3L 10s: Difference between revisions

Revision as of 23:46, 6 June 2012

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 2012-06-06 23:46:56 UTC.

The original revision id was 343420642.

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 scale, though it belongs to magic and würschmidt temperaments, is functionally identical to a compromise between the meantone/superpyth diatonic and chromatic scales. However, meantone and superpyth chords are slightly more complex and less accurate because 3125/3072, which is nearly 1/41 of the octave, is tempered out instead of 81/80 or 64/63. As a magic scale, it is uneven enough to fall within the region of optimal melodic tunings for magic[13] (L:s = sqrt(6) to 6-sqrt(6)). Because of this property, magic[13] is a good 19 tone mode for people who want to explore new sounds without having to give up using strongly harmonic fifths (3/2 +/- ~cbrt(145/143)) for building consonant chords.

Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.

|| 1/3 ||   ||   ||   ||   ||   ||   ||   || 800 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 10/31 ||   || 735.48387 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   || 9/28 ||   ||   || 728.57143 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 17/53 ||   || [[tel:724.5283|724.5283]] ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   || 8/25 ||   ||   ||   || 720 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 23/72 ||   || 716.__6__ ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   || 15/47 ||   ||   || 714.89362 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 22/69 ||   || 713.04348 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   || 7/22 ||   ||   ||   ||   || 709.__09__ ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 27/85 ||   || 705.88235 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   || 20/63 ||   ||   || 704.761905 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 33/104 ||   || 703.84615 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   || 13/41 ||   ||   ||   || 702.__43902__ ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 32/101 ||   || 700.__9900__ ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   || 19/60 ||   ||   || 700 ||= Optimal patent val for 5-limit magic ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 25/79 ||   || 698.73418 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   || 6/19 ||   ||   ||   ||   ||   || 694.73684 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 29/92 ||   || 691.30435 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   || 23/73 ||   ||   || 690.41096 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 40/127 ||   || 689.76378 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   || 17/54 ||   ||   ||   || 688.__8__ ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 45/143 ||   || 688.11189 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   || 28/89 ||   ||   || 687.64045 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 39/124 ||   || 687.09677 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   || 11/35 ||   ||   ||   ||   || 685.__714285__ ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 38/121 ||   || 684.29752 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   || 27/86 ||   ||   || 683.72093 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 43/137 ||   || 683.21168 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   || 16/51 ||   ||   ||   || 682.35294 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 37/118 ||   || 681.35593 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   || 21/67 ||   ||   || 680.597015 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   ||   ||   ||   ||   ||   || 26/83 ||   || 679.51807 ||   ||
||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
||   || 5/16 ||   ||   ||   ||   ||   ||   || 675 ||= Boundary of propriety
(Smaller generators are proper) ||
||   ||   ||   ||   ||   ||   || 29/93 ||   || 670.96774 ||   ||
||   ||   ||   ||   ||   || 24/77 ||   ||   || 670.12987 ||=   ||
||   ||   ||   ||   ||   ||   || 43/138 ||   || 669.56522 ||   ||
||   ||   ||   ||   || 19/61 ||   ||   ||   || 668.52459 ||=   ||
||   ||   ||   ||   ||   ||   || 52/167 ||   || 668.26347 ||   ||
||   ||   ||   ||   ||   || 33/106 ||   ||   || 667.92452 ||=   ||
||   ||   ||   ||   ||   ||   || 47/151 ||   || 667.54967 ||   ||
||   ||   ||   || 14/45 ||   ||   ||   ||   || 666.__6__ ||=   ||
||   ||   ||   ||   ||   ||   || 51/164 ||   || 665.__85365__ ||   ||
||   ||   ||   ||   ||   || 37/119 ||   ||   || 665.54622 ||=   ||
||   ||   ||   ||   ||   ||   || 60/193 ||   || 665.28497 ||   ||
||   ||   ||   ||   || 23/74 ||   ||   ||   || 664.__864__ ||=   ||
||   ||   ||   ||   ||   ||   || 55/177 ||   || 664.40678 ||   ||
||   ||   ||   ||   ||   || 32/103 ||   ||   || 664.07767 ||=   ||
||   ||   ||   ||   ||   ||   || 41/132 ||   || 663.__63__ ||   ||
||   ||   || 9/29 ||   ||   ||   ||   ||   || 662.068965 ||=   ||
||   ||   ||   || 13/42 ||   ||   ||   ||   || 657.14286 ||=   ||
|| 4/13 ||   ||   ||   ||   ||   ||   ||   || 646.15385 ||=   ||

