46edo: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 304330236 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 304336094 - Original comment: ** |
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| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-02-23 05: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-02-23 05:48:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>304336094</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 294: | Line 294: | ||
|| 23 || 1\46 || 26.087 || || || || | || 23 || 1\46 || 26.087 || || || || | ||
=Intervals= | =Intervals= | ||
|| degrees of 46edo || cents value || | || degrees of 46edo || cents value || approximate ratios in the [[17-limit]] || | ||
|| 0 || 0.00 || | || 0 || 0.00 || 1/1 || | ||
|| 1 || 26.087 || | || 1 || 26.087 || || | ||
|| 2 || 52.174 || | || 2 || 52.174 || || | ||
|| 3 || 78.261 || | || 3 || 78.261 || || | ||
|| 4 || 104.348 || | || 4 || 104.348 || 16/15, 17/16, 18/17 || | ||
|| 5 || 130.435 || | || 5 || 130.435 || 13/12, 14/13, 15/14 || | ||
|| 6 || 156.522 || | || 6 || 156.522 || 12/11, 11/10 || | ||
|| 7 || 182.609 || | || 7 || 182.609 || 10/9 || | ||
|| 8 || 208.696 || | || 8 || 208.696 || 9/8, 17/15 || | ||
|| 9 || 234.783 || | || 9 || 234.783 || 8/7, 15/13* || | ||
|| 10 || 260.87 || | || 10 || 260.87 || 7/6, 15/13* || | ||
|| 11 || 286.957 || | || 11 || 286.957 || 13/11, 20/17 || | ||
|| 12 || 313.043 || | || 12 || 313.043 || 6/5 || | ||
|| 13 || 339.13 || | || 13 || 339.13 || 11/9, 17/14 || | ||
|| 14 || 365.217 || | || 14 || 365.217 || 16/13 || | ||
|| 15 || 391.304 || | || 15 || 391.304 || 5/4 || | ||
|| 16 || 417.391 || | || 16 || 417.391 || 14/11 || | ||
|| 17 || 443.478 || | || 17 || 443.478 || 9/7, 13/10, 22/17 || | ||
|| 18 || 469.565 || | || 18 || 469.565 || 17/13 || | ||
|| 19 || 495.652 || | || 19 || 495.652 || 4/3 || | ||
|| 20 || 521.739 || | || 20 || 521.739 || || | ||
|| 21 || 547.826 || | || 21 || 547.826 || 11/8, 15/11 || | ||
|| 22 || 573.913 || | || 22 || 573.913 || 7/5, 18/13 || | ||
|| 23 || 600 || | || 23 || 600 || 17/12, 24/17 || | ||
|| 24 || 626.087 || | || 24 || 626.087 || 10/7, 13/9 || | ||
|| 25 || 652.174 || | || 25 || 652.174 || 16/11, 22/15 || | ||
|| 26 || 628.261 || | || 26 || 628.261 || || | ||
|| 27 || 704.348 || | || 27 || 704.348 || 3/2 || | ||
|| 28 || 730.435 || | || 28 || 730.435 || 26/17 || | ||
|| 29 || 756.522 || | || 29 || 756.522 || 14/9, 20/13, 17/11 || | ||
|| 30 || 782.609 || | || 30 || 782.609 || 11/7 || | ||
|| 31 || 808.696 || | || 31 || 808.696 || 8/5 || | ||
|| 32 || 834.783 || | || 32 || 834.783 || 13/8 || | ||
|| 33 || 860.87 || | || 33 || 860.87 || 18/11, 28/17 || | ||
|| 34 || 886.957 || | || 34 || 886.957 || 5/3 || | ||
|| 35 || 913.043 || | || 35 || 913.043 || 22/13, 17/10 || | ||
|| 36 || 939.13 || | || 36 || 939.13 || 12/7, 26/15* || | ||
|| 37 || 965.217 || | || 37 || 965.217 || 7/4, 26/15* || | ||
|| 38 || 991.304 || | || 38 || 991.304 || 16/9, 30/17 || | ||
|| 39 || 1017.391 || | || 39 || 1017.391 || 9/5 || | ||
|| 40 || 1043.478 || | || 40 || 1043.478 || 11/6, 20/11 || | ||
|| 41 || 1069.565 || | || 41 || 1069.565 || 24/13, 13/7, 28/15 || | ||
|| 42 || 1095.652 || | || 42 || 1095.652 || 15/8, 32/17, 17/9 || | ||
|| 43 || 1121.739 || | || 43 || 1121.739 || || | ||
|| 44 || 1147.826 || | || 44 || 1147.826 || || | ||
|| 45 || 1173.913 || | || 45 || 1173.913 || || | ||
*15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not [[consistent]] in the [[15-limit]]. | |||
=Approximation to Mode 8 of the Harmonic Series= | =Approximation to Mode 8 of the Harmonic Series= | ||
| Line 976: | Line 977: | ||
</td> | </td> | ||
<td>cents value<br /> | <td>cents value<br /> | ||
</td> | |||
<td>approximate ratios in the <a class="wiki_link" href="/17-limit">17-limit</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 982: | Line 985: | ||
</td> | </td> | ||
<td>0.00<br /> | <td>0.00<br /> | ||
</td> | |||
