5L 4s: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 385899584 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 399960134 - 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:keenanpepper|keenanpepper]] and made on <tt>2013-01-20 16:22:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>399960134</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">The familiar harmonic entropy minimum with this MOS pattern is [[meantone family#Godzilla|godzilla]], in which a generator is [[8_7|8/7]] or [[7_6|7/6]] (tempered to be the same interval, or even 37/32 if you like) so two of them make a [[4_3|4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[Chromatic pairs#semaphore|semaphore]], there is also a weird scale called "[[pseudo-semaphore]]", in which two different flavors of [[3_2|3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. | <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">The familiar harmonic entropy minimum with this MOS pattern is [[meantone family#Godzilla|godzilla]], in which a generator is [[8_7|8/7]] or [[7_6|7/6]] (tempered to be the same interval, or even 37/32 if you like) so two of them make a [[4_3|4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[Chromatic pairs#semaphore|semaphore]], there is also a weird scale called "[[pseudo-semaphore]]", in which two different flavors of [[3_2|3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. | ||
||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments | ||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments || | ||
|| 1\5 || || || || || || || || || || || 240 | || 1\5 || || || || || || || || || || || 240 ||= || | ||
|| || || || || || || || || || || 12\59 || 244.068 ||= Pseudo-semaphore is around here | || || || || || || || || || || || 12\59 || 244.068 ||= Pseudo-semaphore is around here || | ||
|| || || || || || || || || || 11\54 || || 244.444 | || || || || || || || || || || 11\54 || || 244.444 ||= || | ||
|| || || || || || || || || 10\49 || || || 244.898 | || || || || || || || || || 10\49 || || || 244.898 ||= || | ||
|| || || || || || || || 9\44 || || || || 245.455 | || || || || || || || || 9\44 || || || || 245.455 ||= || | ||
|| || || || || || || 8\39 || || || || || 246.154 | || || || || || || || 8\39 || || || || || 246.154 ||= || | ||
|| || || || || || 7\34 || || || || || || 247.059 | || || || || || || 7\34 || || || || || || 247.059 ||= || | ||
|| || || || || 6\29 || || || || || || || 248.276 | || || || || || 6\29 || || || || || || || 248.276 ||= || | ||
|| || || || || || 11\53 || || || || || || 249.057 ||= Semaphore is around here | || || || || || || 11\53 || || || || || || 249.057 ||= Semaphore is around here || | ||
|| || || || 5\24 || || || || || || || || 250 | || || || || 5\24 || || || || || || || || 250 ||= L/s = 4 || | ||
|| || || 4\19 || || || || || || || || || 252.632 ||= Godzilla is around here | |||
|| || || 4\19 || || || || || || || || || 252.632 ||= Godzilla is around here | L/s = 3 || | ||
|| || 3\14 || || || || || || || || || || 257.143 ||= Boundary of propriety (generators | || || 3\14 || || || || || || || || || || 257.143 ||= Boundary of propriety (generators | ||
larger than this are proper) | larger than this are proper) || | ||
|| || || || 8\37 || || || || || || || || 259.459 | || || || || 8\37 || || || || || || || || 259.459 ||= || | ||
|| || || || || || 21\97 || || || || || || 259.794 | || || || || || || 21\97 || || || || || || 259.794 ||= || | ||
|| || || || || || || || 55\254 || || || || 259.843 | || || || || || || || || 55\254 || || || || 259.843 ||= || | ||
|| || || || || || || || || || 144\665 || || 259.850 | || || || || || || || || || || 144\665 || || 259.850 ||= || | ||
|| || || || || || || || || || || 233\1076 || 259.851 ||= Golden [[superpelog]] | || || || || || || || || || || || 233\1076 || 259.851 ||= Golden [[superpelog]] || | ||
|| || || || || || || || || 89\411 || || || 259.854 | || || || || || || || || || 89\411 || || || 259.854 ||= || | ||
|| || || || || || || 34\157 || || || || || 259.873 | || || || || || || || 34\157 || || || || || 259.873 ||= || | ||
|| || || || || 13\60 || || || || || || || 260 | || || || || || 13\60 || || || || || || || 260 ||= || | ||
|| || || 5\23 || || || || || || || || || 260.870 ||= Optimum rank range (L/s=3/2) superpelog | || || || 5\23 || || || || || || || || || 260.870 ||= Optimum rank range (L/s=3/2) superpelog || | ||
|| || || || 7\32 || || || || || || || || 262.5 | || || || || 7\32 || || || || || || || || 262.5 ||= || | ||
|| || || || || 9\41 || || || || || || || 263.415 | || || || || || 9\41 || || || || || || || 263.415 ||= || | ||
|| || || || || || 11\50 || || || || || || 264 | || || || || || || 11\50 || || || || || || 264 ||= || | ||
|| || || || || || || 13\59 || || || || || 264.407 | || || || || || || || 13\59 || || || || || 264.407 ||= || | ||
|| || || || || || || || 15\68 || || || || 264.706 | || || || || || || || || 15\68 || || || || 264.706 ||= || | ||
|| || || || || || || || || 17\77 || || || 264.935 | || || || || || || || || || 17\77 || || || 264.935 ||= || | ||
|| || || || || || || || || || 19\86 || || 265.116 | || || || || || || || || || || 19\86 || || 265.116 ||= || | ||
|| || || || || || || || || || || 21\95 || 265.263 | || || || || || || || || || || || 21\95 || 265.263 ||= || | ||
