3L 6s: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 599896900 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 599920156 - 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>2016-11-20 | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-20 20:51:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599920156</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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|| 1\9 || || || || || 133.333 ||= || | || 1\9 || || || || || 133.333 ||= || | ||
From a standard diatonic point of view, an optimized (MOD)MOS pattern of 3L+6s works out to become one of the modes of the Mohajira diatonic or Rast scale extended to a minor tenth, the MOS itself being the tritetrachordal | From a standard diatonic point of view, an optimized (MOD)MOS pattern of 3L+6s works out to become one of the modes of the Mohajira diatonic or Rast scale extended to a minor tenth, the MOS itself being the tritetrachordal Rast b10 scale, the interesting property of which being that it treats a seventh as a perfect interval rather than a fifth, however far off it may be from a perfect 7/4. As a temperament, it has period ~4/3 and generator up to 1/3 of that, making a subrange of the range between its median and maximum generators represent an ~12/11 (given harmonic entropy as coarse as that of [[Mavila]], 120 cents can be an acceptable 12\11). | ||
||||||||||~ Minor Tenth ||~ Fourth ||~ | ||||||||||~ Minor Tenth ||~ Fourth ||~ Hemififth ||||||||~ <span style="display: block; text-align: center;">Generator</span> || | ||
||||||||||~ ||~ ||~ ||~ <span style="display: block; text-align: center;">Mean</span> ||~ <span style="display: block; text-align: center;">Median</span> ||~ <span style="display: block; text-align: center;">Golden</span> ||~ Maximum || | ||||||||||~ ||~ ||~ ||~ <span style="display: block; text-align: center;">Mean</span> ||~ <span style="display: block; text-align: center;">Median</span> ||~ <span style="display: block; text-align: center;">Golden</span> ||~ Maximum || | ||
|| 9\7 || || || || || 514.286 || 342.857 || 85.714 || 128.571 || 142.145 || 171.429 || | || 9\7 || || || || || 514.286 || 342.857 || 85.714 || 128.571 || 142.145 || 171.429 || | ||
|| || || || || 48\38 || 505.263 || 347.368 || 84.2105 || 126.316 || 139.651 || 168.421 || | || || || || || 48\38 || 505.263 || 347.368 || 84.2105 || 126.316 || 139.651 || 168.421 || | ||
|| || || || 39\31 || || 503.226 || 348.387 || 83.871 || [[tel | || || || || 39\31 || || 503.226 || 348.387 || 83.871 || [[tel/125.8065|125.8065]] || 139.088 || 167.742 || | ||
|| || || || || 69\55 || 506.667 || 349.091 || 83.636 || [[tel | || || || || || 69\55 || 506.667 || 349.091 || 83.636 || [[tel/125.4545|125.4545]] || 138.699 || 167.273 || | ||
|| || || 30\24 || || || 500 || 350 || 83.333 || 125 || 138.197 || 166.667 || | || || || 30\24 || || || 500 || 350 || 83.333 || 125 || 138.197 || 166.667 || | ||
|| || || || || 81\65 || [[tel | || || || || || 81\65 || [[tel/498.4615|498.4615]] || 350.769 || 83.076 || 124.615 || 137.771 || 166.154 || | ||
|| || || || 51\41 || || 497.561 || [[tel | || || || || 51\41 || || 497.561 || [[tel/351.2195|351.2195]] || 82.927 || 124.39 || [[tel/137.5225|137.5225]] || 165.854 || | ||
|| || || || || 72\58 || 496.552 || 351.724 || 82.758 || 124.137 || [[tel | || || || || || 72\58 || 496.552 || 351.724 || 82.758 || 124.137 || [[tel/137.2435|137.2435]] || 165.517 || | ||
|| || 21\17 || || || || 494.116 || 325.941 || 82.352 || 123.529 || 136.571 || 164.706 || | || || 21\17 || || || || 494.116 || 325.941 || 82.352 || 123.529 || 136.571 || 164.706 || | ||
|| || || || || 75\61 || 491.803 || 354.098 || 81.967 || 122.951 || 135.931 || 163.934 || | || || || || || 75\61 || 491.803 || 354.098 || 81.967 || 122.951 || 135.931 || 163.934 || | ||
