46edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 239557427 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 240945749 - Original comment: ** |
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<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: | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-12 02:09:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>240945749</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> | ||
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---- | ---- | ||
=<span style="color: #300094; font-size: | =<span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;">46 tone equal temperament</span>= | ||
The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent]]s, an interval close in size to [[66_65|66/65]], the interval from [[13_11|13/11]] to [[6_5|6/5]]. | The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent]]s, an interval close in size to [[66_65|66/65]], the interval from [[13_11|13/11]] to [[6_5|6/5]]. | ||
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The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad. | The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad. | ||
46edo can be treated as two [[23edo]]'s separated by an interval of 26. | 46edo can be treated as two [[23edo]]'s separated by an interval of 26.087 cents. | ||
=46edo srutis= | =46edo srutis= | ||
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|| degrees of 46edo || cents value || | || degrees of 46edo || cents value || | ||
|| 0 || 0.00 || | || 0 || 0.00 || | ||
|| 1 || 26. | || 1 || 26.087 || | ||
|| 2 || 52. | || 2 || 52.174 || | ||
|| 3 || 78. | || 3 || 78.261 || | ||
|| 4 || 104. | || 4 || 104.348 || | ||
|| 5 || 130. | || 5 || 130.435 || | ||
|| 6 || 156. | || 6 || 156.522 || | ||
|| 7 || 182. | || 7 || 182.609 || | ||
|| 8 || 208. | || 8 || 208.696 || | ||
|| 9 || 234. | || 9 || 234.783 || | ||
|| 10 || 260.87 || | || 10 || 260.87 || | ||
|| 11 || 286. | || 11 || 286.957 || | ||
|| 12 || 313. | || 12 || 313.043 || | ||
|| 13 || 339.13 || | || 13 || 339.13 || | ||
|| 14 || 365. | || 14 || 365.217 || | ||
|| 15 || 391. | || 15 || 391.304 || | ||
|| 16 || 417. | || 16 || 417.391 || | ||
|| 17 || 443. | || 17 || 443.478 || | ||
|| 18 || 469. | || 18 || 469.565 || | ||
|| 19 || 495. | || 19 || 495.652 || | ||
|| 20 || 521. | || 20 || 521.739 || | ||
|| 21 || 547. | || 21 || 547.826 || | ||
|| 22 || 573. | || 22 || 573.913 || | ||
|| 23 || 600 | || 23 || 600 || | ||
|| 24 || 626. | || 24 || 626.087 || | ||
|| 25 || 652. | || 25 || 652.174 || | ||
|| 26 || 628. | || 26 || 628.261 || | ||
|| 27 || 704. | || 27 || 704.348 || | ||
|| 28 || 730. | || 28 || 730.435 || | ||
|| 29 || 756. | || 29 || 756.522 || | ||
|| 30 || 782. | || 30 || 782.609 || | ||
|| 31 || 808. | || 31 || 808.696 || | ||
|| 32 || 834. | || 32 || 834.783 || | ||
|| 33 || 860.87 || | || 33 || 860.87 || | ||
|| 34 || 886. | || 34 || 886.957 || | ||
|| 35 || 913. | || 35 || 913.043 || | ||
|| 36 || 939.13 || | || 36 || 939.13 || | ||
|| 37 || 965. | || 37 || 965.217 || | ||
|| 38 || 991. | || 38 || 991.304 || | ||
|| 39 || 1017. | || 39 || 1017.391 || | ||
|| 40 || 1043. | || 40 || 1043.478 || | ||
|| 41 || 1069. | || 41 || 1069.565 || | ||
|| 42 || 1095. | || 42 || 1095.652 || | ||
|| 43 || 1121. | || 43 || 1121.739 || | ||
|| 44 || 1147. | || 44 || 1147.826 || | ||
|| 45 || 1173. | || 45 || 1173.913 || | ||
=Approximation to Mode 8 of the Harmonic Series= | =Approximation to Mode 8 of the Harmonic Series= | ||
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<!-- ws:end:WikiTextTocRule:19 --><hr /> | <!-- ws:end:WikiTextTocRule:19 --><hr /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x46 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #300094; font-size: | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x46 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;">46 tone equal temperament</span></h1> | ||
The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 <a class="wiki_link" href="/cent">cent</a>s, an interval close in size to <a class="wiki_link" href="/66_65">66/65</a>, the interval from <a class="wiki_link" href="/13_11">13/11</a> to <a class="wiki_link" href="/6_5">6/5</a>.<br /> | The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 <a class="wiki_link" href="/cent">cent</a>s, an interval close in size to <a class="wiki_link" href="/66_65">66/65</a>, the interval from <a class="wiki_link" href="/13_11">13/11</a> to <a class="wiki_link" href="/6_5">6/5</a>.<br /> | ||
<br /> | <br /> | ||
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The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the <a class="wiki_link" href="/just%20fifth">just fifth</a> and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.<br /> | The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the <a class="wiki_link" href="/just%20fifth">just fifth</a> and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.<br /> | ||
<br /> | <br /> | ||
46edo can be treated as two <a class="wiki_link" href="/23edo">23edo</a>'s separated by an interval of 26. | 46edo can be treated as two <a class="wiki_link" href="/23edo">23edo</a>'s separated by an interval of 26.087 cents.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x46edo srutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->46edo srutis</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x46edo srutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->46edo srutis</h1> | ||
Line 126: | Line 126: | ||
<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>26. | <td>26.087<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 132: | Line 132: | ||
<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>52. | <td>52.174<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 138: | Line 138: | ||
