4L 5s: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 532835698 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 540651568 - 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:JosephRuhf|JosephRuhf]] and made on <tt> | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-11 15:10:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>540651568</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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||||||||||~ Generator ||~ Scale ||~ Generator in cents ||~ Comments || | ||||||||||~ Generator ||~ Scale ||~ Generator in cents ||~ Comments || | ||
|| 2\9 || || || || || 1 1 1 1 1 1 1 1 1 || 266.667 ||= || | || 2\9 || || || || ||= 1 1 1 1 1 1 1 1 1 || 266.667 ||= || | ||
|| || || || || 9\40 || 5 4 5 4 5 4 5 4 | || || || || || 9\40 ||= 4 5 4 5 4 5 4 5 4 || 270 || || | ||
|| || || || 7\31 || || 3 4 3 4 3 4 3 4 3 || 270.968 ||= || | || || || || 7\31 || ||= 3 4 3 4 3 4 3 4 3 || 270.968 ||= || | ||
|| || || || || 12\53 || 5 7 5 7 5 7 5 7 5 || 271.698 ||= Orwell is around here || | || || || || || 12\53 ||= 5 7 5 7 5 7 5 7 5 || 271.698 ||= Orwell is around here || | ||
|| || || 5\22 || || || 2 3 2 3 2 3 2 3 2 || 272.727 ||= Optimum rank range (L/s=3/2) orwell || | || || || 5\22 || || ||= 2 3 2 3 2 3 2 3 2 || 272.727 ||= Optimum rank range (L/s=3/2) orwell || | ||
|| || || || || 13\57 || 5 8 5 8 5 8 5 8 5 || 273.684 ||= Golden orwell (bad tuning) || | || || || || || 13\57 ||= 5 8 5 8 5 8 5 8 5 || 273.684 ||= Golden orwell (bad tuning) || | ||
|| || || || 8\35 || || 3 5 3 5 3 5 3 5 3 || 274.286 ||= || | || || || || 8\35 || ||= 3 5 3 5 3 5 3 5 3 || 274.286 ||= || | ||
|| || || || || 11\48 || 4 7 4 7 4 7 4 7 4 || 275 || || | || || || || || 11\48 ||= 4 7 4 7 4 7 4 7 4 || 275 || || | ||
|| || 3\13 || || || || 1 2 1 2 1 2 1 2 1 || 276.923 ||= Boundary of propriety: | || || 3\13 || || || ||= 1 2 1 2 1 2 1 2 1 || 276.923 ||= Boundary of propriety: | ||
generators smaller than this are proper || | generators smaller than this are proper || | ||
|| || || || || 10\43 || 3 7 3 7 3 7 3 7 3 || 279.07 || || | || || || || || 10\43 ||= 3 7 3 7 3 7 3 7 3 || 279.07 || || | ||
|| || || || 7\30 || || 2 5 2 5 2 5 2 5 2 || 280.000 ||= || | || || || || 7\30 || ||= 2 5 2 5 2 5 2 5 2 || 280.000 ||= || | ||
|| || || || || 11\47 || 3 8 3 8 3 8 3 8 3 || 280.851 || || | || || || || || 11\47 ||= 3 8 3 8 3 8 3 8 3 || 280.851 || || | ||
|| || || 4\17 || || || 1 3 1 3 1 3 1 3 1 || 282.353 ||= L/s = 3 || | || || || || || ||= 1 2.97 1 2.97 1 2.97 1 2.97 1 || 282.238 ||= <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> || | ||
|| || || || || 9\38 || 2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span> || 284.2105 || || | || || || 4\17 || || ||= 1 3 1 3 1 3 1 3 1 || 282.353 ||= L/s = 3 || | ||
|| || || || 5\21 || || 1 4 1 4 1 4 1 4 1 || 285.714 ||= L/s = 4 || | || || || || || ||= 1 3.03 1 3.03 1 3.03 1 3.03 1 || 282.468 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> || | ||
|| || || || || 6\25 || 1 5 1 5 1 5 1 5 1 || 288 || || | || || || || || 9\38 ||= 2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span> || 284.2105 || || | ||
|| 1\4 || || || || || 0 1 0 1 0 1 0 1 0 || 300.000 ||= || | || || || || 5\21 || ||= 1 4 1 4 1 4 1 4 1 || 285.714 ||= L/s = 4 || | ||
|| || || || || 6\25 ||= 1 5 1 5 1 5 1 5 1 || 288 || || | |||
|| 1\4 || || || || ||= 0 1 0 1 0 1 0 1 0 || 300.000 ||= || | |||
Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.</pre></div> | Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.</pre></div> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>1 1 1 1 1 1 1 1 1<br /> | <td style="text-align: center;">1 1 1 1 1 1 1 1 1<br /> | ||
</td> | </td> | ||
<td>266.667<br /> | <td>266.667<br /> | ||
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<td>9\40<br /> | <td>9\40<br /> | ||
</td> | </td> | ||
<td>5 4 5 4 5 4 5 4 | <td style="text-align: center;">4 5 4 5 4 5 4 5 4<br /> | ||
