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5L 3s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| en = 5L 3s
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-05 11:45:02 UTC</tt>.<br>
| de =  
: The original revision id was <tt>565323793</tt>.<br>
| es =  
: The revision comment was: <tt></tt><br>
| ja =  
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| ko = 5L3s (Korean)
<h4>Original Wikitext content:</h4>
}}
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of [[5edo]] = 480¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this:
{{Infobox MOS
||||||||||||||||~ generator ||~ &lt;span style="display: block; text-align: center;"&gt;tetrachord&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;g in cents&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;2g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;3g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;4g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;Comments&lt;/span&gt; ||
| Neutral = 2L 6s
|| 2\5 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;1 0 1&lt;/span&gt; ||= 480.000 ||= 960.000 ||= 240.00 ||= &lt;span style="line-height: 15.6000003814697px;"&gt;720.000&lt;/span&gt; ||=  ||
}}
|| 21\53 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;10 1 10&lt;/span&gt; ||= 475.472 ||= 950.943 ||= 226.415 ||= 701.887 ||= &lt;span style="display: block; text-align: center;"&gt;Vulture/Buzzard is around here&lt;/span&gt; ||
: ''For the tritave-equivalent MOS structure with the same step pattern, see [[5L&nbsp;3s (3/1-equivalent)]].''
|| 19\48 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;9 1 9&lt;/span&gt; ||= 475 ||= 950 ||= 225 ||= 700 ||=  ||
{{MOS intro}}
|| 17\43 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;8 1 8&lt;/span&gt; ||= 474.419 ||= 948.837 ||= 223.256 ||= 697.674 ||=  ||
5L&nbsp;3s can be seen as a [[Warped diatonic|warped diatonic scale]], because it has one extra small step compared to diatonic ([[5L&nbsp;2s]]).
|| 15\38 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;7 1 7&lt;/span&gt; ||= 473.684 ||= 947.368 ||= 221.053 ||= 694.737 ||=  ||
|| 13\33 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;6 1 6&lt;/span&gt; ||= 472.727 ||= 945.455 ||= 218.181 ||= 690.909 ||=  ||
|| 11\28 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;5 1 5&lt;/span&gt; ||= 471.429 ||= 942.857 ||= 214.286 ||= 685.714 ||=  ||
|| 9\23 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;4 1 4&lt;/span&gt; ||= 469.565 ||= 939.130 ||= 208.696 ||= 678.261 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 4&lt;/span&gt; ||
||  ||  ||  ||  ||  ||  ||  ||  ||= pi 1 pi ||= 467.171 ||= 934.3425 ||= 201.514 ||= 668.685 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
|| 7\18 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;3 1 3&lt;/span&gt; ||= 466.667 ||= 933.333 ||= 200.000 ||= 666.667 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3&lt;/span&gt; ||
||  ||  ||  ||  ||  ||  ||  ||  ||= e 1 e ||= 465.535 ||= 931.069 ||= 196.604 ||= 662.139 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
||  ||  || 19\49 ||  ||  ||  ||  ||  ||= 8 3 8 ||= 465.306 ||= 930.612 ||= 195.918 ||= 661.2245 ||  ||
||  ||  ||  ||  || 50\129 ||  ||  ||  ||= 21 8 21 ||= 465.116 ||= 930.233 ||= 195.349 ||= 660.465 ||  ||
||  ||  ||  ||  ||  ||  || 131\338 ||  ||= 55 21 55 ||= 465.089 ||= 930.1775 ||= 195.266 ||= 660.335 ||  ||
||  ||  ||  ||  ||  ||  ||  || 212\547 ||= 89 34 89 ||= 465.082 ||= 930.1645 ||= 195.247 ||= 660.329 ||  ||
