="text-align: center;">946.1<br />
| |
| </td>
| |
| <td style="text-align: center;">19/11<br />
| |
| </td>
| |
| <td style="text-align: center;">–0.1¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">35<br />
| |
| </td>
| |
| <td style="text-align: center;">1068<br />
| |
| </td>
| |
| <td style="text-align: center;">13/7<br />
| |
| </td>
| |
| <td style="text-align: center;">–3.5¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">46<br />
| |
| </td>
| |
| <td style="text-align: center;">1404<br />
| |
| </td>
| |
| <td style="text-align: center;">9/4<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">48<br />
| |
| </td>
| |
| <td style="text-align: center;">1465<br />
| |
| </td>
| |
| <td style="text-align: center;">7/3<br />
| |
| </td>
| |
| <td style="text-align: center;">–1.9¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">52<br />
| |
| </td>
| |
| <td style="text-align: center;">1587<br />
| |
| </td>
| |
| <td style="text-align: center;">5/2<br />
| |
| </td>
| |
| <td style="text-align: center;">+0.7¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">55<br />
| |
| </td>
| |
| <td style="text-align: center;">1679<br />
| |
| </td>
| |
| <td style="text-align: center;">29/11<br />
| |
| </td>
| |
| <td style="text-align: center;">+0.3¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">58<br />
| |
| </td>
| |
| <td style="text-align: center;">1770<br />
| |
| </td>
| |
| <td style="text-align: center;">25/9<br />
| |
| </td>
| |
| <td style="text-align: center;">+1.4¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">71<br />
| |
| </td>
| |
| <td style="text-align: center;">2167<br />
| |
| </td>
| |
| <td style="text-align: center;">7/2<br />
| |
| </td>
| |
| <td style="text-align: center;">–1.9¢<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| –Todd Harrop (June 2015)</body></html></pre></div>
| | '''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¢ |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | |} |
| | –Todd Harrop (June 2015) |
| | [[Category:31edo]] |
| | [[Category:edf]] |
| | [[Category:nonoctave]] |
| | [[Category:what_is]] |
| | [[Category:wiki]] |
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 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.
(JI) 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 (June 2015)