Original HTML content:

<html><head><title>3L 10s</title></head><body>This scale, though it belongs to magic and würschmidt temperaments, is functionally identical to a compromise between the meantone/superpyth diatonic and chromatic scales. However, meantone and superpyth chords are slightly more complex and less accurate because 3125/3072, which is nearly 1/41 of the octave, is tempered out instead of 81/80 or 64/63. As a magic scale, it is uneven enough to fall within the region of optimal melodic tunings for magic[13] (L:s = sqrt(6) to 6-sqrt(6)). Because of this property, magic[13] is a good 19 tone mode for people who want to explore new sounds without having to give up using strongly harmonic fifths (3/2 +/- ~cbrt(145/143)) for building consonant chords.<br />
<br />
Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.<br />
<br />


<table class="wiki_table">
    <tr>
        <td>1/3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>800<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10/31<br />
</td>
        <td><br />
</td>
        <td>735.48387<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9/28<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>728.57143<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17/53<br />
</td>
        <td><br />
</td>
        <td><a class="wiki_link" href="http://tel.wikispaces.com/724.5283">724.5283</a><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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8/25<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>720<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>23/72<br />
</td>
        <td><br />
</td>
        <td>716.<u>6</u><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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>15/47<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>714.89362<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>22/69<br />
</td>
        <td><br />
</td>
        <td>713.04348<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7/22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>709.<u>09</u><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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>27/85<br />
</td>
        <td><br />
</td>
        <td>705.88235<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>20/63<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>704.761905<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>33/104<br />
</td>
        <td><br />
</td>
        <td>703.84615<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13/41<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>702.<u>43902</u><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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>32/101<br />
</td>
        <td><br />
</td>
        <td>700.<u>9900</u><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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>19/60<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>700<br />
</td>
        <td style="text-align: center;">Optimal patent val for 5-limit magic<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>25/79<br />
</td>
        <td><br />
</td>
        <td>698.73418<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>6/19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>694.73684<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
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</td>
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</td>
    </tr>
    <tr>
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</td>
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</td>
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</td>
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</td>
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</td>
        <td><br />
</td>
        <td>29/92<br />
</td>
        <td><br />
</td>
        <td>691.30435<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>23/73<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>690.41096<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>40/127<br />
</td>
        <td><br />
</td>
        <td>689.76378<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17/54<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>688.<u>8</u><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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>45/143<br />
</td>
        <td><br />
</td>
        <td>688.11189<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>28/89<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>687.64045<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>39/124<br />
</td>
        <td><br />
</td>
        <td>687.09677<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11/35<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>685.<u>714285</u><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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>38/121<br />
</td>
        <td><br />
</td>
        <td>684.29752<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>27/86<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>683.72093<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>43/137<br />
</td>
        <td><br />
</td>
        <td>683.21168<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>16/51<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>682.35294<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>37/118<br />
</td>
        <td><br />
</td>
        <td>681.35593<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>21/67<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>680.597015<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>26/83<br />
</td>
        <td><br />
</td>
        <td>679.51807<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><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5/16<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>675<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>29/93<br />
</td>
        <td><br />
</td>
        <td>670.96774<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>24/77<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>670.12987<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>43/138<br />
</td>
        <td><br />
</td>
        <td>669.56522<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>19/61<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>668.52459<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>52/167<br />
</td>
        <td><br />
</td>
        <td>668.26347<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>33/106<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>667.92452<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>47/151<br />
</td>
        <td><br />
</td>
        <td>667.54967<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>14/45<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>666.<u>6</u><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>51/164<br />
</td>
        <td><br />
</td>
        <td>665.<u>85365</u><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>37/119<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>665.54622<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>60/193<br />
</td>
        <td><br />
</td>
        <td>665.28497<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>23/74<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>664.<u>864</u><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>55/177<br />
</td>
        <td><br />
</td>
        <td>664.40678<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>32/103<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>664.07767<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>41/132<br />
</td>
        <td><br />
</td>
        <td>663.<u>63</u><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>9/29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>662.068965<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13/42<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>657.14286<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>4/13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>646.15385<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

