5L 3s: Difference between revisions

Revision as of 04:14, 29 August 2011

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This revision was by author guest and made on 2011-08-29 04:14:25 UTC.

The original revision id was 249049467.

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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 ||   ||   ||   ||=   ||
||   ||   ||   ||   ||   ||   ||   || 17\43 ||   ||   ||= 8 1 8 8 1 8 1 8 || 474.419 ||   ||   ||   ||=   ||
||   ||   ||   ||   ||   ||   || 15\38 ||   ||   ||   ||= 7 1 7 7 1 7 1 7 || 473.684 ||   ||   ||   ||=   ||
||   ||   ||   ||   ||   || 13\33 ||   ||   ||   ||   ||= 6 1 6 6 1 6 1 6 || 472.727 ||   ||   ||   ||=   ||
||   ||   ||   ||   || 11\28 ||   ||   ||   ||   ||   ||= 5 1 5 5 1 5 1 5 || 471.429 ||   ||   ||   ||=   ||
||   ||   ||   || 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 ||   ||   ||   ||= Golden father ||
||   ||   ||   ||   || 21\55 ||   ||   ||   ||   ||   ||= 8 5 8 8 5 8 5 8 || 458.182 ||   ||   ||   ||=   ||
||   ||   || 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><br />
</td>
        <td><br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><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><br />
</td>
        <td><br />
</td>
        <td><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>

@@ 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:guest|guest]] and made on <tt>2011-08-28 03:12:36 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-29 04:14:25 UTC</tt>.<br>
-: The original revision id was <tt>248869459</tt>.<br>
+: The original revision id was <tt>249049467</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>
 <h4>Original Wikitext content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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:
-||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||= scale || g in cents || 2g || 3g || 4g || Comments ||
+||||||||||||||||||||~ 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 ||   ||
+|| 2\5 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||= 1 0 1 1 0 1 0 1 || 480.000 || 960.000 || 240.000 || 720.000 ||=   ||
-||   ||   ||   ||   ||   ||   ||   ||   ||   || 21\53 ||= 10 1 10 10 1 10 1 10 || 475.472 || 950.943 || 226.415 || 701.887 || Vulture/Buzzard is around here ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   || 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 ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   || 19\48 ||   ||= 9 1 9 9 1 9 1 9 || 475 ||   ||   ||   ||=   ||
-||   ||   ||   ||   ||   ||   ||   || 17\43 ||   ||   ||= 8 1 8 8 1 8 1 8 || 474.419 ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   ||   || 17\43 ||   ||   ||= 8 1 8 8 1 8 1 8 || 474.419 ||   ||   ||   ||=   ||
-||   ||   ||   ||   ||   ||   || 15\38 ||   ||   ||   ||= 7 1 7 7 1 7 1 7 || 473.684 ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 15\38 ||   ||   ||   ||= 7 1 7 7 1 7 1 7 || 473.684 ||   ||   ||   ||=   ||
-||   ||   ||   ||   ||   || 13\33 ||   ||   ||   ||   ||= 6 1 6 6 1 6 1 6 || 472.727 ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 13\33 ||   ||   ||   ||   ||= 6 1 6 6 1 6 1 6 || 472.727 ||   ||   ||   ||=   ||
-||   ||   ||   ||   || 11\28 ||   ||   ||   ||   ||   ||= 5 1 5 5 1 5 1 5 || 471.429 ||   ||   ||   ||   ||
+||   ||   ||   ||   || 11\28 ||   ||   ||   ||   ||   ||= 5 1 5 5 1 5 1 5 || 471.429 ||   ||   ||   ||=   ||
-||   ||   ||   || 9\23 ||   ||   ||   ||   ||   ||   ||= 4 1 4 4 1 4 1 4 || 469.565 || 939.130 || 208.696 || 678.261 ||   ||
+||   ||   ||   || 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 ||   ||
+||   ||   || 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 ||   ||
+||   ||   ||   || 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 ||   ||
+||   || 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 ||   ||
+||   ||   ||   || 13\34 ||   ||   ||   ||   ||   ||   ||= 5 3 5 5 3 5 3 5 || 458.824 || 917.647 || 176.471 || 635.294 ||=   ||
-||   ||   ||   ||   ||   || 34\89 ||   ||   ||   ||   ||= 13 8 13 13 8 13 8 13 || 458.427 ||   ||   ||   || Golden father ||
+||   ||   ||   ||   ||   || 34\89 ||   ||   ||   ||   ||= 13 8... || 458.427 ||   ||   ||   ||= Golden father ||
-||   ||   ||   ||   || 21\55 ||   ||   ||   ||   ||   ||= 8 5 8 8 5 8 5 8 || 458.182 ||   ||   ||   ||   ||
+||   ||   ||   ||   || 21\55 ||   ||   ||   ||   ||   ||= 8 5 8 8 5 8 5 8 || 458.182 ||   ||   ||   ||=   ||
-||   ||   || 8\21 ||   ||   ||   ||   ||   ||   ||   ||= 3 2 3 3 2 3 2 3 || 457.143 || 914.286 || 171.429 || 628.571 ||   ||
+||   ||   || 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 ||   ||
+||   ||   ||   || 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 ||   ||
+|| 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.</pre></div>
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