3L 6s: Difference between revisions
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Wikispaces>JosephRuhf **Imported revision 599920156 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 602432596 - 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- | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-18 07:27:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602432596</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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|| 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 || | || || || || 39\31 || || 503.226 || 348.387 || 83.871 || 125.806'5 || 139.088 || 167.742 || | ||
|| || || || || 69\55 || 506.667 || 349.091 || 83.636 | | || || || || || 69\55 || 506.667 || 349.091 || 83.636 || 125.454'5 || 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 || | || || || || || 81\65 || 498.461'5 || 350.769 || 83.076 || 124.615 || 137.771 || 166.154 || | ||
|| || || || 51\41 || || 497.561 | | || || || || 51\41 || || 497.561 || 351.219'5 || 82.927 || 124.39 || 137.522'5 || 165.854 || | ||
|| || || || || 72\58 || 496.552 || 351.724 || 82.758 || 124.137 | | || || || || || 72\58 || 496.552 || 351.724 || 82.758 || 124.137 || 137.243'5 || 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 || | || || || || 54\44 || || 490.909 || 354.545'5 || 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 || || | || || || || 45\37 || || 486.486'5 || 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 || | || 12\10 || || || || || 480 || 360 || 80 || 120 || 132.669 || 160 || | ||
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|| 9\7 || || || || || 514.286 || 85.714 |||| 128.571 |||| 142.145 || 171.429 || | || 9\7 || || || || || 514.286 || 85.714 |||| 128.571 |||| 142.145 || 171.429 || | ||
|| || || || || 48\37 || 518.919 || 86.4865 |||| 129.73 |||| 143.426 || 172.973 || | || || || || || 48\37 || 518.919 || 86.4865 |||| 129.73 |||| 143.426 || 172.973 || | ||
|| || || || 39\30 || || 520 || 86.667 |||| 130 |||| 143. | || || || || 39\30 || || 520 || 86.667 |||| 130 |||| 143.724'5 || 173.333 || | ||
|| || || || || 69\53 || 520.755 || 86.7925 |||| 130.189 |||| 143.933 || 173.585 || | || || || || || 69\53 || 520.755 || 86.7925 |||| 130.189 |||| 143.933 || 173.585 || | ||
|| || || 30\23 || || || 521.739 || 86.9565 |||| 130.435 |||| 144.205 || 173.913 || | || || || 30\23 || || || 521.739 || 86.9565 |||| 130.435 |||| 144.205 || 173.913 || | ||
|| || || || || 81\62 || 522.582 || 87.079 |||| 130.645 |||| 144.438 || 174.194 || | || || || || || 81\62 || 522.582 || 87.079 |||| 130.645 |||| 144.438 || 174.194 || | ||
|| || || || 51\39 || || 523.077 || 87.1795 |||| 130.769 |||| 144.575 || 174.359 || | || || || || 51\39 || || 523.077 || 87.1795 |||| 130.769 |||| 144.575 || 174.359 || | ||
|| || || || || 72\55 || 523.636 || 87.273 |||| 130.909 |||| 144. | || || || || || 72\55 || 523.636 || 87.273 |||| 130.909 |||| 144.729'5 || 174.545'5 || | ||
|| || 21\16 || || || || 525 || 87.5 |||| 131.25 |||| 145.106 || 175 || | || || 21\16 || || || || 525 || 87.5 |||| 131.25 |||| 145.106 || 175 || | ||
|| || || || || 75\57 || 526.316 || 87.719 |||| 131.579 |||| 145.47 || 175.439 || | || || || || || 75\57 || 526.316 || 87.719 |||| 131.579 |||| 145.47 || 175.439 || | ||
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|| || || || || 87\66 || 527.273 || 87.879 |||| 131.818 |||| 145.735 || 175.758 || | || || || || || 87\66 || 527.273 || 87.879 |||| 131.818 |||| 145.735 || 175.758 || | ||
|| || || 33\25 || || || 528 || 88 |||| 132 |||| 145.936 || 176 || | || || || 33\25 || || || 528 || 88 |||| 132 |||| 145.936 || 176 || | ||
|| || || || || 78\59 || 528.814 || 88.136 |||| 132.203 |||| 146. | || || || || || 78\59 || 528.814 || 88.136 |||| 132.203 |||| 146.160'5 || 176.271 || | ||
|| || || || 45\34 || || 529.412 || 88.235 |||| 132.353 |||| 146.326 || 176.471 || | || || || || 45\34 || || 529.412 || 88.235 |||| 132.353 |||| 146.326 || 176.471 || | ||
|| || || || || 57\43 || 530.233 || 88.372 |||| 132.558 |||| 146.553 || 176.744 || | || || || || || 57\43 || 530.233 || 88.372 |||| 132.558 |||| 146.553 || 176.744 || | ||
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<td>83.871<br /> | <td>83.871<br /> | ||
</td> | </td> | ||
<td | <td>125.806'5<br /> | ||
</td> | </td> | ||
<td>139.088<br /> | <td>139.088<br /> | ||
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<td>83.636<br /> | <td>83.636<br /> | ||
</td> | </td> | ||
