10L 3s

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This revision was by author JosephRuhf and made on 2014-11-27 18:42:54 UTC.
The original revision id was 532960614.
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Original Wikitext content:

This is the chromatic scale of the Sephiroth temperament explicated on the page for [[3L 7s]]. However, a tempered-flat chain of the 13th harmonic really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" modes the degrees are to be taken as numbered is descending order so that the the tempered 13th harmonic is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.
(Circle of fifths) (ascending scale)
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X</span> || L L L L s L L L s L L L s || <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">Mode Tishrei</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">x-I</span><span style="font-size: 12.8000001907349px;">-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI</span> || <span style="font-size: 12.8000001907349px;">L L L s L L L s L L L s L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Cheshvan</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II</span> || <span style="font-size: 12.8000001907349px;">L L s L L L s L L L s L L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Kislev</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">ii-</span><span style="font-size: 12.8000001907349px;">vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI</span> || <span style="font-size: 12.8000001907349px;">L s L L L s L L L s L L L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Tevet</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII</span> || <span style="font-size: 12.8000001907349px;">s L L L s L L L s L L L L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Shvat</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">vii-</span><span style="font-size: 12.8000001907349px;">xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III</span> || <span style="font-size: 12.8000001907349px;">L L L s L L L s L L L L s</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Adar minor</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">iii-vii</span><span style="font-size: 12.8000001907349px;">-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII</span> || <span style="font-size: 12.8000001907349px;">L L s L L L s L L L L s L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Adar major</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">xii-</span><span style="font-size: 12.8000001907349px;">iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII</span> || <span style="font-size: 12.8000001907349px;">L s L L L s L L L L s L L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Nisan</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">viii-</span><span style="font-size: 12.8000001907349px;">xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV</span> || <span style="font-size: 12.8000001907349px;">s L L L s L L L L s L L L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Iyar</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">iv-</span><span style="font-size: 12.8000001907349px;">viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII</span> || <span style="font-size: 12.8000001907349px;">L L L s L L L L s L L L s</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Sivan</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX</span> || <span style="font-size: 12.8000001907349px;">L L s L L L L s L L L s L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Tammuz</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V</span> || <span style="font-size: 12.8000001907349px;">L s L L L L s L L L s L L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Av</span> ||
|| <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">v-</span><span style="font-size: 12.8000001907349px;">ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I</span> || <span style="font-size: 12.8000001907349px;">s L L L L s L L L s L L L</span> || <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Elul</span> ||

|| 3/10 ||   || 360 ||
|| 16/53 ||   || 362 14/53 ||
|| 13/43 ||   || 362 34/43 ||
|| 10/33 ||   || 363 9/11 ||
||   || 17/56 || 364 2/7 ||
|| 7/23 ||   || 365 5/23 ||
|| 11/36 ||   || 366 2/3 ||
|| 15/49 ||   || 367 17/49 ||
|| 19/62 ||   || 367 18/31 ||
|| 4/13 ||   || 369 3/13 ||

Original HTML content:

<html><head><title>10L 3s</title></head><body>This is the chromatic scale of the Sephiroth temperament explicated on the page for <a class="wiki_link" href="/3L%207s">3L 7s</a>. However, a tempered-flat chain of the 13th harmonic really comes into its own as a distinct scale when extended to 13 tones. In these &quot;Luach&quot; modes the degrees are to be taken as numbered is descending order so that the the tempered 13th harmonic is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.<br />
(Circle of fifths) (ascending scale)<br />


<table class="wiki_table">
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X</span><br />
</td>
        <td>L L L L s L L L s L L L s<br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">Mode Tishrei</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">x-I</span><span style="font-size: 12.8000001907349px;">-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L L L s L L L s L L L s L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Cheshvan</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L L s L L L s L L L s L L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Kislev</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">ii-</span><span style="font-size: 12.8000001907349px;">vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L s L L L s L L L s L L L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Tevet</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">s L L L s L L L s L L L L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Shvat</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">vii-</span><span style="font-size: 12.8000001907349px;">xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L L L s L L L s L L L L s</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Adar minor</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">iii-vii</span><span style="font-size: 12.8000001907349px;">-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L L s L L L s L L L L s L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Adar major</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">xii-</span><span style="font-size: 12.8000001907349px;">iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L s L L L s L L L L s L L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Nisan</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">viii-</span><span style="font-size: 12.8000001907349px;">xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">s L L L s L L L L s L L L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Iyar</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">iv-</span><span style="font-size: 12.8000001907349px;">viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L L L s L L L L s L L L s</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Sivan</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L L s L L L L s L L L s L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Tammuz</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">L s L L L L s L L L s L L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Av</span><br />
</td>
    </tr>
    <tr>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">v-</span><span style="font-size: 12.8000001907349px;">ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px;">s L L L L s L L L s L L L</span><br />
</td>
        <td><span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Elul</span><br />
</td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <td>3/10<br />
</td>
        <td><br />
</td>
        <td>360<br />
</td>
    </tr>
    <tr>
        <td>16/53<br />
</td>
        <td><br />
</td>
        <td>362 14/53<br />
</td>
    </tr>
    <tr>
        <td>13/43<br />
</td>
        <td><br />
</td>
        <td>362 34/43<br />
</td>
    </tr>
    <tr>
        <td>10/33<br />
</td>
        <td><br />
</td>
        <td>363 9/11<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>17/56<br />
</td>
        <td>364 2/7<br />
</td>
    </tr>
    <tr>
        <td>7/23<br />
</td>
        <td><br />
</td>
        <td>365 5/23<br />
</td>
    </tr>
    <tr>
        <td>11/36<br />
</td>
        <td><br />
</td>
        <td>366 2/3<br />
</td>
    </tr>
    <tr>
        <td>15/49<br />
</td>
        <td><br />
</td>
        <td>367 17/49<br />
</td>
    </tr>
    <tr>
        <td>19/62<br />
</td>
        <td><br />
</td>
        <td>367 18/31<br />
</td>
    </tr>
    <tr>
        <td>4/13<br />
</td>
        <td><br />
</td>
        <td>369 3/13<br />
</td>
    </tr>
</table>

</body></html>
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