3L 6s: Difference between revisions

Revision as of 13:44, 20 November 2016

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author JosephRuhf and made on 2016-11-20 13:44:53 UTC.

The original revision id was 599896900.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

This MOS has generators which range between 0 and 133.333 cents and three periods per octave and runs Lss Lss Lss.

||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\3 ||   ||   ||   ||   || 0 ||=   ||
||   ||   ||   || 1\18 ||   || 66.667 ||= L/s=4 ||
||   ||   ||   ||   ||   || 400/(2+pi) ||   ||
||   ||   || 1\15 ||   ||   || 80 ||= L/s=3 ||
||   ||   ||   ||   ||   || 400/(2+e) ||   ||
||   ||   ||   ||   || 3\42 || 85.714 ||   ||
||   ||   ||   ||   ||   || 400/(3+phi) ||   ||
||   ||   ||   || 2\27 ||   || 88.889 ||= Augene is around here ||
||   || 1\12 ||   ||   ||   || 100 ||= Boundary of propriety (generators
larger than this are proper) ||
||   ||   ||   ||   ||   || 400/(2+sqrt(3)) ||   ||
||   ||   ||   || 3\33 ||   || 109.091 ||= August is around here ||
||   ||   ||   ||   ||   || 400/(2+phi) ||   ||
||   ||   ||   ||   || 5\54 || 111.111 ||   ||
||   ||   ||   ||   ||   || 400/(2+pi/2) ||   ||
||   ||   || 2\21 ||   ||   || 114.286 ||=   ||
||   ||   ||   || 3\30 ||   || 120 ||=   ||
|| 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 || [[tel:125.8065|125.8065]] || 139.088 || 167.742 ||
||   ||   ||   ||   || 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 ||
||   ||   ||   ||   || 81\65 || [[tel:498.4615|498.4615]] || 350.769 || 83.076 || 124.615 || 137.771 || 166.154 ||
||   ||   ||   || 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:137.2435|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 || [[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 ||
||   ||   || 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 ||   || [[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 ||
|| 12\10 ||   ||   ||   ||   || 480 || 360 || 80 || 120 || 132.669 || 160 ||

Original HTML content:

<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 />
<br />


<table class="wiki_table">
    <tr>
        <th colspan="5">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>0\3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>0<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\18<br />
</td>
        <td><br />
</td>
        <td>66.667<br />
</td>
        <td style="text-align: center;">L/s=4<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400/(2+pi)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1\15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>80<br />
</td>
        <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>400/(2+e)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\42<br />
</td>
        <td>85.714<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400/(3+phi)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\27<br />
</td>
        <td><br />
</td>
        <td>88.889<br />
</td>
        <td style="text-align: center;">Augene is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>1\12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>100<br />
</td>
        <td style="text-align: center;">Boundary of propriety (generators<br />
larger than this are proper)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400/(2+sqrt(3))<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\33<br />
</td>
        <td><br />
</td>
        <td>109.091<br />
</td>
        <td style="text-align: center;">August is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400/(2+phi)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\54<br />
</td>
        <td>111.111<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400/(2+pi/2)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>2\21<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>114.286<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\30<br />
</td>
        <td><br />
</td>
        <td>120<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>1\9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>133.333<br />
</td>
        <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><a class="wiki_link" href="http://tel.wikispaces.com/125.8065">125.8065</a><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><a class="wiki_link" href="http://tel.wikispaces.com/125.4545">125.4545</a><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><a class="wiki_link" href="http://tel.wikispaces.com/498.4615">498.4615</a><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><a class="wiki_link" href="http://tel.wikispaces.com/351.2195">351.2195</a><br />
</td>
        <td>82.927<br />
</td>
        <td>124.39<br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/137.5225">137.5225</a><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><a class="wiki_link" href="http://tel.wikispaces.com/137.2435">137.2435</a><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><a class="wiki_link" href="http://tel.wikispaces.com/354.5455">354.5455</a><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><a class="wiki_link" href="http://tel.wikispaces.com/486.4865">486.4865</a><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>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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 13:28:40 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-20 13:44:53 UTC</tt>.<br>
-: The original revision id was <tt>599895808</tt>.<br>
+: The original revision id was <tt>599896900</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>
@@ Line 34: / Line 34: @@
 || 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 ||
+||   ||   ||   || 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 || 125.4545 || 138.699 || 167.273 ||
+||   ||   ||   ||   || 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 ||
-||   ||   ||   ||   || 81\65 || 498.4615 || 350.769 || 83.076 || 124.615 || 137.771 || 166.154 ||
+||   ||   ||   ||   || 81\65 || [[tel:498.4615|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 ||
+||   ||   ||   || 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 || 137.2435 || 165.517 ||
+||   ||   ||   ||   || 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 ||
 ||   ||   ||   ||   || 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 ||
+||   ||   ||   || 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 ||
 ||   ||   || 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 ||
+||   ||   ||   || 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 ||
 || 12\10 ||   ||   ||   ||   || 480 || 360 || 80 || 120 || 132.669 || 160 ||</pre></div>
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          &lt;td&gt;124.39&lt;br /&gt;
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+         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/137.5225"&gt;137.5225&lt;/a&gt;&lt;br /&gt;
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@@ Line 557: / Line 557: @@
          &lt;td&gt;124.137&lt;br /&gt;
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-         &lt;td&gt;137.2435&lt;br /&gt;
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-         &lt;td&gt;486.4865&lt;br /&gt;
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          &lt;td&gt;356.757&lt;br /&gt;

3L 6s: Difference between revisions

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