|| || || || 54\44 || || 490.909 || [[tel | || || || || 54\44 || || 490.909 || [[tel/354.5455|354.5455]] || 81.818 || 122.727 || 135.684 || 163.636 || | ||
|| || || || || 87\71 || 490.141 || 354.93 || 81.69 || 122.535 || 135.472 || 163.38 || | || || || || || 87\71 || 490.141 || 354.93 || 81.69 || 122.535 || 135.472 || 163.38 || | ||
|| || || 33\27 || || || 488.889 || 355.556 || 81.481 || 122.222 || 135.126 || 162.462 || | || || || 33\27 || || || 488.889 || 355.556 || 81.481 || 122.222 || 135.126 || 162.462 || | ||
|| || || || || 78\64 || 487.5 || 356.25 || 81.25 || 121.875 || 134.742 || 162.5 || | || || || || || 78\64 || 487.5 || 356.25 || 81.25 || 121.875 || 134.742 || 162.5 || | ||
|| || || || 45\37 || || [[tel | || || || || 45\37 || || [[tel/486.4865|486.4865]] || 356.757 || 81.081 || 121.622 || 134.462 || 162.162 || | ||
|| || || || || 57\47 || 485.106 || 357.447 || 80.851 || 121.277 || 134.08 || 162.702 || | || || || || || 57\47 || 485.106 || 357.447 || 80.851 || 121.277 || 134.08 || 162.702 || | ||
|| 12\10 || || || || || 480 || 360 || 80 || 120 || 132.669 || 160 ||</pre></div> | || 12\10 || || || || || 480 || 360 || 80 || 120 || 132.669 || 160 || | ||
From an antidiatonic point of view, an optimized (MOD)MOS pattern of 3L+6s works out to become one of the modes of the (Neapolitan/Melodic) antimajor scale extended to a major tenth, the MOS itself being the tritetrachordal Antimixolydian p10 scale, the interesting property of which being that it treats a seventh as a perfect interval rather than a fifth, however far off it may be from a perfect 11\6. As a temperament, it has period ~4/3 and generator up to 1/3 of that, making the range between its median and maximum generators represent an ~12/11 (given that it is an extended mode of [[Mavila]], 178 cents can be an acceptable 12\11). | |||
||||||||||~ Major Tenth ||~ Fourth ||~ ||||||||||~ Generator || | |||
||||||||||~ ||~ ||~ <span style="display: block; text-align: center;">Mean</span> ||||~ <span style="display: block; text-align: center;">Median</span> ||~ Golden ||~ ||~ Maximum || | |||
|| 9\7 || || || || || 514.286 || 85.714 |||| 128.571 |||| 142.145 || 171.429 || | |||
|| || || || || 48\37 || 518.919 || 86.4865 |||| 129.73 |||| 143.426 || 172.973 || | |||
|| || || || 39\30 || || 520 || 86.667 |||| 130 |||| 143.7245 || 173.333 || | |||
|| || || || || 69\53 || 520.755 || 86.7925 |||| 130.189 |||| 143.933 || 173.585 || | |||
|| || || 30\23 || || || 521.739 || 86.9565 |||| 130.435 |||| 144.205 || 173.913 || | |||
|| || || || || 81\62 || 522.582 || 87.079 |||| 130.645 |||| 144.438 || 174.194 || | |||
|| || || || 51\39 || || 523.077 || 87.1795 |||| 130.769 |||| 144.575 || 174.359 || | |||
|| || || || || 72\55 || 523.636 || 87.273 |||| 130.909 |||| 144.7295 || 174.5455 || | |||
|| || 21\16 || || || || 525 || 87.5 |||| 131.25 |||| 145.106 || 175 || | |||
|| || || || || 75\57 || 526.316 || 87.719 |||| 131.579 |||| 145.47 || 175.439 || | |||
|| || || || 54\41 || || 526.829 || 87.805 |||| 131.707 |||| 145.612 || 175.61 || | |||
|| || || || || 87\66 || 527.273 || 87.879 |||| 131.818 |||| 145.735 || 175.758 || | |||
|| || || 33\25 || || || 528 || 88 |||| 132 |||| 145.936 || 176 || | |||
|| || || || || 78\59 || 528.814 || 88.136 |||| 132.203 |||| 146.1605 || 176.271 || | |||
|| || || || 45\34 || || 529.412 || 88.235 |||| 132.353 |||| 146.326 || 176.471 || | |||
|| || || || || 57\43 || 530.233 || 88.372 |||| 132.558 |||| 146.553 || 176.744 || | |||
|| 12\9 || || || || || 533.333 || 88.889 |||| 133.333 |||| 147.41 || 177.778 ||</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>3L 6s</title></head><body>This MOS has generators which range between 0 and 133.333 cents and three periods per octave and runs Lss Lss Lss.<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>3L 6s</title></head><body>This MOS has generators which range between 0 and 133.333 cents and three periods per octave and runs Lss Lss Lss.<br /> | ||
