Shruti: Difference between revisions
Wikispaces>diagonalia **Imported revision 603073208 - Original comment: ** |
Wikispaces>diagonalia **Imported revision 603074006 - 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:diagonalia|diagonalia]] and made on <tt>2017-01-04 10: | : This revision was by author [[User:diagonalia|diagonalia]] and made on <tt>2017-01-04 10:48:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>603074006</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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==Regular temperaments of the full-status shrutis== | ==Regular temperaments of the full-status shrutis== | ||
**Note: generators in italics will generate a | **Note: generators in italics will generate a 19 or 22 tone diatonic set which is too weakly tonal for serious practice** | ||
==== ==== | ==== ==== | ||
=Underlying= | =Underlying= | ||
||~ Large-small numbers ||~ Status ||~ Generator range ||~ <span style="background-color: #ffffff; color: #000000;">Midpoint</span> ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step || | ||~ Large-small numbers ||~ Status ||~ Generator range ||~ <span style="background-color: #ffffff; color: #000000;">Midpoint</span> ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step || | ||
|| | || 1L18s || "half" || 18\19 < g < 1 || g = 37\38 || g = //19\20, 20\21, 21\22// || 18g-17 || 1-g || | ||
|| | || 2L17s || full || 9\19 < g < 1\2 || g = 37\76 || g = //10\21//, 11\23, 12\25 || 17g-8 || 1-2g || | ||
|| | || 3L16s || full || 6\19 < g < 1\3 || g = 37\114 || g = //7\22//, 8\25, 10\31 || 16g-5 || 1-3g || | ||
|| | || 4L15s || full || 14\19 < g < 3\4 || g = 113\152 || g = 17\23, 20\27, 23\31 || 15g-11 || 3-4g || | ||
|| | || 5L14s || full || 15\19 < g < 4\5 || g = 151\190 || g = 19\24, 23\29, 27\34 || 14g-11 || 4-5g || | ||
|| | || 6L13s || full || 3\19 < g < 1\6 || g = 37\228 || g = 4\25, 5\31, 6/37 || 13g-2 || 1-6g || | ||
|| | || 7L12s || full || 8\19 < g < 3\7 || g = 113\266 || g = 11\26, 14\33, 17\40 || 12g-5 || 3-7g || | ||
|| | || 8L11s || full || 7\19 < g < 3\8 || g = 113\304 || g = 10\27, 13\35, 16\43 || 11g-4 || 3-8g || | ||
|| | || 9L10s || full || 2\19 < g < 1\9 || g = 37\342 || g = 3\28, 4\37, 5\46 || 10g-1 || 1-9g || | ||
|| | || 10L9s || full || 17\19 < g < 9\10 || g = 341\380 || g = 26\29, 35\39, 44\49 || 9g-8 || 9-10g || | ||
|| | || 11L8s || full || 12\19 < g < 7\11 || g = 265\418 || g = 19\30, 26\41, 33\52 || 8g-5 || 7-11g || | ||
|| | || 12L7s || full || 11\19 < g < 7\12 || g = 265\456 || g = 18\31, 25\43, 32\55 || 7g-4 || 7-12g || | ||
|| | || 13L6s || full || 16\19 < g < 11\13 || g = 417\494 || g = 27\32, 38\45, 49\58 || 6g-5 || 11-13g || | ||
|| | || 14L5s || full || 4\19 < g < 3\14 || g = 113\532 || g = 7\33, 10\47, 13\61 || 5g-1 || 3-14g || | ||
|| | || 15L4s || full || 5\19 < g < 4\15 || g = 151\570 || g = 9\34, 13\49, 17\64 || 4g-1 || 4-15g || | ||
|| | || 16L3s || full || 13\19 < g < 11\16 || g = 417\608 || g = 24\35, 35\51, 46\67 || 3g-2 || 11-16g || | ||
|| | || 17L2s || full || 10\19 < g < 9\17 || g = 341\646 || g = 19\36, 28\53, 37\70 || 2g-1 || 9-17g || | ||
|| | || 18L1s || "half" || 1\19 < g < 1\18 || g = 37\684 || g = 2\37, 3\55, 4\73 || g || 1-18g || | ||
=Quoted= | =Quoted= | ||
||~ Large-small numbers ||~ Status ||~ Generator range ||~ <span style="background-color: #ffffff; color: #000000;">Midpoint</span> ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step || | ||~ Large-small numbers ||~ Status ||~ Generator range ||~ <span style="background-color: #ffffff; color: #000000;">Midpoint</span> ||~ Boundaries of propriety, maximum expressiveness, diatonicity ||~ Large step ||~ Small step || | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Regular temperaments of the full-status shrutis"></a><!-- ws:end:WikiTextHeadingRule:0 -->Regular temperaments of the full-status shrutis</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Regular temperaments of the full-status shrutis"></a><!-- ws:end:WikiTextHeadingRule:0 -->Regular temperaments of the full-status shrutis</h2> | ||