||  ||  ||  ||  ||  || 81\209 ||  ||  ||= 34 13 34 ||= 465.072 ||= 930.1435 ||= 195.215 ||= 660.287 ||  ||
||  ||  ||  || 31\80 ||  ||  ||  ||  ||= 13 5 13 ||= 465 ||= 930 ||= 195 ||= 660 ||  ||
||  || 12\31 ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;5 2 5&lt;/span&gt; ||= 464.516 ||= 929.032 ||= 193.549 ||= 658.065 ||=  ||
|| 5\13 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;2 1 2&lt;/span&gt; ||= 461.538 ||= 923.077 ||= 184.615 ||= 646.154 ||=  ||
||  ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="background-color: #ffffff;"&gt;√3 1 √3&lt;/span&gt; ||= 459.417 ||= 918.8345 ||= 178.252 ||= 637.669 ||  ||
||  || 13\34 ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;5 3 5&lt;/span&gt; ||= 458.824 ||= 917.647 ||= 176.471 ||= 635.294 ||=  ||
||  ||  ||  || 34\89 ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;13 8 13&lt;/span&gt; ||= 458.427 ||= 916.854 ||= 175.281 ||= 633.708 ||=  ||
||  ||  ||  ||  ||  || 89\233 ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;34 21 34&lt;/span&gt; ||= &lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;916.738&lt;/span&gt; ||= 175.107 ||= &lt;span style="line-height: 15.6000003814697px;"&gt;633.473&lt;/span&gt; ||=  ||
||  ||  ||  ||  ||  ||  ||  || 233\610 ||= &lt;span style="display: block; text-align: center;"&gt;89 55 89&lt;/span&gt; ||= 458.361 ||= 916.721 ||= 175.082 ||= 633.443 ||= &lt;span style="display: block; text-align: center;"&gt;Golden father&lt;/span&gt; ||
||  ||  ||  ||  ||  ||  || 144\377 ||  ||= &lt;span style="display: block; text-align: center;"&gt;55 34 55&lt;/span&gt; ||= 458.355 ||= 916.711 ||= 175.066 ||= 633.422 ||=  ||
||  ||  ||  ||  || 55\144 ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;21 13 21&lt;/span&gt; ||= 458.333 ||= 916.666 ||= 175 ||= 633.333 ||=  ||
||  ||  || 21\55 ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;8 5 8&lt;/span&gt; ||= 458.182 ||= 916.364 ||= 174.545 ||= 632.727 ||=  ||
||  ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;pi 1 pi&lt;/span&gt; ||= 457.883 ||= 915.777 ||= 173.665 ||= 631.553 ||  ||
|| 8\21 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;3 2 3&lt;/span&gt; ||= 457.143 ||= 914.286 ||= 171.429 ||= 628.571 ||= &lt;span style="display: block; text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt; ||
|| 11\29 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;4 3 4&lt;/span&gt; ||= 455.172 ||= 910.345 ||= 165.517 ||= 620.690 ||=  ||
|| 14\37 ||  ||  ||  ||  ||  ||  ||  ||= 5 4 5 ||= 454.054 ||= 908.108 ||= 162.162 ||= 616.216 ||  ||
|| 17\45 ||  ||  ||  ||  ||  ||  ||  ||= 6 5 6 ||= 453.333 ||= 906.667 ||= 160 ||= 613.333 ||  ||
|| 20\53 ||  ||  ||  ||  ||  ||  ||  ||= 7 6 7 ||= 452.83 ||= 905.66 ||= 158.491 ||= 611.321 ||  ||
|| 23\61 ||  ||  ||  ||  ||  ||  ||  ||= 8 7 8 ||= 452.459 ||= 904.918 ||= 157.377 ||= 609.836 ||  ||
|| 26\69 ||  ||  ||  ||  ||  ||  ||  ||= 9 8 9 ||= 452.174 ||= 904.348 ||= 156.522 ||= 608.696 ||  ||
|| 29\77 ||  ||  ||  ||  ||  ||  ||  ||= 10 9 10 ||= 451.948 ||= 903.896 ||= 155.844 ||= 607.792 ||  ||
|| 3\8 ||  ||  ||  ||  ||  ||  ||  ||= &lt;span style="display: block; text-align: center;"&gt;1 1 1&lt;/span&gt; ||= 450.000 ||= 900.000 ||= 150.000 ||= 600.000 ||=  ||
The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.</pre></div>
<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;5L 3s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; = 480¢) to 3\8 (three degrees of &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt; = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this:&lt;br /&gt;


