5L 6s: Difference between revisions

Revision as of 14:05, 9 November 2015

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 2015-11-09 14:05:59 UTC.

The original revision id was 565763613.

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 pattern, with a generator between 2\11 (218.182 cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.

|| 1\5 ||   ||   ||   ||   ||   ||   ||   ||   || 240 ||=   ||
||   ||   ||   ||   ||   ||   ||   || 9\46 ||   || 234.783 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   || 17\87 || 234.483 ||= Rodan is around here ||
||   ||   ||   ||   ||   ||   || 8\41 ||   ||   || 234.146 ||=   ||
||   ||   ||   ||   ||   ||   ||   || 15\77 ||   || 233.766 ||= Slendric is around here ||
||   ||   ||   ||   ||   || 7\36 ||   ||   ||   || 233.333 ||=   ||
||   ||   ||   ||   ||   ||   || 13\67 ||   ||   || 232.836 ||=   ||
||   ||   ||   ||   || 6\31 ||   ||   ||   ||   || 232.258 ||= Cynder/mothra is around here ||
||   ||   ||   ||   ||   || 11\57 ||   ||   ||   || 231.579 ||=   ||
||   ||   ||   || 5\26 ||   ||   ||   ||   ||   || 230.769 ||=   ||
||   ||   ||   ||   || 9\47 ||   ||   ||   ||   || 229.787 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 228.944 ||   ||
||   ||   || 4\21 ||   ||   ||   ||   ||   ||   || 228.571 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 227.75 ||   ||
||   ||   ||   ||   || 11\58 ||   ||   ||   ||   || 227.586 ||   ||
||   ||   ||   ||   ||   ||   || 29\153 ||   ||   || 227.451 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 76\401 || 227.431 ||   ||
||   ||   ||   ||   ||   ||   ||   || 47\248 ||   || 227.419 ||   ||
||   ||   ||   ||   ||   || 18\95 ||   ||   ||   || 227.368 ||   ||
||   ||   ||   || 7\37 ||   ||   ||   ||   ||   || 227.027 ||=   ||
||   || 3\16 ||   ||   ||   ||   ||   ||   ||   || 225 ||= Boundary of propriety
(smaller generators are proper) ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 223.692 ||   ||
||   ||   ||   || 8\43 ||   ||   ||   ||   ||   || 223.256 ||=   ||
||   ||   ||   ||   ||   || 21\113 ||   ||   ||   || 223.009 ||   ||
||   ||   ||   ||   ||   ||   ||   || 55\296 ||   || 222.973 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 89\479 || 222.9645 ||   ||
||   ||   ||   ||   ||   ||   || 34\183 ||   ||   || 222.951 ||   ||
||   ||   ||   ||   || 13\70 ||   ||   ||   ||   || 222.857 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   || 222.6765 ||   ||
||   ||   || 5\27 ||   ||   ||   ||   ||   ||   || 222.222 ||=   ||
||   ||   ||   || 7\38 ||   ||   ||   ||   ||   || 221.035 ||=   ||
||   ||   ||   ||   || 9\49 ||   ||   ||   ||   || 220.408 ||=   ||
||   ||   ||   ||   ||   || 11\60 ||   ||   ||   || 220 ||   ||
||   ||   ||   ||   ||   ||   || 13\71 ||   ||   || 219.718 ||   ||
||   ||   ||   ||   ||   ||   ||   || 15\82 ||   || 219.512 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   || 17\93 || 219.355 ||   ||
|| 2\11 ||   ||   ||   ||   ||   ||   ||   ||   || 218.182 ||= Machine is around here ||

Original HTML content:

<html><head><title>5L 6s</title></head><body>This pattern, with a generator between 2\11 (218.182 cents) and 1\5 (240), has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root.<br />
<br />


<table class="wiki_table">
    <tr>
        <td>1\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>240<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>9\46<br />
</td>
        <td><br />
</td>
        <td>234.783<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>17\87<br />
</td>
        <td>234.483<br />
</td>
        <td style="text-align: center;">Rodan 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>8\41<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>234.146<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>15\77<br />
</td>
        <td><br />
</td>
        <td>233.766<br />
</td>
        <td style="text-align: center;">Slendric is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\36<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>233.333<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>13\67<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>232.836<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6\31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>232.258<br />
</td>
        <td style="text-align: center;">Cynder/mothra is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\57<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>231.579<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\26<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>230.769<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9\47<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>229.787<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>228.944<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\21<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>228.571<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>227.75<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\58<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>227.586<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>29\153<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>227.451<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>76\401<br />
</td>
        <td>227.431<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>47\248<br />
</td>
        <td><br />
</td>
        <td>227.419<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>18\95<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>227.368<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\37<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>227.027<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>3\16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>225<br />
</td>
        <td style="text-align: center;">Boundary of propriety<br />
(smaller generators are proper)<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>223.692<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8\43<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>223.256<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>21\113<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>223.009<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>55\296<br />
</td>
        <td><br />
</td>
        <td>222.973<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>89\479<br />
</td>
        <td>222.9645<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>34\183<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>222.951<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13\70<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>222.857<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>222.6765<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\27<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>222.222<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\38<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>221.035<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9\49<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>220.408<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>11\60<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>220<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\71<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>219.718<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>15\82<br />
</td>
        <td><br />
</td>
        <td>219.512<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>17\93<br />
</td>
        <td>219.355<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2\11<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>218.182<br />
</td>
        <td style="text-align: center;">Machine is around here<br />
</td>
    </tr>
</table>

</body></html>

5L 6s: Difference between revisions

Revision as of 14:05, 9 November 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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