<td>1/1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 988: | Line 993: | ||
</td> | </td> | ||
<td>26.087<br /> | <td>26.087<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 994: | Line 1,001: | ||
</td> | </td> | ||
<td>52.174<br /> | <td>52.174<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,000: | Line 1,009: | ||
</td> | </td> | ||
<td>78.261<br /> | <td>78.261<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,006: | Line 1,017: | ||
</td> | </td> | ||
<td>104.348<br /> | <td>104.348<br /> | ||
</td> | |||
<td>16/15, 17/16, 18/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,012: | Line 1,025: | ||
</td> | </td> | ||
<td>130.435<br /> | <td>130.435<br /> | ||
</td> | |||
<td>13/12, 14/13, 15/14<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,018: | Line 1,033: | ||
</td> | </td> | ||
<td>156.522<br /> | <td>156.522<br /> | ||
</td> | |||
<td>12/11, 11/10<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,024: | Line 1,041: | ||
</td> | </td> | ||
<td>182.609<br /> | <td>182.609<br /> | ||
</td> | |||
<td>10/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,030: | Line 1,049: | ||
</td> | </td> | ||
<td>208.696<br /> | <td>208.696<br /> | ||
</td> | |||
<td>9/8, 17/15<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,036: | Line 1,057: | ||
</td> | </td> | ||
<td>234.783<br /> | <td>234.783<br /> | ||
</td> | |||
<td>8/7, 15/13*<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,042: | Line 1,065: | ||
</td> | </td> | ||
<td>260.87<br /> | <td>260.87<br /> | ||
</td> | |||
<td>7/6, 15/13*<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,048: | Line 1,073: | ||
</td> | </td> | ||
<td>286.957<br /> | <td>286.957<br /> | ||
</td> | |||
<td>13/11, 20/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,054: | Line 1,081: | ||
</td> | </td> | ||
<td>313.043<br /> | <td>313.043<br /> | ||
</td> | |||
<td>6/5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,060: | Line 1,089: | ||
</td> | </td> | ||
<td>339.13<br /> | <td>339.13<br /> | ||
</td> | |||
<td>11/9, 17/14<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,066: | Line 1,097: | ||
</td> | </td> | ||
<td>365.217<br /> | <td>365.217<br /> | ||
</td> | |||
<td>16/13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,072: | Line 1,105: | ||
</td> | </td> | ||
<td>391.304<br /> | <td>391.304<br /> | ||
</td> | |||
<td>5/4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,078: | Line 1,113: | ||
</td> | </td> | ||
<td>417.391<br /> | <td>417.391<br /> | ||
</td> | |||
<td>14/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,084: | Line 1,121: | ||
</td> | </td> | ||
<td>443.478<br /> | <td>443.478<br /> | ||
</td> | |||
<td>9/7, 13/10, 22/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,090: | Line 1,129: | ||
</td> | </td> | ||
<td>469.565<br /> | <td>469.565<br /> | ||
</td> | |||
<td>17/13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,096: | Line 1,137: | ||
</td> | </td> | ||
<td>495.652<br /> | <td>495.652<br /> | ||
</td> | |||
<td>4/3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,102: | Line 1,145: | ||
</td> | </td> | ||
<td>521.739<br /> | <td>521.739<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,108: | Line 1,153: | ||
</td> | </td> | ||
<td>547.826<br /> | <td>547.826<br /> | ||
</td> | |||
<td>11/8, 15/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,114: | Line 1,161: | ||
</td> | </td> | ||
<td>573.913<br /> | <td>573.913<br /> | ||
</td> | |||
<td>7/5, 18/13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,120: | Line 1,169: | ||
</td> | </td> | ||
<td>600<br /> | <td>600<br /> | ||
</td> | |||
<td>17/12, 24/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,126: | Line 1,177: | ||
</td> | </td> | ||
<td>626.087<br /> | <td>626.087<br /> | ||
</td> | |||
<td>10/7, 13/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,132: | Line 1,185: | ||
</td> | </td> | ||
<td>652.174<br /> | <td>652.174<br /> | ||
</td> | |||