== Name ==
{{TAMNAMS name}} 'Oneiro' is sometimes used as a shortened form.


&lt;table class="wiki_table"&gt;
'Father' is sometimes also used to denote 5L&nbsp;3s, but it's a misnomer, as [[father]] is technically an abstract [[regular temperament]] (although a very inaccurate one), not a generator range. There are father tunings which generate 3L&nbsp;5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate [[3L&nbsp;2s]].
    &lt;tr&gt;
        &lt;th colspan="8"&gt;generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;tetrachord&lt;/span&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;g in cents&lt;/span&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;2g&lt;/span&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;3g&lt;/span&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;4g&lt;/span&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;Comments&lt;/span&gt;&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2\5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1 0 1&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;480.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;960.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;240.00&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;720.000&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21\53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;10 1 10&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;475.472&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;950.943&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;226.415&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;701.887&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Vulture/Buzzard is around here&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19\48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;9 1 9&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;475&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;950&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;225&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;700&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17\43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;8 1 8&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;474.419&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;948.837&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;223.256&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;697.674&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15\38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;7 1 7&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;473.684&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;947.368&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;221.053&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;694.737&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13\33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;6 1 6&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;472.727&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;945.455&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;218.181&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;690.909&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11\28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;5 1 5&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;471.429&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;942.857&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;214.286&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;685.714&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9\23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;4 1 4&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;469.565&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;939.130&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;208.696&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;678.261&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = 4&lt;/span&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;pi 1 pi&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;467.171&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;934.3425&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;201.514&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;668.685&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;3 1 3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;466.667&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;933.333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;200.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;666.667&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = 3&lt;/span&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;e 1 e&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;465.535&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;931.069&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;196.604&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;662.139&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt;&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;19\49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8 3 8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;465.306&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;930.612&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;195.918&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;661.2245&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;50\129&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;21 8 21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;465.116&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;930.233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;195.349&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;660.465&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;131\338&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;55 21 55&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;465.089&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;930.1775&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;195.266&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;660.335&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;212\547&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;89 34 89&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;465.082&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;930.1645&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;195.247&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;660.329&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;81\209&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;34 13 34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;465.072&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;930.1435&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;195.215&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;660.287&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31\80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13 5 13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;465&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;930&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;195&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;660&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;5 2 5&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;464.516&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;929.032&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;193.549&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;658.065&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5\13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;2 1 2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;461.538&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;923.077&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;184.615&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;646.154&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff;"&gt;√3 1 √3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;459.417&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;918.8345&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;178.252&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;637.669&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13\34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;5 3 5&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;458.824&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;917.647&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;176.471&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;635.294&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;34\89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;13 8 13&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;458.427&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;916.854&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;175.281&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;633.708&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;89\233&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;34 21 34&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;916.738&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;175.107&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;633.473&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;233\610&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;89 55 89&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;458.361&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;916.721&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;175.082&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;633.443&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Golden father&lt;/span&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;144\377&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;55 34 55&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;458.355&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;916.711&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;175.066&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;633.422&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;55\144&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;21 13 21&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;458.333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;916.666&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;175&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;633.333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;21\55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;8 5 8&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;458.182&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;916.364&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;174.545&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;632.727&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;pi 1 pi&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;457.883&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;915.777&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;173.665&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;631.553&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;3 2 3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;457.143&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;914.286&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;171.429&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;628.571&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11\29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;4 3 4&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;455.172&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;910.345&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;165.517&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;620.690&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14\37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5 4 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;454.054&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;908.108&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;162.162&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;616.216&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17\45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6 5 6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;453.333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;906.667&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;160&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;613.333&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20\53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7 6 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;452.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;905.66&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;158.491&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;611.321&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23\61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8 7 8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;452.459&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;904.918&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;157.377&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;609.836&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26\69&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9 8 9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;452.174&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;904.348&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;156.522&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;608.696&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29\77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10 9 10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;451.948&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;903.896&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;155.844&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;607.792&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3\8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1 1 1&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;450.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;900.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;150.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;600.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


The only notable harmonic entropy minimum is Vulture/&lt;a class="wiki_link" href="/Hemifamity%20temperaments"&gt;Buzzard&lt;/a&gt;, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.&lt;/body&gt;&lt;/html&gt;</pre></div>
== Scale properties ==
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
==== Proposed mode names ====
The following names have been proposed for the modes of 5L 3s, and are named after cities in the Dreamlands.
{{MOS modes
| Mode Names=
Dylathian $
Ilarnekian $
Celephaïsian $
Ultharian $
Mnarian $
Kadathian $
Hlanithian $
Sarnathian $
| Collapsed=1
}}
 
== Tunings==
=== Simple tunings ===
The simplest tuning for 5L&nbsp;3s correspond to 13edo, 18edo, and 21edo, with step ratios 2:1, 3:1, and 3:2, respectively.
 