</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:JosephRuhf|JosephRuhf]] and made on <tt>2012-06-06 00:37:00 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-06-06 23:46:56 UTC</tt>.<br>
-: The original revision id was <tt>343054540</tt>.<br>
+: The original revision id was <tt>343420642</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>
@@ Line 10: / Line 10: @@
 Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.
-|| 1/3 ||   ||   ||   ||   ||   ||   || 800 ||=   ||
+|| 1/3 ||   ||   ||   ||   ||   ||   ||   || 800 ||=   ||
-||   ||   ||   ||   ||   ||   || 10/31 || 735.48387 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   ||   || 9/28 ||   || 728.57143 ||=   ||
+||   ||   ||   ||   ||   ||   || 10/31 ||   || 735.48387 ||=   ||
-||   ||   ||   ||   ||   ||   || 17/53 || 724.5283 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   || 8/25 ||   ||   || 720 ||=   ||
+||   ||   ||   ||   ||   || 9/28 ||   ||   || 728.57143 ||=   ||
-||   ||   ||   ||   ||   ||   || 23/72 || 716.__6__ ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   ||   || 15/47 ||   || 714.89362 ||=   ||
+||   ||   ||   ||   ||   ||   || 17/53 ||   || [[tel:724.5283|724.5283]] ||=   ||
-||   ||   ||   ||   ||   ||   || 22/69 || 713.04348 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   || 7/22 ||   ||   ||   || 709.__09__ ||=   ||
+||   ||   ||   ||   || 8/25 ||   ||   ||   || 720 ||=   ||
-||   ||   ||   ||   ||   ||   || 27/85 || 705.88235 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   ||   || 20/63 ||   || 704.761905 ||=   ||
+||   ||   ||   ||   ||   ||   || 23/72 ||   || 716.__6__ ||   ||
-||   ||   ||   ||   ||   ||   || 33/104 || 703.84615 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   || 13/41 ||   ||   || 702.__43902__ ||=   ||
+||   ||   ||   ||   ||   || 15/47 ||   ||   || 714.89362 ||=   ||
-||   ||   ||   ||   ||   ||   || 32/101 || 700.__9900__ ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   ||   || 19/60 ||   || 700 ||= Optimal patent val for 5-limit magic ||
+||   ||   ||   ||   ||   ||   || 22/69 ||   || 713.04348 ||   ||
-||   ||   ||   ||   ||   ||   || 25/79 || 698.73418 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   || 6/19 ||   ||   ||   ||   || 694.73684 ||=   ||
+||   ||   ||   || 7/22 ||   ||   ||   ||   || 709.__09__ ||=   ||
-||   ||   ||   ||   ||   ||   || 29/92 || 691.30435 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   ||   || 23/73 ||   || 690.41096 ||=   ||
+||   ||   ||   ||   ||   ||   || 27/85 ||   || 705.88235 ||   ||
-||   ||   ||   ||   ||   ||   || 40/127 || 689.76378 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   || 17/54 ||   ||   || 688.__8__ ||=   ||
+||   ||   ||   ||   ||   || 20/63 ||   ||   || 704.761905 ||=   ||
-||   ||   ||   ||   ||   ||   || 45/143 || 688.11189 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   ||   || 28/89 ||   || 687.64045 ||=   ||
+||   ||   ||   ||   ||   ||   || 33/104 ||   || 703.84615 ||   ||
-||   ||   ||   ||   ||   ||   || 39/124 || 687.09677 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   || 11/35 ||   ||   ||   || 685.__714285__ ||=   ||
+||   ||   ||   ||   || 13/41 ||   ||   ||   || 702.__43902__ ||=   ||
-||   ||   ||   ||   ||   ||   || 38/121 || 684.29752 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   ||   || 27/86 ||   || 683.72093 ||=   ||
+||   ||   ||   ||   ||   ||   || 32/101 ||   || 700.__9900__ ||   ||
-||   ||   ||   ||   ||   ||   || 43/137 || 683.21168 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   || 16/51 ||   ||   || 682.35294 ||=   ||
+||   ||   ||   ||   ||   || 19/60 ||   ||   || 700 ||= Optimal patent val for 5-limit magic ||
-||   ||   ||   ||   ||   ||   || 37/118 || 681.35593 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   ||   ||   ||   ||   || 21/67 ||   || 680.597015 ||=   ||
+||   ||   ||   ||   ||   ||   || 25/79 ||   || 698.73418 ||   ||
-||   ||   ||   ||   ||   ||   || 26/83 || 679.51807 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
-||   || 5/16 ||   ||   ||   ||   ||   || 675 ||= Boundary of propriety
+||   ||   || 6/19 ||   ||   ||   ||   ||   || 694.73684 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 29/92 ||   || 691.30435 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 23/73 ||   ||   || 690.41096 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 40/127 ||   || 689.76378 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   || 17/54 ||   ||   ||   || 688.__8__ ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 45/143 ||   || 688.11189 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 28/89 ||   ||   || 687.64045 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 39/124 ||   || 687.09677 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   || 11/35 ||   ||   ||   ||   || 685.__714285__ ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 38/121 ||   || 684.29752 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 27/86 ||   ||   || 683.72093 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 43/137 ||   || 683.21168 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   || 16/51 ||   ||   ||   || 682.35294 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 37/118 ||   || 681.35593 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 21/67 ||   ||   || 680.597015 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   ||   || 26/83 ||   || 679.51807 ||   ||
