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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is the chromatic scale of the Sephiroth temperament explicated on the page for [[3L_7s|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.
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>2015-11-13 15:32:12 UTC</tt>.<br>
: The original revision id was <tt>566387165</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">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.
||~ &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;(Circle of fifths)&lt;/span&gt; ||~ &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;(ascending scale)&lt;/span&gt; ||~  ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X&lt;/span&gt; || L L L L s L L L s L L L s || &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;Mode Tishrei&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;x-I&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L L L s L L L s L L L s L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Cheshvan&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L L s L L L s L L L s L L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Kislev&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;ii-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L s L L L s L L L s L L L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Tevet&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;s L L L s L L L s L L L L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Shvat&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;vii-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L L L s L L L s L L L L s&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Adar minor&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;iii-vii&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L L s L L L s L L L L s L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Adar major&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;xii-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L s L L L s L L L L s L L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Nisan&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;viii-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;s L L L s L L L L s L L L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Iyar&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;iv-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L L L s L L L L s L L L s&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Sivan&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L L s L L L L s L L L s L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Tammuz&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;L s L L L L s L L L s L L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Av&lt;/span&gt; ||
|| &lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;v-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px;"&gt;s L L L L s L L L s L L L&lt;/span&gt; || &lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Elul&lt;/span&gt; ||


|| 3/10 ||  || 360 ||
{| class="wikitable"
|| 16/53 ||  || 362.264 ||
|-
|| 13/43 ||   || 362.791 ||
! | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">(Circle of fifths)</span>
||   ||  || 363.487 ||
! | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">(ascending scale)</span>
|| 10/33 ||   || 363.818 ||
! |  
||   ||  || 363.976 ||
|-
||   || 27/89 || 364.045 ||
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X</span>
||   ||  || 364.112 ||
| | L L L L s L L L s L L L s
||   || 17/56 || 364.286 ||
| | <span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;">Mode Tishrei</span>
|| 7/23 ||   || 365.217 ||
|-
||   ||  || 365.904 ||
| | <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>
||   || 18/59 || 366.102 ||
| | <span style="font-size: 12.8000001907349px;">L L L s L L L s L L L s L</span>
||   ||  || 366.256 ||
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Cheshvan</span>
||   || 29/95 || 366.316 ||
|-
||   ||  || 366.414 ||
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II</span>
|| 11/36 ||   || 366.667 ||
| | <span style="font-size: 12.8000001907349px;">L L s L L L s L L L s L L</span>
|| 15/49 ||  || 367.347 ||
| | <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">Kislev</span>
|| 19/62 ||   || 367.742 ||
|-
|| 4/13 ||  || 369.231 ||</pre></div>
| | <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>
<h4>Original HTML content:</h4>
| | <span style="font-size: 12.8000001907349px;">L s L L L s L L L s L L L</span>
<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;10L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is the chromatic scale of the Sephiroth temperament explicated on the page for &lt;a class="wiki_link" href="/3L%207s"&gt;3L 7s&lt;/a&gt;. 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 &amp;quot;Luach&amp;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.&lt;br /&gt;
| | <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>
|}


 
{| class="wikitable"
&lt;table class="wiki_table"&gt;
|-
    &lt;tr&gt;
| | 3/10
        &lt;th&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;(Circle of fifths)&lt;/span&gt;&lt;br /&gt;
| |
&lt;/th&gt;
| | 360
        &lt;th&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;(ascending scale)&lt;/span&gt;&lt;br /&gt;
|-
&lt;/th&gt;
| | 16/53
        &lt;th&gt;&lt;br /&gt;
| |
&lt;/th&gt;
| | 362.264
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 13/43
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 362.791
        &lt;td&gt;L L L L s L L L s L L L s&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;Mode Tishrei&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 363.487
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 10/33
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;x-I&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 363.818
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L L L s L L L s L L L s L&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Cheshvan&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 363.976
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II&lt;/span&gt;&lt;br /&gt;
| | 27/89
&lt;/td&gt;
| | 364.045
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L L s L L L s L L L s L L&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Kislev&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 364.112
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;ii-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI&lt;/span&gt;&lt;br /&gt;
| | 17/56
&lt;/td&gt;
| | 364.286
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L s L L L s L L L s L L L&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| | 7/23
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Tevet&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 365.217
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 365.904
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;s L L L s L L L s L L L L&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Shvat&lt;/span&gt;&lt;br /&gt;
| | 18/59
&lt;/td&gt;
| | 366.102
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;vii-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 366.256
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L L L s L L L s L L L L s&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Adar minor&lt;/span&gt;&lt;br /&gt;
| | 29/95
&lt;/td&gt;
| | 366.316
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;iii-vii&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 366.414
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L L s L L L s L L L L s L&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| | 11/36
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Adar major&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 366.667
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 15/49
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;xii-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 367.347
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L s L L L s L L L L s L L&lt;/span&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| | 19/62
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Nisan&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 367.742
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| | 4/13
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;viii-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 369.231
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;s L L L s L L L L s L L L&lt;/span&gt;&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Iyar&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;iv-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L L L s L L L L s L L L s&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Sivan&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L L s L L L L s L L L s L&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Tammuz&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;L s L L L L s L L L s L L&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Av&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.6000003814697px;"&gt;v-&lt;/span&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px;"&gt;s L L L L s L L L s L L L&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;"&gt;Elul&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;3/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;360&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;362.264&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;362.791&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363.487&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363.818&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;363.976&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364.045&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364.112&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364.286&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;365.217&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;365.904&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;366.102&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;366.256&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29/95&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;366.316&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;366.414&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;366.667&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;367.347&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19/62&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;367.742&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &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;369.231&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

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)
I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X L L L L s L L L s L L L s Mode Tishrei
x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI L L L s L L L s L L L s L Cheshvan
vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II L L s L L L s L L L s L L Kislev
ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI L s L L L s L L L s L L L Tevet
xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII s L L L s L L L s L L L L Shvat
vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III L L L s L L L s L L L L s Adar minor
iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII L L s L L L s L L L L s L Adar major
xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII L s L L L s L L L L s L L Nisan
viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV s L L L s L L L L s L L L Iyar
iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII L L L s L L L L s L L L s Sivan
xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX L L s L L L L s L L L s L Tammuz
ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V L s L L L L s L L L s L L Av
v-ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I s L L L L s L L L s L L L Elul
3/10 360
16/53 362.264
13/43 362.791
363.487
10/33 363.818
363.976
27/89 364.045
364.112
17/56 364.286
7/23 365.217
365.904
18/59 366.102
366.256
29/95 366.316
366.414
11/36 366.667
15/49 367.347
19/62 367.742
4/13 369.231
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