|| 2\9 || || || || || || || || || || || 266.667 | || 2\9 || || || || || || || || || || || 266.667 ||= ||</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>5L 4s</title></head><body>The familiar harmonic entropy minimum with this MOS pattern is <a class="wiki_link" href="/meantone%20family#Godzilla">godzilla</a>, in which a generator is <a class="wiki_link" href="/8_7">8/7</a> or <a class="wiki_link" href="/7_6">7/6</a> (tempered to be the same interval, or even 37/32 if you like) so two of them make a <a class="wiki_link" href="/4_3">4/3</a>. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament <a class="wiki_link" href="/Chromatic%20pairs#semaphore">semaphore</a>, there is also a weird scale called &quot;<a class="wiki_link" href="/pseudo-semaphore">pseudo-semaphore</a>&quot;, in which two different flavors of <a class="wiki_link" href="/3_2">3/2</a> exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2.<br /> | <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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>5L 4s</title></head><body>The familiar harmonic entropy minimum with this MOS pattern is <a class="wiki_link" href="/meantone%20family#Godzilla">godzilla</a>, in which a generator is <a class="wiki_link" href="/8_7">8/7</a> or <a class="wiki_link" href="/7_6">7/6</a> (tempered to be the same interval, or even 37/32 if you like) so two of them make a <a class="wiki_link" href="/4_3">4/3</a>. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament <a class="wiki_link" href="/Chromatic%20pairs#semaphore">semaphore</a>, there is also a weird scale called &quot;<a class="wiki_link" href="/pseudo-semaphore">pseudo-semaphore</a>&quot;, in which two different flavors of <a class="wiki_link" href="/3_2">3/2</a> exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2.<br /> | ||
| Line 52: | Line 51: | ||
</th> | </th> | ||
<th>Comments<br /> | <th>Comments<br /> | ||
</th> | </th> | ||
</tr> | </tr> | ||
| Line 80: | Line 77: | ||
</td> | </td> | ||
<td>240<br /> | <td>240<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 112: | Line 107: | ||
</td> | </td> | ||
<td style="text-align: center;">Pseudo-semaphore is around here<br /> | <td style="text-align: center;">Pseudo-semaphore is around here<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 140: | Line 133: | ||
</td> | </td> | ||
<td>244.444<br /> | <td>244.444<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 170: | Line 161: | ||
</td> | </td> | ||
<td>244.898<br /> | <td>244.898<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 200: | Line 189: | ||
</td> | </td> | ||
<td>245.455<br /> | <td>245.455<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 230: | Line 217: | ||
</td> | </td> | ||
<td>246.154<br /> | <td>246.154<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 260: | Line 245: | ||
</td> | </td> | ||
<td>247.059<br /> | <td>247.059<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 290: | Line 273: | ||
</td> | </td> | ||
<td>248.276<br /> | <td>248.276<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 322: | Line 303: | ||
</td> | </td> | ||
<td style="text-align: center;">Semaphore is around here<br /> | <td style="text-align: center;">Semaphore is around here<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 351: | Line 330: | ||
<td>250<br /> | <td>250<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">L/s = 4<br /> | |||
<td style="text-align: center;">L/s=4 | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 383: | Line 359: | ||
</td> | </td> | ||
<td style="text-align: center;">Godzilla is around here<br /> | <td style="text-align: center;">Godzilla is around here<br /> | ||
L/s = 3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 415: | Line 389: | ||
<td style="text-align: center;">Boundary of propriety (generators<br /> | <td style="text-align: center;">Boundary of propriety (generators<br /> | ||
larger than this are proper)<br /> | larger than this are proper)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 443: | Line 415: | ||
</td> | </td> | ||
<td>259.459<br /> | <td>259.459<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 473: | Line 443: | ||
</td> | </td> | ||
<td>259.794<br /> | <td>259.794<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 503: | Line 471: | ||
</td> | </td> | ||
<td>259.843<br /> | <td>259.843<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 533: | Line 499: | ||
</td> | </td> | ||
<td>259.850<br /> | <td>259.850<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 565: | Line 529: | ||
</td> | </td> | ||
<td style="text-align: center;">Golden <a class="wiki_link" href="/superpelog">superpelog</a><br /> | <td style="text-align: center;">Golden <a class="wiki_link" href="/superpelog">superpelog</a><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 593: | Line 555: | ||
</td> | </td> | ||
<td>259.854<br /> | <td>259.854<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 623: | Line 583: | ||
</td> | </td> | ||
<td>259.873<br /> | <td>259.873<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 653: | Line 611: | ||
</td> | </td> | ||
<td>260<br /> | <td>260<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 685: | Line 641: | ||
</td> | </td> | ||
<td style="text-align: center;">Optimum rank range (L/s=3/2) superpelog<br /> | <td style="text-align: center;">Optimum rank range (L/s=3/2) superpelog<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 713: | Line 667: | ||
</td> | </td> | ||
<td>262.5<br /> | <td>262.5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 743: | Line 695: | ||
</td> | </td> | ||
<td>263.415<br /> | <td>263.415<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 773: | Line 723: | ||
</td> | </td> | ||
<td>264<br /> | <td>264<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 803: | Line 751: | ||
</td> | </td> | ||
<td>264.407<br /> | <td>264.407<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 833: | Line 779: | ||
</td> | </td> | ||
<td>264.706<br /> | <td>264.706<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 863: | Line 807: | ||
</td> | </td> | ||
<td>264.935<br /> | <td>264.935<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 893: | Line 835: | ||
</td> | </td> | ||
<td>265.116<br /> | <td>265.116<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 923: | Line 863: | ||
</td> | </td> | ||
<td>265.263<br /> | <td>265.263<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 953: | Line 891: | ||
</td> | </td> | ||
<td>266.667<br /> | <td>266.667<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||