<strong>Note: generators in italics will generate a | <strong>Note: generators in italics will generate a 19 or 22 tone diatonic set which is too weakly tonal for serious practice</strong><br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h4&gt; --><h4 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h4> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h4&gt; --><h4 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h4> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Underlying"></a><!-- ws:end:WikiTextHeadingRule:4 -->Underlying</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Underlying"></a><!-- ws:end:WikiTextHeadingRule:4 -->Underlying</h1> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>1L18s<br /> | ||
</td> | </td> | ||
<td>&quot;half&quot;<br /> | <td>&quot;half&quot;<br /> | ||
</td> | </td> | ||
<td>19 | <td>18\19 &lt; g &lt; 1<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 37\38<br /> | ||
</td> | </td> | ||
<td>g = <em>20\21, 21\22 | <td>g = <em>19\20, 20\21, 21\22</em><br /> | ||
</td> | </td> | ||
<td> | <td>18g-17<br /> | ||
</td> | </td> | ||
<td>1-g<br /> | <td>1-g<br /> | ||
| Line 222: | Line 221: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>2L17s<br /> | ||
</td> | </td> | ||
<td> | <td>full<br /> | ||
</td> | </td> | ||
<td>9\ | <td>9\19 &lt; g &lt; 1\2<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 37\76<br /> | ||
</td> | </td> | ||
<td>g = <em>10\ | <td>g = <em>10\21</em>, 11\23, 12\25<br /> | ||
</td> | </td> | ||
<td> | <td>17g-8<br /> | ||
</td> | </td> | ||
<td>1 | <td>1-2g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>3L16s<br /> | ||
</td> | </td> | ||
<td>full<br /> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>6\19 &lt; g &lt; 1\3<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 37\114<br /> | ||
</td> | </td> | ||
<td>g = <em> | <td>g = <em>7\22</em>, 8\25, 10\31<br /> | ||
</td> | </td> | ||
<td> | <td>16g-5<br /> | ||
</td> | </td> | ||
<td> | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>4L15s<br /> | ||
</td> | </td> | ||
<td> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>14\19 &lt; g &lt; 3\4<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 113\152<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 17\23, 20\27, 23\31<br /> | ||
</td> | </td> | ||
<td> | <td>15g-11<br /> | ||
</td> | </td> | ||
<td> | <td>3-4g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>5L14s<br /> | ||
</td> | </td> | ||
<td>full<br /> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>15\19 &lt; g &lt; 4\5<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 151\190<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 19\24, 23\29, 27\34<br /> | ||
</td> | </td> | ||
<td> | <td>14g-11<br /> | ||
</td> | </td> | ||
<td> | <td>4-5g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>6L13s<br /> | ||
</td> | </td> | ||
<td> | <td>full<br /> | ||
</td> | </td> | ||
<td>3\ | <td>3\19 &lt; g &lt; 1\6<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 37\228<br /> | ||
</td> | </td> | ||
<td>g = 4\ | <td>g = 4\25, 5\31, 6/37<br /> | ||
</td> | </td> | ||
<td> | <td>13g-2<br /> | ||
</td> | </td> | ||
<td>1 | <td>1-6g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>7L12s<br /> | ||
</td> | </td> | ||
<td>full<br /> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>8\19 &lt; g &lt; 3\7<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 113\266<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 11\26, 14\33, 17\40<br /> | ||
</td> | </td> | ||
<td> | <td>12g-5<br /> | ||
</td> | </td> | ||
<td> | <td>3-7g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>8L11s<br /> | ||
</td> | </td> | ||
<td> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>7\19 &lt; g &lt; 3\8<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 113\304<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 10\27, 13\35, 16\43<br /> | ||
</td> | </td> | ||
<td> | <td>11g-4<br /> | ||
</td> | </td> | ||
<td> | <td>3-8g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>9L10s<br /> | ||
