19edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 239657189 - Original comment: ** |
Wikispaces>igliashon **Imported revision 241974254 - 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:igliashon|igliashon]] and made on <tt>2011-07-19 14:39:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>241974254</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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==As an approximation of other temperaments== | ==As an approximation of other temperaments== | ||
The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone# |meantone]] temperament. It is also a suitable for [[Regular Temperaments#magic|magic]] temperament, because five of its major thirds are equivalent to one of its //twelfths//. | The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#|meantone]] temperament. It is also a suitable for [[Regular Temperaments#magic|magic]] temperament, because five of its major thirds are equivalent to one of its //twelfths//. | ||
For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. | For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it. | ||
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|| 0 ||= 0 || || | || 0 ||= 0 || || | ||
|| 1 || 63.1579 || || | || 1 || 63.1579 || || | ||
|| 2 || 126.326 || | || 2 || 126.326 || Negri || | ||
|| 3 || 189.474 || | || 3 || 189.474 || Deutone || | ||
|| 4 || 252.632 || | || 4 || 252.632 || Godzilla || | ||
|| 5 || 315.789 || Kleismic || | || 5 || 315.789 || Kleismic || | ||
|| 6 || 378.947 || | || 6 || 378.947 || Magic || | ||
|| 7 || 442.105 || | || 7 || 442.105 || Sensi || | ||
|| 8 || 505.263 || Meantone || | || 8 || 505.263 || Meantone || | ||
|| 9 || 568.421 || | || 9 || 568.421 || Triton || | ||
|| 10 || 631.579 || | || 10 || 631.579 || Triton || | ||
|| 11 || 694.737 || Meantone || | || 11 || 694.737 || Meantone || | ||
|| 12 || 757.895 || | || 12 || 757.895 || Sensi || | ||
|| 13 || 821.053 || | || 13 || 821.053 || Magic || | ||
|| 14 || 884.211 || | || 14 || 884.211 || Kleismic || | ||
|| 15 || 947.368 || | || 15 || 947.368 || Godzilla || | ||
|| 16 || 1010.53 || | || 16 || 1010.53 || Deutone || | ||
|| 17 || 1073.68 || | || 17 || 1073.68 || Negri || | ||
|| 18 || 1136.84 || || | || 18 || 1136.84 || || | ||
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<!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:3 -->As an approximation of other temperaments</h2> | <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:3 -->As an approximation of other temperaments</h2> | ||
<br /> | <br /> | ||
The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for | The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#|meantone]] temperament. It is also a suitable for <a class="wiki_link" href="/Regular%20Temperaments#magic">magic</a> temperament, because five of its major thirds are equivalent to one of its <em>twelfths</em>.<br /> | ||
<br /> | <br /> | ||
For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is <a class="wiki_link" href="/31edo">31 equal temperament</a>. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; <a class="wiki_link" href="/41edo">41 equal temperament</a> more closely matches it.<br /> | For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is <a class="wiki_link" href="/31edo">31 equal temperament</a>. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; <a class="wiki_link" href="/41edo">41 equal temperament</a> more closely matches it.<br /> | ||
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<td>126.326<br /> | <td>126.326<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Negri<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>189.474<br /> | <td>189.474<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Deutone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 188: | Line 188: | ||
<td>252.632<br /> | <td>252.632<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Godzilla<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 204: | Line 204: | ||
<td>378.947<br /> | <td>378.947<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Magic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 212: | Line 212: | ||
<td>442.105<br /> | <td>442.105<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Sensi<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>568.421<br /> | <td>568.421<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Triton<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 236: | Line 236: | ||
<td>631.579<br /> | <td>631.579<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Triton<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 252: | Line 252: | ||
<td>757.895<br /> | <td>757.895<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Sensi<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 260: | Line 260: | ||
<td>821.053<br /> | <td>821.053<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Magic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 268: | Line 268: | ||
<td>884.211<br /> | <td>884.211<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Kleismic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 276: | Line 276: | ||
<td>947.368<br /> | <td>947.368<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Godzilla<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 284: | Line 284: | ||
<td>1010.53<br /> | <td>1010.53<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Deutone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 292: | Line 292: | ||
<td>1073.68<br /> | <td>1073.68<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Negri<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||