2L 6s
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Two notable harmonic entropy minima for this [[MOSScales|MOS]] pattern are [[Diaschismic family|srutal/pajara]] and shrutar. They are both improper. As for proper scales, I can't think of any. In addition to the true MOS form, LsssLsss, these scales also have an interesting near-MOS form, LssLssss, in which the period is the only generic interval represented by more than two specific intervals. ||||||||||||||||||||~ Generator ||~ Cents ||~ Comments || || 0\2 || || || || || || || || || || 0 ||= || || || || || || || || || || || 1\26 || 46.15 || || || || || || || || || || || 1\24 || || 50 ||= || || || || || || || || || || || 2\46 || 52.17 ||= Shrutar is around here || || || || || || || || || 1\22 || || || 54.55 ||= || || || || || || || || 1\20 || || || || 60 ||= || || || || || || || 1\18 || || || || || 66.67 ||= || || || || || || 1\16 || || || || || || 75 ||= || || || || || 1\14 || || || || || || || 85.71 ||= L/s=4: generators smaller than this are "impractical" || || || || 1\12 || || || || || || || || 100 ||= L/s=3: generators smaller than this may be considered "impractical" || || || || || || 3\34 || || || || || || 105.88 ||= Srutal/Pajara is around here || || || || || 2\22 || || || || || || || 109.09 ||= || || || 1\10 || || || || || || || || || 120 ||= Boundary of propriety (generators larger than this are proper) || || || || || 3\28 || || || || || || || 128.57 ||= Supersharp || || || || || || || 8\74 || || || || || 129.73 ||= Supersharp || || || || || || || || || 21\194 || || || 129.9 || || || || || || || || || || || || 55\508 || 129.92 ||= Unnamed golden temperament || || || || || || || || || || 34\314 || || 129.94 || || || || || || || || || 13\120 || || || || 130 ||= || || || || || || 5\46 || || || || || || 130.43 ||= Twothirdtonic || || || || 2\18 || || || || || || || || 133.33 ||= Optimum rank range (L/s=3/2) || || 1\8 || || || || || || || || || || 150 ||= ||
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<html><head><title>2L 6s</title></head><body>Two notable harmonic entropy minima for this <a class="wiki_link" href="/MOSScales">MOS</a> pattern are <a class="wiki_link" href="/Diaschismic%20family">srutal/pajara</a> and shrutar. They are both improper. As for proper scales, I can't think of any.<br /> <br /> In addition to the true MOS form, LsssLsss, these scales also have an interesting near-MOS form, LssLssss, in which the period is the only generic interval represented by more than two specific intervals.<br /> <table class="wiki_table"> <tr> <th colspan="10">Generator<br /> </th> <th>Cents<br /> </th> <th>Comments<br /> </th> </tr> <tr> <td>0\2<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><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><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>1\26<br /> </td> <td>46.15<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>1\24<br /> </td> <td><br /> </td> <td>50<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>2\46<br /> </td> <td>52.17<br /> </td> <td style="text-align: center;">Shrutar is around here<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>1\22<br /> </td> <td><br /> </td> <td><br /> </td> <td>54.55<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>1\20<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>60<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>1\18<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>66.67<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>1\16<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>75<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>1\14<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>85.71<br /> </td> <td style="text-align: center;">L/s=4:<br /> generators smaller than this are "impractical"<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td>1\12<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>100<br /> </td> <td style="text-align: center;">L/s=3:<br /> generators smaller than this may be considered "impractical"<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>3\34<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>105.88<br /> </td> <td style="text-align: center;">Srutal/Pajara is around here<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>2\22<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>109.09<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td>1\10<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>120<br /> </td> <td style="text-align: center;">Boundary of propriety<br /> (generators larger than this are proper)<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>3\28<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>128.57<br /> </td> <td style="text-align: center;">Supersharp<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>8\74<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>129.73<br /> </td> <td style="text-align: center;">Supersharp<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>21\194<br /> </td> <td><br /> </td> <td><br /> </td> <td>129.9<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>55\508<br /> </td> <td>129.92<br /> </td> <td style="text-align: center;">Unnamed golden temperament<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>34\314<br /> </td> <td><br /> </td> <td>129.94<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>13\120<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>130<br /> </td> <td style="text-align: center;"><br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>5\46<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>130.43<br /> </td> <td style="text-align: center;">Twothirdtonic<br /> </td> </tr> <tr> <td><br /> </td> <td><br /> </td> <td>2\18<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>133.33<br /> </td> <td style="text-align: center;">Optimum rank range (L/s=3/2)<br /> </td> </tr> <tr> <td>1\8<br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td><br /> </td> <td>150<br /> </td> <td style="text-align: center;"><br /> </td> </tr> </table> </body></html>