{{MOS tunings|JI Ratios=Int Limit: 30; Prime Limit: 19; Tenney Height: 7.7}}
 
=== Hypohard tunings ===
[[Hypohard]] oneirotonic tunings have step ratios between 2:1 and 3:1 and can be considered "meantone oneirotonic", sharing the following features with [[meantone]] diatonic tunings:
* The large step is a "meantone", around the range of [[10/9]] to [[9/8]].
* The major 2-mosstep is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third.
 
With step ratios between 5:2 and 2:1, the minor 2-mosstep is close to [[7/6]].
 
EDOs that are in the hypohard range include [[13edo]], [[18edo]], and [[31edo]], and are associated with [[5L 3s/Temperaments#A-Team|A-Team]] temperament.
* 13edo has characteristically small 1-mossteps of about 185{{c}}. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all hypohard tunings.
* 18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3{{c}}, a perfect 5-mosstep) and falling fifths (666.7{{c}}, a major 4-mosstep) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
* 31edo can be used to make the major 2-mosstep a near-just 5/4.
* [[44edo]] (generator {{nowrap|17\44 {{=}} 463.64{{c}}}}), [[57edo]] (generator {{nowrap|22\57 {{=}} 463.16{{c}}}}), and [[70edo]] (generator 27\70 {{=}} 462.857{{c}}}}) offer a compromise between 31edo's major third and 13edo's 11/8 and 13/8. In particular, 70edo has an essentially pure 13/8.
 
{{MOS tunings|Step Ratios=Hypohard|JI Ratios=Subgroup: 2.5.9.21; Int Limit:40; Complements Only: 1|Tolerance=15}}
 
=== Hyposoft tunings ===
[[Hyposoft]] oneirotonic tunings have step ratios between 3:2 and 2:1, which remains relatively unexplored. In these tunings,
* The large step of oneirotonic tends to be intermediate in size between [[10/9]] and [[11/10]]; the small step size is a semitone close to [[17/16]], about 92{{c}} to 114{{c}}.
* The major 2-mosstep (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342{{c}}) to 4\13 (369{{c}}).
 
* [[21edo]]'s P1-L1ms-L2ms-L4ms approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71{{c}}) and Baroque diatonic semitones (114.29{{c}}, close to quarter-comma meantone's 117.11{{c}}).
* [[34edo]]'s 9:10:11:13 is even better.
 
This set of JI identifications is associated with [[5L 3s/Temperaments#Petrtri|petrtri]] temperament. (P1-M1ms-P3ms could be said to approximate 5:11:13 in all soft-of-basic tunings, which is what "basic" [[petrtri]] temperament is.)
 
{{MOS tunings
| Step Ratios = Hyposoft
| JI Ratios =
1/1;
16/15;
10/9; 11/10;
13/11; 20/17;
11/9;
5/4;
13/10;
18/13; 32/23;
13/9; 23/16;
20/13;
8/5;
18/11;
22/13; 17/10;
9/5;
15/8;
2/1
}}
 
=== Parasoft and ultrasoft tunings ===
The range of oneirotonic tunings of step ratio between 6:5 and 3:2 is closely related to [[porcupine]] temperament; these tunings equate three oneirotonic large steps to a diatonic perfect fourth, i.e. they equate the oneirotonic large step to a [[porcupine]] generator. The chord 10:11:13 is very well approximated in 29edo.
 