<td | <td>125.454'5<br /> | ||
</td> | </td> | ||
<td>138.699<br /> | <td>138.699<br /> | ||
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<td>81\65<br /> | <td>81\65<br /> | ||
</td> | </td> | ||
<td | <td>498.461'5<br /> | ||
</td> | </td> | ||
<td>350.769<br /> | <td>350.769<br /> | ||
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<td>497.561<br /> | <td>497.561<br /> | ||
</td> | </td> | ||
<td | <td>351.219'5<br /> | ||
</td> | </td> | ||
<td>82.927<br /> | <td>82.927<br /> | ||
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<td>124.39<br /> | <td>124.39<br /> | ||
</td> | </td> | ||
<td | <td>137.522'5<br /> | ||
</td> | </td> | ||
<td>165.854<br /> | <td>165.854<br /> | ||
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<td>124.137<br /> | <td>124.137<br /> | ||
</td> | </td> | ||
<td | <td>137.243'5<br /> | ||
</td> | </td> | ||
<td>165.517<br /> | <td>165.517<br /> | ||
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<td>490.909<br /> | <td>490.909<br /> | ||
</td> | </td> | ||
<td | <td>354.545'5<br /> | ||
</td> | </td> | ||
<td>81.818<br /> | <td>81.818<br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>486.486'5<br /> | ||
</td> | </td> | ||
<td>356.757<br /> | <td>356.757<br /> | ||
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<td colspan="2">130<br /> | <td colspan="2">130<br /> | ||
</td> | </td> | ||
<td colspan="2">143. | <td colspan="2">143.724'5<br /> | ||
</td> | </td> | ||
<td>173.333<br /> | <td>173.333<br /> | ||
Line 1,005: | Line 1,005: | ||
<td colspan="2">130.909<br /> | <td colspan="2">130.909<br /> | ||
</td> | </td> | ||
<td colspan="2">144. | <td colspan="2">144.729'5<br /> | ||
</td> | </td> | ||
<td>174. | <td>174.545'5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 1,137: | Line 1,137: | ||
<td colspan="2">132.203<br /> | <td colspan="2">132.203<br /> | ||
</td> | </td> | ||
<td colspan="2">146. | <td colspan="2">146.160'5<br /> | ||
</td> | </td> | ||
<td>176.271<br /> | <td>176.271<br /> |
Revision as of 07:27, 18 December 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 2016-12-18 07:27:51 UTC.
- The original revision id was 602432596.
- 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 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 ||~ 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 || || 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 || 125.806'5 || 139.088 || 167.742 || || || || || || 69\55 || 506.667 || 349.091 || 83.636 || 125.454'5 || 138.699 || 167.273 || || || || 30\24 || || || 500 || 350 || 83.333 || 125 || 138.197 || 166.667 || || || || || || 81\65 || 498.461'5 || 350.769 || 83.076 || 124.615 || 137.771 || 166.154 || || || || || 51\41 || || 497.561 || 351.219'5 || 82.927 || 124.39 || 137.522'5 || 165.854 || || || || || || 72\58 || 496.552 || 351.724 || 82.758 || 124.137 || 137.243'5 || 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 || 354.545'5 || 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 || || 486.486'5 || 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 || 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 |||| 143.724'5 || 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 |||| 144.729'5 || 174.545'5 || || || 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 |||| 146.160'5 || 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 ||
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 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 /> <table class="wiki_table"> <tr> <th colspan="5">Minor Tenth<br /> </th> <th>Fourth<br /> </th> <th>Hemififth<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>125.806'5<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>125.454'5<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>498.461'5<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>351.219'5<br /> </td> <td>82.927<br /> </td> <td>124.39<br /> </td> <td>137.522'5<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>137.243'5<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>354.545'5<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>486.486'5<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> <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">143.724'5<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">144.729'5<br /> </td> <td>174.545'5<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">146.160'5<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> </tr> </table> </body></html>