+||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
+||   || 5/16 ||   ||   ||   ||   ||   ||   || 675 ||= Boundary of propriety
 (Smaller generators are proper) ||
-||   ||   ||   ||   ||   ||   || 29/93 || 670.96774 ||   ||
+||   ||   ||   ||   ||   ||   || 29/93 ||   || 670.96774 ||   ||
-||   ||   ||   ||   ||   || 24/77 ||   || 670.12987 ||=   ||
+||   ||   ||   ||   ||   || 24/77 ||   ||   || 670.12987 ||=   ||
-||   ||   ||   ||   ||   ||   || 43/138 || 669.56522 ||   ||
+||   ||   ||   ||   ||   ||   || 43/138 ||   || 669.56522 ||   ||
-||   ||   ||   ||   || 19/61 ||   ||   || 668.52459 ||=   ||
+||   ||   ||   ||   || 19/61 ||   ||   ||   || 668.52459 ||=   ||
-||   ||   ||   ||   ||   ||   || 52/167 || 668.26347 ||   ||
+||   ||   ||   ||   ||   ||   || 52/167 ||   || 668.26347 ||   ||
-||   ||   ||   ||   ||   || 33/106 ||   || 667.92452 ||=   ||
+||   ||   ||   ||   ||   || 33/106 ||   ||   || 667.92452 ||=   ||
-||   ||   ||   ||   ||   ||   || 47/151 || 667.54967 ||   ||
+||   ||   ||   ||   ||   ||   || 47/151 ||   || 667.54967 ||   ||
-||   ||   ||   || 14/45 ||   ||   ||   || 666.__6__ ||=   ||
+||   ||   ||   || 14/45 ||   ||   ||   ||   || 666.__6__ ||=   ||
-||   ||   ||   ||   ||   ||   || 51/164 || 665.__85365__ ||   ||
+||   ||   ||   ||   ||   ||   || 51/164 ||   || 665.__85365__ ||   ||
-||   ||   ||   ||   ||   || 37/119 ||   || 665.54622 ||=   ||
+||   ||   ||   ||   ||   || 37/119 ||   ||   || 665.54622 ||=   ||
-||   ||   ||   ||   ||   ||   || 60/193 || 665.28497 ||   ||
+||   ||   ||   ||   ||   ||   || 60/193 ||   || 665.28497 ||   ||
-||   ||   ||   ||   || 23/74 ||   ||   || 664.__864__ ||=   ||
+||   ||   ||   ||   || 23/74 ||   ||   ||   || 664.__864__ ||=   ||
-||   ||   ||   ||   ||   ||   || 55/177 || 664.40678 ||   ||
+||   ||   ||   ||   ||   ||   || 55/177 ||   || 664.40678 ||   ||
-||   ||   ||   ||   ||   || 32/103 ||   || 664.07767 ||=   ||
+||   ||   ||   ||   ||   || 32/103 ||   ||   || 664.07767 ||=   ||
-||   ||   ||   ||   ||   ||   || 41/132 || 663.__63__ ||   ||
+||   ||   ||   ||   ||   ||   || 41/132 ||   || 663.__63__ ||   ||
-||   ||   || 9/29 ||   ||   ||   ||   || 662.068965 ||=   ||
+||   ||   || 9/29 ||   ||   ||   ||   ||   || 662.068965 ||=   ||
-||   ||   ||   || 13/42 ||   ||   ||   || 657.14286 ||=   ||
+||   ||   ||   || 13/42 ||   ||   ||   ||   || 657.14286 ||=   ||
-|| 4/13 ||   ||   ||   ||   ||   ||   || 646.15385 ||=   ||</pre></div>
+|| 4/13 ||   ||   ||   ||   ||   ||   ||   || 646.15385 ||=   ||</pre></div>
 <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;3L 10s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This scale, though it belongs to magic and würschmidt temperaments, is functionally identical to a compromise between the meantone/superpyth diatonic and chromatic scales. However, meantone and superpyth chords are slightly more complex and less accurate because 3125/3072, which is nearly 1/41 of the octave, is tempered out instead of 81/80 or 64/63. As a magic scale, it is uneven enough to fall within the region of optimal melodic tunings for magic[13] (L:s = sqrt(6) to 6-sqrt(6)). Because of this property, magic[13] is a good 19 tone mode for people who want to explore new sounds without having to give up using strongly harmonic fifths (3/2 +/- ~cbrt(145/143)) for building consonant chords.&lt;br /&gt;
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@@ Line 224: / Line 424: @@
 &lt;/td&gt;
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+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
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          &lt;td&gt;713.04348&lt;br /&gt;
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@@ Line 238: / Line 462: @@
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+&lt;/td&gt;
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@@ Line 248: / Line 474: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 264: / Line 512: @@
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@@ Line 282: / Line 554: @@
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+&lt;/td&gt;
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@@ Line 288: / Line 562: @@
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@@ Line 304: / Line 600: @@
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+&lt;/td&gt;
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@@ Line 320: / Line 640: @@
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+&lt;/td&gt;
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@@ Line 328: / Line 650: @@
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@@ Line 344: / Line 688: @@
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+&lt;/td&gt;
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@@ Line 362: / Line 730: @@