| Line 339: | Line 361: | ||
<br /> | <br /> | ||
From a standard diatonic point of view, an optimized (MOD)MOS pattern of 3L+6s works out to become one of the modes of the Mohajira diatonic or Rast scale extended to a minor tenth, the MOS itself being the tritetrachordal | From a standard diatonic point of view, an optimized (MOD)MOS pattern of 3L+6s works out to become one of the modes of the Mohajira diatonic or Rast scale extended to a minor tenth, the MOS itself being the tritetrachordal Rast b10 scale, the interesting property of which being that it treats a seventh as a perfect interval rather than a fifth, however far off it may be from a perfect 7/4. As a temperament, it has period ~4/3 and generator up to 1/3 of that, making a subrange of the range between its median and maximum generators represent an ~12/11 (given harmonic entropy as coarse as that of <a class="wiki_link" href="/Mavila">Mavila</a>, 120 cents can be an acceptable 12\11).<br /> | ||
<br /> | <br /> | ||
| Line 349: | Line 371: | ||
<th>Fourth<br /> | <th>Fourth<br /> | ||
</th> | </th> | ||
<th> | <th>Hemififth<br /> | ||
</th> | </th> | ||
<th colspan="4"><span style="display: block; text-align: center;">Generator</span><br /> | <th colspan="4"><span style="display: block; text-align: center;">Generator</span><br /> | ||
| Line 776: | Line 798: | ||
</td> | </td> | ||
<td>160<br /> | <td>160<br /> | ||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
From an antidiatonic point of view, an optimized (MOD)MOS pattern of 3L+6s works out to become one of the modes of the (Neapolitan/Melodic) antimajor scale extended to a major tenth, the MOS itself being the tritetrachordal Antimixolydian p10 scale, the interesting property of which being that it treats a seventh as a perfect interval rather than a fifth, however far off it may be from a perfect 11\6. As a temperament, it has period ~4/3 and generator up to 1/3 of that, making the range between its median and maximum generators represent an ~12/11 (given that it is an extended mode of <a class="wiki_link" href="/Mavila">Mavila</a>, 178 cents can be an acceptable 12\11).<br /> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th colspan="5">Major Tenth<br /> | |||
</th> | |||
<th>Fourth<br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th colspan="5">Generator<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<th colspan="5"><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><span style="display: block; text-align: center;">Mean</span><br /> | |||
</th> | |||
<th colspan="2"><span style="display: block; text-align: center;">Median</span><br /> | |||
</th> | |||
<th>Golden<br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th>Maximum<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>9\7<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>514.286<br /> | |||
</td> | |||
<td>85.714<br /> | |||
</td> | |||
<td colspan="2">128.571<br /> | |||
</td> | |||
<td colspan="2">142.145<br /> | |||
</td> | |||
<td>171.429<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>48\37<br /> | |||
</td> | |||
<td>518.919<br /> | |||
</td> | |||
<td>86.4865<br /> | |||
</td> | |||
<td colspan="2">129.73<br /> | |||
</td> | |||
<td colspan="2">143.426<br /> | |||
</td> | |||
<td>172.973<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>39\30<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>520<br /> | |||
</td> | |||
<td>86.667<br /> | |||
</td> | |||
<td colspan="2">130<br /> | |||
</td> | |||
<td colspan="2">143.7245<br /> | |||
</td> | |||
<td>173.333<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>69\53<br /> | |||
</td> | |||