<td>16/11, 22/15<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,138: | Line 1,193: | ||
</td> | </td> | ||
<td>628.261<br /> | <td>628.261<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,144: | Line 1,201: | ||
</td> | </td> | ||
<td>704.348<br /> | <td>704.348<br /> | ||
</td> | |||
<td>3/2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,150: | Line 1,209: | ||
</td> | </td> | ||
<td>730.435<br /> | <td>730.435<br /> | ||
</td> | |||
<td>26/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,156: | Line 1,217: | ||
</td> | </td> | ||
<td>756.522<br /> | <td>756.522<br /> | ||
</td> | |||
<td>14/9, 20/13, 17/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,162: | Line 1,225: | ||
</td> | </td> | ||
<td>782.609<br /> | <td>782.609<br /> | ||
</td> | |||
<td>11/7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,168: | Line 1,233: | ||
</td> | </td> | ||
<td>808.696<br /> | <td>808.696<br /> | ||
</td> | |||
<td>8/5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,174: | Line 1,241: | ||
</td> | </td> | ||
<td>834.783<br /> | <td>834.783<br /> | ||
</td> | |||
<td>13/8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,180: | Line 1,249: | ||
</td> | </td> | ||
<td>860.87<br /> | <td>860.87<br /> | ||
</td> | |||
<td>18/11, 28/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,186: | Line 1,257: | ||
</td> | </td> | ||
<td>886.957<br /> | <td>886.957<br /> | ||
</td> | |||
<td>5/3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,192: | Line 1,265: | ||
</td> | </td> | ||
<td>913.043<br /> | <td>913.043<br /> | ||
</td> | |||
<td>22/13, 17/10<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,198: | Line 1,273: | ||
</td> | </td> | ||
<td>939.13<br /> | <td>939.13<br /> | ||
</td> | |||
<td>12/7, 26/15*<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,204: | Line 1,281: | ||
</td> | </td> | ||
<td>965.217<br /> | <td>965.217<br /> | ||
</td> | |||
<td>7/4, 26/15*<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,210: | Line 1,289: | ||
</td> | </td> | ||
<td>991.304<br /> | <td>991.304<br /> | ||
</td> | |||
<td>16/9, 30/17<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,216: | Line 1,297: | ||
</td> | </td> | ||
<td>1017.391<br /> | <td>1017.391<br /> | ||
</td> | |||
<td>9/5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,222: | Line 1,305: | ||
</td> | </td> | ||
<td>1043.478<br /> | <td>1043.478<br /> | ||
</td> | |||
<td>11/6, 20/11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,228: | Line 1,313: | ||
</td> | </td> | ||
<td>1069.565<br /> | <td>1069.565<br /> | ||
</td> | |||
<td>24/13, 13/7, 28/15<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,234: | Line 1,321: | ||
</td> | </td> | ||
<td>1095.652<br /> | <td>1095.652<br /> | ||
</td> | |||
<td>15/8, 32/17, 17/9<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,240: | Line 1,329: | ||
</td> | </td> | ||
<td>1121.739<br /> | <td>1121.739<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,246: | Line 1,337: | ||
</td> | </td> | ||
<td>1147.826<br /> | <td>1147.826<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,252: | Line 1,345: | ||
</td> | </td> | ||
<td>1173.913<br /> | <td>1173.913<br /> | ||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
*15/13 (and its inversion 26/15) appears twice on the list. 9\46edo is closest to 15/13 by a hair; 10\46edo represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13. This discrepancy occurs because 46edo is not <a class="wiki_link" href="/consistent">consistent</a> in the <a class="wiki_link" href="/15-limit">15-limit</a>.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Approximation to Mode 8 of the Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:8 -->Approximation to Mode 8 of the Harmonic Series</h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Approximation to Mode 8 of the Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:8 -->Approximation to Mode 8 of the Harmonic Series</h1> | ||