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@@ Line 368: / Line 738: @@
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          &lt;td style="text-align: center;"&gt;Optimal patent val for 5-limit magic&lt;br /&gt;
+&lt;/td&gt;
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@@ Line 384: / Line 776: @@
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@@ Line 396: / Line 812: @@
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+&lt;/td&gt;
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@@ Line 408: / Line 826: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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      &lt;/tr&gt;
@@ Line 424: / Line 864: @@
 &lt;/td&gt;
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+&lt;/td&gt;
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@@ Line 442: / Line 906: @@
 &lt;/td&gt;
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 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 448: / Line 914: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 464: / Line 952: @@
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+&lt;/td&gt;
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@@ Line 480: / Line 992: @@
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 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 488: / Line 1,002: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 504: / Line 1,040: @@
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@@ Line 522: / Line 1,082: @@
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@@ Line 528: / Line 1,090: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 544: / Line 1,128: @@
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@@ Line 558: / Line 1,166: @@
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          &lt;td&gt;11/35&lt;br /&gt;
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@@ Line 568: / Line 1,178: @@
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          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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@@ Line 584: / Line 1,216: @@
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          &lt;td&gt;684.29752&lt;br /&gt;
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@@ Line 602: / Line 1,258: @@
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@@ Line 608: / Line 1,266: @@
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@@ Line 624: / Line 1,304: @@
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@@ Line 640: / Line 1,344: @@
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@@ Line 648: / Line 1,354: @@
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@@ Line 682: / Line 1,434: @@
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@@ Line 688: / Line 1,442: @@
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@@ Line 704: / Line 1,480: @@
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@@ Line 714: / Line 1,514: @@
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@@ Line 745: / Line 1,547: @@
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@@ Line 763: / Line 1,567: @@
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@@ Line 785: / Line 1,591: @@
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@@ Line 801: / Line 1,609: @@
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          &lt;td&gt;19/61&lt;br /&gt;
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@@ Line 825: / Line 1,635: @@
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@@ Line 865: / Line 1,679: @@
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@@ Line 879: / Line 1,695: @@
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          &lt;td&gt;14/45&lt;br /&gt;
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@@ Line 905: / Line 1,723: @@
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          &lt;td&gt;665.&lt;u&gt;85365&lt;/u&gt;&lt;br /&gt;
@@ Line 923: / Line 1,743: @@
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@@ Line 945: / Line 1,767: @@
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@@ Line 961: / Line 1,785: @@
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@@ Line 985: / Line 1,811: @@
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          &lt;td&gt;664.40678&lt;br /&gt;
@@ Line 1,003: / Line 1,831: @@
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@@ Line 1,025: / Line 1,855: @@
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@@ Line 1,037: / Line 1,869: @@
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+&lt;/td&gt;
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@@ Line 1,059: / Line 1,893: @@
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+&lt;/td&gt;
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          &lt;td&gt;&lt;br /&gt;
@@ Line 1,073: / Line 1,909: @@
      &lt;tr&gt;
          &lt;td&gt;4/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;

3L 10s: Difference between revisions

Revision as of 23:46, 6 June 2012

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