</td> | </td> | ||
<td>full<br /> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>2\19 &lt; g &lt; 1\9<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 37\342<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 3\28, 4\37, 5\46<br /> | ||
</td> | </td> | ||
<td> | <td>10g-1<br /> | ||
</td> | </td> | ||
<td> | <td>1-9g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>10L9s<br /> | ||
</td> | </td> | ||
<td> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>17\19 &lt; g &lt; 9\10<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 341\380<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 26\29, 35\39, 44\49<br /> | ||
</td> | </td> | ||
<td> | <td>9g-8<br /> | ||
</td> | </td> | ||
<td> | <td>9-10g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>11L8s<br /> | ||
</td> | </td> | ||
<td>full<br /> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>12\19 &lt; g &lt; 7\11<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 265\418<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 19\30, 26\41, 33\52<br /> | ||
</td> | </td> | ||
<td> | <td>8g-5<br /> | ||
</td> | </td> | ||
<td> | <td>7-11g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>12L7s<br /> | ||
</td> | </td> | ||
<td> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>11\19 &lt; g &lt; 7\12<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 265\456<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 18\31, 25\43, 32\55<br /> | ||
</td> | </td> | ||
<td> | <td>7g-4<br /> | ||
</td> | </td> | ||
<td> | <td>7-12g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>13L6s<br /> | ||
</td> | </td> | ||
<td>full<br /> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>16\19 &lt; g &lt; 11\13<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 417\494<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 27\32, 38\45, 49\58<br /> | ||
</td> | </td> | ||
<td> | <td>6g-5<br /> | ||
</td> | </td> | ||
<td> | <td>11-13g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>14L5s<br /> | ||
</td> | </td> | ||
<td> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>4\19 &lt; g &lt; 3\14<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 113\532<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 7\33, 10\47, 13\61<br /> | ||
</td> | </td> | ||
<td> | <td>5g-1<br /> | ||
</td> | </td> | ||
<td> | <td>3-14g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>15L4s<br /> | ||
</td> | </td> | ||
<td>full<br /> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>5\19 &lt; g &lt; 4\15<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 151\570<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 9\34, 13\49, 17\64<br /> | ||
</td> | </td> | ||
<td> | <td>4g-1<br /> | ||
</td> | </td> | ||
<td> | <td>4-15g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>16L3s<br /> | ||
</td> | </td> | ||
<td> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>13\19 &lt; g &lt; 11\16<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 417\608<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 24\35, 35\51, 46\67<br /> | ||
</td> | </td> | ||
<td> | <td>3g-2<br /> | ||
</td> | </td> | ||
<td> | <td>11-16g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>17L2s<br /> | ||
</td> | </td> | ||
<td>full<br /> | <td>full<br /> | ||
</td> | </td> | ||
<td> | <td>10\19 &lt; g &lt; 9\17<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 341\646<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 19\36, 28\53, 37\70<br /> | ||
</td> | </td> | ||
<td> | <td>2g-1<br /> | ||
</td> | </td> | ||
<td> | <td>9-17g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>18L1s<br /> | ||
</td> | </td> | ||
<td>&quot;half&quot;<br /> | <td>&quot;half&quot;<br /> | ||
</td> | </td> | ||
<td>1\ | <td>1\19 &lt; g &lt; 1\18<br /> | ||
</td> | </td> | ||
<td>g = | <td>g = 37\684<br /> | ||
</td> | </td> | ||
<td>g = 2\ | <td>g = 2\37, 3\55, 4\73<br /> | ||
</td> | </td> | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>- | <td>1-18g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||