3L 6s
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 13:28:40 UTC.
- The original revision id was 599895808.
- 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 || 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 ||
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>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>
</tr>
</table>
</body></html>