3L 6s: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 565341749 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 599895808 - 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>2016-11-20 13:28:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599895808</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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|| || || 2\21 || || || 114.286 ||= || | || || || 2\21 || || || 114.286 ||= || | ||
|| || || || 3\30 || || 120 ||= || | || || || || 3\30 || || 120 ||= || | ||
|| 1\9 || || || || || 133.333 ||= ||</pre></div> | || 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 Mixolydian 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 ||~ Neutral Third ||||||||~ <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 || | |||
|| 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 || | |||
|| || || || 39\31 || || 503.226 || 348.387 || 83.871 || 125.8065 || 139.088 || 167.742 || | |||
|| || || || || 69\55 || 506.667 || 349.091 || 83.636 || 125.4545 || 138.699 || 167.273 || | |||
|| || || 30\24 || || || 500 || 350 || 83.333 || 125 || 138.197 || 166.667 || | |||
|| || || || || 81\65 || 498.4615 || 350.769 || 83.076 || 124.615 || 137.771 || 166.154 || | |||
|| || || || 51\41 || || 497.561 || 351.2195 || 82.927 || 124.39 || 137.5225 || 165.854 || | |||
|| || || || || 72\58 || 496.552 || 351.724 || 82.758 || 124.137 || 137.2435 || 165.517 || | |||
|| || 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 || | |||
|| || || || 54\44 || || 490.909 || 354.5455 || 81.818 || 122.727 || 135.684 || 163.636 || | |||
|| || || || || 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 || | |||
|| || || || || 78\64 || 487.5 || 356.25 || 81.25 || 121.875 || 134.742 || 162.5 || | |||
|| || || || 45\37 || || 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 || | |||
|| 12\10 || || || || || 480 || 360 || 80 || 120 || 132.669 || 160 ||</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 /> | ||
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</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
</td> | |||
</tr> | |||
</table> | |||
<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 Mixolydian 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 /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th colspan="5">Minor Tenth<br /> | |||
</th> | |||
<th>Fourth<br /> | |||
</th> | |||
<th>Neutral Third<br /> | |||
</th> | |||
<th colspan="4"><span style="display: block; text-align: center;">Generator</span><br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<th colspan="5"><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><span style="display: block; text-align: center;">Mean</span><br /> | |||
</th> | |||
<th><span style="display: block; text-align: center;">Median</span><br /> | |||
</th> | |||
<th><span style="display: block; text-align: center;">Golden</span><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>342.857<br /> | |||
</td> | |||
<td>85.714<br /> | |||
</td> | |||
<td>128.571<br /> | |||
</td> | |||
<td>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\38<br /> | |||
</td> | |||
<td>505.263<br /> | |||
</td> | |||
<td>347.368<br /> | |||
</td> | |||
<td>84.2105<br /> | |||
</td> | |||
<td>126.316<br /> | |||
</td> | |||
<td>139.651<br /> | |||
</td> | |||
<td>168.421<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>39\31<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>503.226<br /> | |||
</td> | |||
<td>348.387<br /> | |||
</td> | |||
<td>83.871<br /> | |||
</td> | |||
<td>125.8065<br /> | |||
</td> | |||
<td>139.088<br /> | |||
</td> | |||
<td>167.742<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>69\55<br /> | |||
</td> | |||
<td>506.667<br /> | |||
</td> | |||
<td>349.091<br /> | |||
</td> | |||
<td>83.636<br /> | |||
</td> | |||
<td>125.4545<br /> | |||
</td> | |||
<td>138.699<br /> | |||
</td> | |||
<td>167.273<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>30\24<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>500<br /> | |||
</td> | |||
<td>350<br /> | |||
</td> | |||
<td>83.333<br /> | |||
</td> | |||
<td>125<br /> | |||
</td> | |||
<td>138.197<br /> | |||
</td> | |||
<td>166.667<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>81\65<br /> | |||
</td> | |||
<td>498.4615<br /> | |||
</td> | |||
<td>350.769<br /> | |||
</td> | |||
<td>83.076<br /> | |||
</td> | |||
<td>124.615<br /> | |||
</td> | |||
<td>137.771<br /> | |||
</td> | |||
<td>166.154<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>51\41<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>497.561<br /> | |||
</td> | |||
<td>351.2195<br /> | |||
</td> | |||
<td>82.927<br /> | |||
</td> | |||
<td>124.39<br /> | |||
</td> | |||
<td>137.5225<br /> | |||
</td> | |||
<td>165.854<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>72\58<br /> | |||
</td> | |||
<td>496.552<br /> | |||
</td> | |||
<td>351.724<br /> | |||
</td> | |||
<td>82.758<br /> | |||
</td> | |||
<td>124.137<br /> | |||
</td> | |||
<td>137.2435<br /> | |||
</td> | |||
<td>165.517<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>21\17<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>494.116<br /> | |||
</td> | |||
<td>325.941<br /> | |||
</td> | |||
<td>82.352<br /> | |||
</td> | |||
<td>123.529<br /> | |||
</td> | |||
<td>136.571<br /> | |||
</td> | |||
<td>164.706<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>75\61<br /> | |||
</td> | |||
<td>491.803<br /> | |||
</td> | |||
<td>354.098<br /> | |||
</td> | |||
<td>81.967<br /> | |||
</td> | |||
<td>122.951<br /> | |||
</td> | |||
<td>135.931<br /> | |||
</td> | |||
<td>163.934<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>54\44<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>490.909<br /> | |||
</td> | |||
<td>354.5455<br /> | |||
</td> | |||
<td>81.818<br /> | |||
</td> | |||
<td>122.727<br /> | |||
</td> | |||
<td>135.684<br /> | |||
</td> | |||
<td>163.636<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>87\71<br /> | |||
</td> | |||
<td>490.141<br /> | |||
</td> | |||
<td>354.93<br /> | |||
</td> | |||
<td>81.69<br /> | |||
</td> | |||
<td>122.535<br /> | |||
</td> | |||
<td>135.472<br /> | |||
</td> | |||
<td>163.38<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>33\27<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>488.889<br /> | |||
</td> | |||
<td>355.556<br /> | |||
</td> | |||
<td>81.481<br /> | |||
</td> | |||
<td>122.222<br /> | |||
</td> | |||
<td>135.126<br /> | |||
</td> | |||
<td>162.462<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>78\64<br /> | |||
</td> | |||
<td>487.5<br /> | |||
</td> | |||
<td>356.25<br /> | |||
</td> | |||
<td>81.25<br /> | |||
</td> | |||
<td>121.875<br /> | |||
</td> | |||
<td>134.742<br /> | |||
</td> | |||
<td>162.5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>45\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>486.4865<br /> | |||
</td> | |||
<td>356.757<br /> | |||
</td> | |||
<td>81.081<br /> | |||
</td> | |||
<td>121.622<br /> | |||
</td> | |||
<td>134.462<br /> | |||
</td> | |||
<td>162.162<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>57\47<br /> | |||
</td> | |||
<td>485.106<br /> | |||
</td> | |||
<td>357.447<br /> | |||
</td> | |||
<td>80.851<br /> | |||
</td> | |||
<td>121.277<br /> | |||
</td> | |||
<td>134.08<br /> | |||
</td> | |||
<td>162.702<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12\10<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>480<br /> | |||
</td> | |||
<td>360<br /> | |||
</td> | |||
<td>80<br /> | |||
</td> | |||
<td>120<br /> | |||
</td> | |||
<td>132.669<br /> | |||
</td> | |||
<td>160<br /> | |||
</td> | </td> | ||
</tr> | </tr> |