{{MOS tunings
| Step Ratios = 6/5; 3/2; 4/3
| JI Ratios =
1/1;
14/13;
11/10;
9/8;
15/13;
13/11;
14/11;
13/10;
4/3;
15/11;
7/5;
10/7;
22/15;
3/2;
20/13;
11/7;
22/13;
26/15;
16/9;
20/11;
13/7;
2/1
}}
 
=== Parahard tunings ===
23edo oneiro combines the sound of neogothic tunings like [[46edo]] and the sounds of "superpyth" and "semaphore" scales. This is because 23edo oneirotonic has a large step of 208.7¢, same as [[46edo]]'s neogothic major second, and is both a warped [[22edo]] [[superpyth]] [[diatonic]] and a warped [[24edo]] [[semaphore]] [[semiquartal]] (and both nearby scales are [[superhard]] MOSes).
 
{{MOS tunings
| JI Ratios =
1/1;
21/17;
17/16;
14/11;
6/5;
21/16;
21/17;
34/21;
32/21;
5/3;
11/7;
32/17;
34/21;
2/1
| Step Ratios = 4/1
}}
 
=== Ultrahard tunings ===
{{Main|5L&nbsp;3s/Temperaments#Buzzard}}
 
[[Buzzard]] is a rank-2 temperament in the [[Step ratio|pseudocollapsed]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum.
 
In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into its own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well.
 
Beyond that, it's a question of which intervals you want to favor. [[53edo]] has an essentially perfect [[3/2]], [[58edo]] gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while [[63edo]] does the same for the basic 4:6:7 triad. You could in theory go up to [[83edo]] if you want to favor the [[7/4]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic.
 
{{MOS tunings
| JI Ratios =
1/1;
8/7;
13/10;
21/16;
3/2;
12/7, 22/13;
26/15;
49/25, 160/81;
2/1
| Step Ratios = 7/1; 10/1; 12/1
| Tolerance = 30
}}
 
== Approaches ==
* [[5L&nbsp;3s/Temperaments]]
 
== Samples ==
[[File:The Angels' Library edo.mp3]] [[:File:The Angels' Library edo.mp3|The Angels' Library]] by [[Inthar]] in the Sarnathian (23233233) mode of 21edo oneirotonic ([[:File:The Angels' Library Score.pdf|score]])
 
[[File:13edo Prelude in J Oneirominor.mp3]]
 
[[WT13C]] [[:File:13edo Prelude in J Oneirominor.mp3|Prelude II (J Oneirominor)]] ([[:File:13edo Prelude in J Oneirominor Score.pdf|score]]) – Simple two-part Baroque piece. It stays in oneirotonic even though it modulates to other keys a little.
 
[[File:13edo_1MC.mp3]]
 
(13edo, first 30 seconds is in J Celephaïsian)
 
[[File:A Moment of Respite.mp3]]
 
(13edo, L Ilarnekian)
 
[[File:Lunar Approach.mp3]]
 
(by [[Igliashon Jones]], 13edo, J Celephaïsian)
 
=== 13edo Oneirotonic Modal Studies ===
* [[File:Inthar-13edo Oneirotonic Studies 1 Dylathian.mp3]]: Tonal Study in Dylathian
* [[File:Inthar-13edo Oneirotonic Studies 2 Ultharian.mp3]]: Tonal Study in Ultharian
* [[File:Inthar-13edo Oneirotonic Studies 3 Hlanithian.mp3]]: Tonal Study in Hlanithian
* [[File:Inthar-13edo Oneirotonic Studies 4 Illarnekian.mp3]]: Tonal Study in Ilarnekian
* [[File:Inthar-13edo Oneirotonic Studies 5 Mnarian.mp3]]: Tonal Study in Mnarian
* [[File:Inthar-13edo Oneirotonic Studies 6 Sarnathian.mp3]]: Tonal Study in Sarnathian
* [[File:Inthar-13edo Oneirotonic Studies 7 Celephaisian.mp3]]: Tonal Study in Celephaïsian
* [[File:Inthar-13edo Oneirotonic Studies 8 Kadathian.mp3]]: Tonal Study in Kadathian
 
== Scale tree ==
{{MOS tuning spectrum
| 13/8 = Golden oneirotonic (458.3592{{c}})
| 13/5 = Golden A-Team (465.0841{{c}})
}}
 
[[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A -->
[[Category:Pages with internal sound examples]]
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