<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>78. | <td>78.261<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 144: | Line 144: | ||
<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>104. | <td>104.348<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 150: | Line 150: | ||
<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td>130. | <td>130.435<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 156: | Line 156: | ||
<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>156. | <td>156.522<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 162: | Line 162: | ||
<td>7<br /> | <td>7<br /> | ||
</td> | </td> | ||
<td>182. | <td>182.609<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 168: | Line 168: | ||
<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>208. | <td>208.696<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 174: | Line 174: | ||
<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td>234. | <td>234.783<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 186: | Line 186: | ||
<td>11<br /> | <td>11<br /> | ||
</td> | </td> | ||
<td>286. | <td>286.957<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 192: | Line 192: | ||
<td>12<br /> | <td>12<br /> | ||
</td> | </td> | ||
<td>313. | <td>313.043<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 204: | Line 204: | ||
<td>14<br /> | <td>14<br /> | ||
</td> | </td> | ||
<td>365. | <td>365.217<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 210: | Line 210: | ||
<td>15<br /> | <td>15<br /> | ||
</td> | </td> | ||
<td>391. | <td>391.304<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 216: | Line 216: | ||
<td>16<br /> | <td>16<br /> | ||
</td> | </td> | ||
<td>417. | <td>417.391<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 222: | Line 222: | ||
<td>17<br /> | <td>17<br /> | ||
</td> | </td> | ||
<td>443. | <td>443.478<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 228: | Line 228: | ||
<td>18<br /> | <td>18<br /> | ||
</td> | </td> | ||
<td>469. | <td>469.565<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 234: | Line 234: | ||
<td>19<br /> | <td>19<br /> | ||
</td> | </td> | ||
<td>495. | <td>495.652<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 240: | Line 240: | ||
<td>20<br /> | <td>20<br /> | ||
</td> | </td> | ||
<td>521. | <td>521.739<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 246: | Line 246: | ||
<td>21<br /> | <td>21<br /> | ||
</td> | </td> | ||
<td>547. | <td>547.826<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 252: | Line 252: | ||
<td>22<br /> | <td>22<br /> | ||
</td> | </td> | ||
<td>573. | <td>573.913<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 258: | Line 258: | ||
<td>23<br /> | <td>23<br /> | ||
</td> | </td> | ||
<td>600 | <td>600<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 264: | Line 264: | ||
<td>24<br /> | <td>24<br /> | ||
</td> | </td> | ||
<td>626. | <td>626.087<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 270: | Line 270: | ||
<td>25<br /> | <td>25<br /> | ||
</td> | </td> | ||
<td>652. | <td>652.174<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 276: | Line 276: | ||
<td>26<br /> | <td>26<br /> | ||
</td> | </td> | ||
<td>628. | <td>628.261<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 282: | Line 282: | ||
<td>27<br /> | <td>27<br /> | ||
</td> | </td> | ||
<td>704. | <td>704.348<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 288: | Line 288: | ||
<td>28<br /> | <td>28<br /> | ||
</td> | </td> | ||
<td>730. | <td>730.435<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 294: | Line 294: | ||
<td>29<br /> | <td>29<br /> | ||
</td> | </td> | ||
<td>756. | <td>756.522<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 300: | Line 300: | ||
<td>30<br /> | <td>30<br /> | ||
</td> | </td> | ||
<td>782. | <td>782.609<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 306: | Line 306: | ||
<td>31<br /> | <td>31<br /> | ||
</td> | </td> | ||
<td>808. | <td>808.696<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 312: | Line 312: | ||
<td>32<br /> | <td>32<br /> | ||
</td> | </td> | ||
<td>834. | <td>834.783<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 324: | Line 324: | ||
<td>34<br /> | <td>34<br /> | ||
</td> | </td> | ||
<td>886. | <td>886.957<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 330: | Line 330: | ||
<td>35<br /> | <td>35<br /> | ||
</td> | </td> | ||
<td>913. | <td>913.043<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 342: | Line 342: | ||
<td>37<br /> | <td>37<br /> | ||
</td> | </td> | ||
<td>965. | <td>965.217<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 348: | Line 348: | ||
<td>38<br /> | <td>38<br /> | ||
</td> | </td> | ||
<td>991. | <td>991.304<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 354: | Line 354: | ||
<td>39<br /> | <td>39<br /> | ||
</td> | </td> | ||
<td>1017. | <td>1017.391<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 360: | Line 360: | ||
<td>40<br /> | <td>40<br /> | ||
</td> | </td> | ||
<td>1043. | <td>1043.478<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 366: | Line 366: | ||
<td>41<br /> | <td>41<br /> | ||
</td> | </td> | ||
<td>1069. | <td>1069.565<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 372: | Line 372: | ||
<td>42<br /> | <td>42<br /> | ||
</td> | </td> | ||
<td>1095. | <td>1095.652<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 378: | Line 378: | ||
<td>43<br /> | <td>43<br /> | ||
</td> | </td> | ||
<td>1121. | <td>1121.739<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 384: | Line 384: | ||
<td>44<br /> | <td>44<br /> | ||
</td> | </td> | ||
<td>1147. | <td>1147.826<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 390: | Line 390: | ||
<td>45<br /> | <td>45<br /> | ||
</td> | </td> | ||
<td>1173. | <td>1173.913<br /> | ||
</td> | </td> | ||
</tr> | </tr> |