4L 3s: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 529852766 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 540552366 - 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>2015-02-10 23:47:54 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>540552366</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of [[4edo]], 300¢) to 2\7edo (two degrees of [[7edo]], or approx. 342.857¢). The spectrum looks like this: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of [[4edo]], 300¢) to 2\7edo (two degrees of [[7edo]], or approx. 342.857¢). The spectrum looks like this: | ||
||||||||||||||~ Generator ||~ | ||||||||||||||~ Generator ||~ Tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments || | ||
|| 1\4 || || || || || || || | || 1\4 || || || || || || || 1 0 1 || 300.000 || 600.000 || 900.000 || 0.000 ||= || | ||
|| || || || || || || 8\31 || | || || || || || || || 8\31 || 7 1 7 || 309.677 || 619.355 || 929.023 || 38.71 ||= Myna is around here || | ||
|| || || || || || 7\27 || || | || || || || || || 7\27 || || 6 1 6 || 311.111 || 622.222 || 933.333 || 44.444 ||= || | ||
|| || || || || 6\23 || || || | || || || || || 6\23 || || || 5 1 5 || 313.043 || 626.087 || 939.13 || 52.174 ||= || | ||
|| || || || 5\19 || || || || | || || || || 5\19 || || || || 4 1 4 || 315.789 || 631.579 || 947.368 || 63.158 ||= L/s = 4 || | ||
|| || || || || 9\34 || || || | || || || || || 9\34 || || || 7 2 7 || 317.647 || 634.294 || 951.941 || 70.588 ||= Hanson/Keemun is around here || | ||
|| || || | || || || || || || || || 3.03 1 3,03 || 319.8525 || 639.705 || 959.558 || 79.410 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> || | ||
|| || || || 7\26 || || || || | || || || 4\15 || || || || || 3 1 3 || 320.000 || 640.000 || 960.000 || 80.000 ||= L/s = 3 || | ||
|| || 3\11 || || || || || || | || || || || || || || || 2.97 1 2.97 || 320.148 || 640.297 || 960.445 || 80.593 || <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> || | ||
|| || || || 7\26 || || || || 5 2 5 || 323.077 || 646.154 || 969.231 || 92.308 ||= Orgone is around here || | |||
|| || 3\11 || || || || || || 2 1 2 || 327.273 || 654.545 || 981.818 || 109.091 ||= Boundary of propriety (generators | |||
larger than this are proper) || | larger than this are proper) || | ||
|| || || || 8\29 || || || || | || || || || 8\29 || || || || 5 3 5 || 331.034 || 662.069 || 993.013 || 124.138 ||= || | ||
|| || || || || || 21\76 || || 13 8 | || || || || || || 21\76 || || 13 8 13 || 331.579 || 663.158 || 994.739 || 126.316 ||= || | ||
|| || || || || || || 34\123 || 21 13 | || || || || || || || 34\123 || 21 13 21 || 331.707 || 663.415 || 995.122 || 126.829 ||= Unnamed golden temperament || | ||
|| || || || || 13\47 || || || | || || || || || 13\47 || || || 8 5 8 || 331.915 || 663.83 || 995.745 || 127.66 ||= || | ||
|| || || 5\18 || || || || || | || || || 5\18 || || || || || 3 2 3 || 333.333 || 666.667 || 1000.000 || 133.333 ||= Optimum rank range (L/s=3/2) || | ||
|| || || || 7\25 || || || || | || || || || 7\25 || || || || 4 3 4 || 336.000 || 672.000 || 1008.000 || 144.000 ||= || | ||
|| || || || || 9\32 || || || | || || || || || 9\32 || || || 5 4 5 || 337.5 || 675.000 || 1012.500 || 150.000 ||= Sixix || | ||
|| || || || || || 11\39 || || | || || || || || || 11\39 || || 6 5 6 || 338.462 || 676.923 || 1015.385 || 153.846 ||= Sixix || | ||
|| || || || || || || 13\46 || | || || || || || || || 13\46 || 7 6 7 || 339.130 || 678.261 || 1017.391 || 156.522 ||= (17/14)^3=9/5 || | ||
|| 2\7 || || || || || || || | || 2\7 || || || || || || || 1 1 1 || 342.857 || 685.714 || 1028.571 || 171.429 ||= || | ||
There are two notable harmonic entropy minima: [[Kleismic family|hanson/keemun]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling temperaments|myna]], in which the generator is also 6/5 but now **10** of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).</pre></div> | There are two notable harmonic entropy minima: [[Kleismic family|hanson/keemun]], in which the generator is 6/5 and 6 of them make a 3/1, and [[Starling temperaments|myna]], in which the generator is also 6/5 but now **10** of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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<th colspan="7">Generator<br /> | <th colspan="7">Generator<br /> | ||
