5L 3s
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Original Wikitext content:
5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of [[5edo]] = 480¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this: ||||||||||||||||||||~ Generator ||~ scale ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments || || 2\5 || || || || || || || || || ||= 1 0 1 1 0 1 0 1 || 480.000 || 960.000 || 240.000 || 720.000 ||= || || || || || || || || || || || 21\53 ||= 10 1... || 475.472 || 950.943 || 226.415 || 701.887 ||= Vulture/Buzzard is around here || || || || || || || || || || 19\48 || ||= 9 1 9 9 1 9 1 9 || 475 || 950 || 225 || 700 ||= || || || || || || || || || 17\43 || || ||= 8 1 8 8 1 8 1 8 || 474.419 || 948.837 || 223.256 || 697.674 ||= || || || || || || || || 15\38 || || || ||= 7 1 7 7 1 7 1 7 || 473.684 || 947.368 || 221.053 || 694.737 ||= || || || || || || || 13\33 || || || || ||= 6 1 6 6 1 6 1 6 || 472.727 || 945.455 || 218.181 || 690.909 ||= || || || || || || 11\28 || || || || || ||= 5 1 5 5 1 5 1 5 || 471.429 || 942.857 || 214.286 || 685.714 ||= || || || || || 9\23 || || || || || || ||= 4 1 4 4 1 4 1 4 || 469.565 || 939.130 || 208.696 || 678.261 ||= || || || || 7\18 || || || || || || || ||= 3 1 3 3 1 3 1 3 || 466.667 || 933.333 || 200.000 || 666.667 ||= || || || || || 12\31 || || || || || || ||= 5 2 5 5 2 5 2 5 || 464.516 || 929.032 || 193.549 || 658.065 ||= || || || 5\13 || || || || || || || || ||= 2 1 2 2 1 2 1 2 || 461.538 || 923.077 || 184.615 || 646.154 ||= || || || || || 13\34 || || || || || || ||= 5 3 5 5 3 5 3 5 || 458.824 || 917.647 || 176.471 || 635.294 ||= || || || || || || || 34\89 || || || || ||= 13 8... || 458.427 || 916.854 || 175.281 || 633.708 ||= Golden father || || || || || || 21\55 || || || || || ||= 8 5 8 8 5 8 5 8 || 458.182 || 916.364 || 174.545 || 632.727 ||= || || || || 8\21 || || || || || || || ||= 3 2 3 3 2 3 2 3 || 457.143 || 914.286 || 171.429 || 628.571 ||= Optimum rank range (L/s=3/2) father || || || || || 11\29 || || || || || || ||= 4 3 4 4 3 4 3 4 || 455.172 || 910.345 || 165.517 || 620.690 ||= || || 3\8 || || || || || || || || || ||= 1 1 1 1 1 1 1 1 || 450.000 || 900.000 || 150.000 || 600.000 ||= || The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.
Original HTML content:
<html><head><title>5L 3s</title></head><body>5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of <a class="wiki_link" href="/5edo">5edo</a> = 480¢) to 3\8 (three degrees of <a class="wiki_link" href="/8edo">8edo</a> = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this:<br />
<table class="wiki_table">
<tr>
<th colspan="10">Generator<br />
</th>
<th>scale<br />
</th>
<th>g in cents<br />
</th>
<th>2g<br />
</th>
<th>3g<br />
</th>
<th>4g<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>2\5<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 style="text-align: center;">1 0 1 1 0 1 0 1<br />
</td>
<td>480.000<br />
</td>
<td>960.000<br />
</td>
<td>240.000<br />
</td>
<td>720.000<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>21\53<br />
</td>
<td style="text-align: center;">10 1...<br />
</td>
<td>475.472<br />
</td>
<td>950.943<br />
</td>
<td>226.415<br />
</td>
<td>701.887<br />
</td>
<td style="text-align: center;">Vulture/Buzzard 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><br />
</td>
<td>19\48<br />
</td>
<td><br />
</td>
<td style="text-align: center;">9 1 9 9 1 9 1 9<br />
</td>
<td>475<br />
</td>
<td>950<br />
</td>
<td>225<br />
</td>
<td>700<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>17\43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">8 1 8 8 1 8 1 8<br />
</td>
<td>474.419<br />
</td>
<td>948.837<br />
</td>
<td>223.256<br />
</td>
<td>697.674<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>15\38<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">7 1 7 7 1 7 1 7<br />
</td>
<td>473.684<br />
</td>
<td>947.368<br />
</td>
<td>221.053<br />
</td>
<td>694.737<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>13\33<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">6 1 6 6 1 6 1 6<br />
</td>
<td>472.727<br />
</td>
<td>945.455<br />
</td>
<td>218.181<br />
</td>
<td>690.909<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11\28<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">5 1 5 5 1 5 1 5<br />
</td>
<td>471.429<br />
</td>
<td>942.857<br />
</td>
<td>214.286<br />
</td>
<td>685.714<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>9\23<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">4 1 4 4 1 4 1 4<br />
</td>
<td>469.565<br />
</td>
<td>939.130<br />
</td>
<td>208.696<br />
</td>
<td>678.261<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>7\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 style="text-align: center;">3 1 3 3 1 3 1 3<br />
</td>
<td>466.667<br />
</td>
<td>933.333<br />
</td>
<td>200.000<br />
</td>
<td>666.667<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>12\31<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">5 2 5 5 2 5 2 5<br />
</td>
<td>464.516<br />
</td>
<td>929.032<br />
</td>
<td>193.549<br />
</td>
<td>658.065<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>5\13<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 style="text-align: center;">2 1 2 2 1 2 1 2<br />
</td>
<td>461.538<br />
</td>
<td>923.077<br />
</td>
<td>184.615<br />
</td>
<td>646.154<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>13\34<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">5 3 5 5 3 5 3 5<br />
</td>
<td>458.824<br />
</td>
<td>917.647<br />
</td>
<td>176.471<br />
</td>
<td>635.294<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>34\89<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">13 8...<br />
</td>
<td>458.427<br />
</td>
<td>916.854<br />
</td>
<td>175.281<br />
</td>
<td>633.708<br />
</td>
<td style="text-align: center;">Golden father<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>21\55<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">8 5 8 8 5 8 5 8<br />
</td>
<td>458.182<br />
</td>
<td>916.364<br />
</td>
<td>174.545<br />
</td>
<td>632.727<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>8\21<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">3 2 3 3 2 3 2 3<br />
</td>
<td>457.143<br />
</td>
<td>914.286<br />
</td>
<td>171.429<br />
</td>
<td>628.571<br />
</td>
<td style="text-align: center;">Optimum rank range (L/s=3/2) father<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11\29<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">4 3 4 4 3 4 3 4<br />
</td>
<td>455.172<br />
</td>
<td>910.345<br />
</td>
<td>165.517<br />
</td>
<td>620.690<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>3\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 style="text-align: center;">1 1 1 1 1 1 1 1<br />
</td>
<td>450.000<br />
</td>
<td>900.000<br />
</td>
<td>150.000<br />
</td>
<td>600.000<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.</body></html>