<td>520.755<br /> | |||
</td> | |||
<td>86.7925<br /> | |||
</td> | |||
<td colspan="2">130.189<br /> | |||
</td> | |||
<td colspan="2">143.933<br /> | |||
</td> | |||
<td>173.585<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>30\23<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>521.739<br /> | |||
</td> | |||
<td>86.9565<br /> | |||
</td> | |||
<td colspan="2">130.435<br /> | |||
</td> | |||
<td colspan="2">144.205<br /> | |||
</td> | |||
<td>173.913<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>81\62<br /> | |||
</td> | |||
<td>522.582<br /> | |||
</td> | |||
<td>87.079<br /> | |||
</td> | |||
<td colspan="2">130.645<br /> | |||
</td> | |||
<td colspan="2">144.438<br /> | |||
</td> | |||
<td>174.194<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>51\39<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>523.077<br /> | |||
</td> | |||
<td>87.1795<br /> | |||
</td> | |||
<td colspan="2">130.769<br /> | |||
</td> | |||
<td colspan="2">144.575<br /> | |||
</td> | |||
<td>174.359<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>72\55<br /> | |||
</td> | |||
<td>523.636<br /> | |||
</td> | |||
<td>87.273<br /> | |||
</td> | |||
<td colspan="2">130.909<br /> | |||
</td> | |||
<td colspan="2">144.7295<br /> | |||
</td> | |||
<td>174.5455<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>21\16<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>525<br /> | |||
</td> | |||
<td>87.5<br /> | |||
</td> | |||
<td colspan="2">131.25<br /> | |||
</td> | |||
<td colspan="2">145.106<br /> | |||
</td> | |||
<td>175<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>75\57<br /> | |||
</td> | |||
<td>526.316<br /> | |||
</td> | |||
<td>87.719<br /> | |||
</td> | |||
<td colspan="2">131.579<br /> | |||
</td> | |||
<td colspan="2">145.47<br /> | |||
</td> | |||
<td>175.439<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>54\41<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>526.829<br /> | |||
</td> | |||
<td>87.805<br /> | |||
</td> | |||
<td colspan="2">131.707<br /> | |||
</td> | |||
<td colspan="2">145.612<br /> | |||
</td> | |||
<td>175.61<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>87\66<br /> | |||
</td> | |||
<td>527.273<br /> | |||
</td> | |||
<td>87.879<br /> | |||
</td> | |||
<td colspan="2">131.818<br /> | |||
</td> | |||
<td colspan="2">145.735<br /> | |||
</td> | |||
<td>175.758<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>33\25<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>528<br /> | |||
</td> | |||
<td>88<br /> | |||
</td> | |||
<td colspan="2">132<br /> | |||
</td> | |||
<td colspan="2">145.936<br /> | |||
</td> | |||
<td>176<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>78\59<br /> | |||
</td> | |||
<td>528.814<br /> | |||
</td> | |||
<td>88.136<br /> | |||
</td> | |||
<td colspan="2">132.203<br /> | |||
</td> | |||
<td colspan="2">146.1605<br /> | |||
</td> | |||
<td>176.271<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>45\34<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>529.412<br /> | |||
</td> | |||
<td>88.235<br /> | |||
</td> | |||
<td colspan="2">132.353<br /> | |||
</td> | |||
<td colspan="2">146.326<br /> | |||
</td> | |||
<td>176.471<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>57\43<br /> | |||
</td> | |||
<td>530.233<br /> | |||
</td> | |||
<td>88.372<br /> | |||
</td> | |||
<td colspan="2">132.558<br /> | |||
</td> | |||
<td colspan="2">146.553<br /> | |||
</td> | |||
<td>176.744<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12\9<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>533.333<br /> | |||
</td> | |||
<td>88.889<br /> | |||
</td> | |||
<td colspan="2">133.333<br /> | |||
</td> | |||
<td colspan="2">147.41<br /> | |||
</td> | |||
<td>177.778<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||