</th> | </th> | ||
<th> | <th>Tetrachord<br /> | ||
</th> | </th> | ||
<th>g in cents<br /> | <th>g in cents<br /> | ||
| Line 65: | Line 67: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>1 0 1<br /> | ||
</td> | </td> | ||
<td>300.000<br /> | <td>300.000<br /> | ||
| Line 93: | Line 95: | ||
<td>8\31<br /> | <td>8\31<br /> | ||
</td> | </td> | ||
<td> | <td>7 1 7<br /> | ||
</td> | </td> | ||
<td>309.677<br /> | <td>309.677<br /> | ||
| Line 121: | Line 123: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>6 1 6<br /> | ||
</td> | </td> | ||
<td>311.111<br /> | <td>311.111<br /> | ||
| Line 149: | Line 151: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>5 1 5<br /> | ||
</td> | </td> | ||
<td>313.043<br /> | <td>313.043<br /> | ||
| Line 177: | Line 179: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>4 1 4<br /> | ||
</td> | </td> | ||
<td>315.789<br /> | <td>315.789<br /> | ||
| Line 205: | Line 207: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>7 2 7<br /> | ||
</td> | </td> | ||
<td>317.647<br /> | <td>317.647<br /> | ||
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</td> | </td> | ||
<td style="text-align: center;">Hanson/Keemun is around here<br /> | <td style="text-align: center;">Hanson/Keemun is around here<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>3.03 1 3,03<br /> | |||
</td> | |||
<td>319.8525<br /> | |||
</td> | |||
<td>639.705<br /> | |||
</td> | |||
<td>959.558<br /> | |||
</td> | |||
<td>79.410<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> | ||
| Line 233: | Line 263: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>3 1 3<br /> | ||
</td> | </td> | ||
<td>320.000<br /> | <td>320.000<br /> | ||
| Line 244: | Line 274: | ||
</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> | |||
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</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>2.97 1 2.97<br /> | |||
</td> | |||
<td>320.148<br /> | |||
</td> | |||
<td>640.297<br /> | |||
</td> | |||
<td>960.445<br /> | |||
</td> | |||
<td>80.593<br /> | |||
</td> | |||
<td><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> | <td>5 2 5<br /> | ||
</td> | </td> | ||
<td>323.077<br /> | <td>323.077<br /> | ||
| Line 289: | Line 347: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>2 1 2<br /> | ||
</td> | </td> | ||
<td>327.273<br /> | <td>327.273<br /> | ||
| Line 318: | Line 376: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>5 3 5<br /> | ||
</td> | </td> | ||
<td>331.034<br /> | <td>331.034<br /> | ||
| Line 346: | Line 404: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>13 8 | <td>13 8 13<br /> | ||
</td> | </td> | ||
<td>331.579<br /> | <td>331.579<br /> | ||
| Line 374: | Line 432: | ||
<td>34\123<br /> | <td>34\123<br /> | ||
</td> | </td> | ||
<td>21 13 | <td>21 13 21<br /> | ||
</td> | </td> | ||
<td>331.707<br /> | <td>331.707<br /> | ||
| Line 402: | Line 460: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>8 5 8<br /> | ||
</td> | </td> | ||
<td>331.915<br /> | <td>331.915<br /> | ||
| Line 430: | Line 488: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>3 2 3<br /> | ||
</td> | </td> | ||
<td>333.333<br /> | <td>333.333<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>4 3 4<br /> | ||
</td> | </td> | ||
<td>336.000<br /> | <td>336.000<br /> | ||
| Line 486: | Line 544: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>5 4 5<br /> | ||
</td> | </td> | ||
<td>337.5<br /> | <td>337.5<br /> | ||
| Line 514: | Line 572: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>6 5 6<br /> | ||
</td> | </td> | ||
<td>338.462<br /> | <td>338.462<br /> | ||
| Line 542: | Line 600: | ||
<td>13\46<br /> | <td>13\46<br /> | ||
</td> | </td> | ||
<td> | <td>7 6 7<br /> | ||
</td> | </td> | ||
<td>339.130<br /> | <td>339.130<br /> | ||
| Line 570: | Line 628: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>1 1 1<br /> | ||
</td> | </td> | ||
<td>342.857<br /> | <td>342.857<br /> | ||