</td> | </td> | ||
<td>270<br /> | <td>270<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>3 4 3 4 3 4 3 4 3<br /> | <td style="text-align: center;">3 4 3 4 3 4 3 4 3<br /> | ||
</td> | </td> | ||
<td>270.968<br /> | <td>270.968<br /> | ||
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<td>12\53<br /> | <td>12\53<br /> | ||
</td> | </td> | ||
<td>5 7 5 7 5 7 5 7 5<br /> | <td style="text-align: center;">5 7 5 7 5 7 5 7 5<br /> | ||
</td> | </td> | ||
<td>271.698<br /> | <td>271.698<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>2 3 2 3 2 3 2 3 2<br /> | <td style="text-align: center;">2 3 2 3 2 3 2 3 2<br /> | ||
</td> | </td> | ||
<td>272.727<br /> | <td>272.727<br /> | ||
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<td>13\57<br /> | <td>13\57<br /> | ||
</td> | </td> | ||
<td>5 8 5 8 5 8 5 8 5<br /> | <td style="text-align: center;">5 8 5 8 5 8 5 8 5<br /> | ||
</td> | </td> | ||
<td>273.684<br /> | <td>273.684<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>3 5 3 5 3 5 3 5 3<br /> | <td style="text-align: center;">3 5 3 5 3 5 3 5 3<br /> | ||
</td> | </td> | ||
<td>274.286<br /> | <td>274.286<br /> | ||
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<td>11\48<br /> | <td>11\48<br /> | ||
</td> | </td> | ||
<td>4 7 4 7 4 7 4 7 4<br /> | <td style="text-align: center;">4 7 4 7 4 7 4 7 4<br /> | ||
</td> | </td> | ||
<td>275<br /> | <td>275<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>1 2 1 2 1 2 1 2 1<br /> | <td style="text-align: center;">1 2 1 2 1 2 1 2 1<br /> | ||
</td> | </td> | ||
<td>276.923<br /> | <td>276.923<br /> | ||
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<td>10\43<br /> | <td>10\43<br /> | ||
</td> | </td> | ||
<td>3 7 3 7 3 7 3 7 3<br /> | <td style="text-align: center;">3 7 3 7 3 7 3 7 3<br /> | ||
</td> | </td> | ||
<td>279.07<br /> | <td>279.07<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>2 5 2 5 2 5 2 5 2<br /> | <td style="text-align: center;">2 5 2 5 2 5 2 5 2<br /> | ||
</td> | </td> | ||
<td>280.000<br /> | <td>280.000<br /> | ||
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<td>11\47<br /> | <td>11\47<br /> | ||
</td> | </td> | ||
<td>3 8 3 8 3 8 3 8 3<br /> | <td style="text-align: center;">3 8 3 8 3 8 3 8 3<br /> | ||
</td> | </td> | ||
<td>280.851<br /> | <td>280.851<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: center;">1 2.97 1 2.97 1 2.97 1 2.97 1<br /> | |||
</td> | |||
<td>282.238<br /> | |||
</td> | |||
<td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>1 3 1 3 1 3 1 3 1<br /> | <td style="text-align: center;">1 3 1 3 1 3 1 3 1<br /> | ||
</td> | </td> | ||
<td>282.353<br /> | <td>282.353<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">L/s = 3<br /> | <td style="text-align: center;">L/s = 3<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: center;">1 3.03 1 3.03 1 3.03 1 3.03 1<br /> | |||
</td> | |||
<td>282.468<br /> | |||
</td> | |||
<td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>9\38<br /> | <td>9\38<br /> | ||
</td> | </td> | ||
<td>2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span><br /> | <td style="text-align: center;">2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span><br /> | ||
</td> | </td> | ||
<td>284.2105<br /> | <td>284.2105<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>1 4 1 4 1 4 1 4 1<br /> | <td style="text-align: center;">1 4 1 4 1 4 1 4 1<br /> | ||
</td> | </td> | ||
<td>285.714<br /> | <td>285.714<br /> | ||
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<td>6\25<br /> | <td>6\25<br /> | ||
</td> | </td> | ||
<td>1 5 1 5 1 5 1 5 1<br /> | <td style="text-align: center;">1 5 1 5 1 5 1 5 1<br /> | ||
</td> | </td> | ||
<td>288<br /> | <td>288<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>0 1 0 1 0 1 0 1 0<br /> | <td style="text-align: center;">0 1 0 1 0 1 0 1 0<br /> | ||
</td> | </td> | ||
<td>300.000<br /> | <td>300.000<br /> |