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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:guest|guest]] and made on <tt>2011-08-28 03:12:36 UTC</tt>.<br>
| de =  
: The original revision id was <tt>248869459</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
||  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||= scale || g in cents || 2g || 3g || 4g || Comments ||
| Neutral = 2L 6s
|| 2\5 ||  ||  ||  ||  ||  ||  ||  ||  ||  ||= 1 0 1 1 0 1 0 1 || 480.000 || 960.000 || 240.000 || 720.000 ||  ||
}}
||  ||  ||  ||  ||  ||  ||  ||  ||  || 21\53 ||= 10 1 10 10 1 10 1 10 || 475.472 || 950.943 || 226.415 || 701.887 || Vulture/Buzzard is around here ||
: ''For the tritave-equivalent MOS structure with the same step pattern, see [[5L&nbsp;3s (3/1-equivalent)]].''
||  ||  ||  ||  ||  ||  ||  ||  || 19\48 ||  ||= 9 1 9 9 1 9 1 9 || 475 ||  ||  ||  ||  ||
{{MOS intro}}
||  ||  ||  ||  ||  ||  ||  || 17\43 ||  ||  ||= 8 1 8 8 1 8 1 8 || 474.419 ||  ||  ||  ||  ||
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 ||  ||  ||  ||= 7 1 7 7 1 7 1 7 || 473.684 ||  ||  ||  ||  ||
||  ||  ||  ||  ||  || 13\33 ||  ||  ||  ||  ||= 6 1 6 6 1 6 1 6 || 472.727 ||  ||  ||  ||  ||
||  ||  ||  ||  || 11\28 ||  ||  ||  ||  ||  ||= 5 1 5 5 1 5 1 5 || 471.429 ||  ||  ||  ||  ||
||  ||  ||  || 9\23 ||  ||  ||  ||  ||  ||  ||= 4 1 4 4 1 4 1 4 || 469.565 || 939.130 || 208.696 || 678.261 ||  ||
||  ||  || 7\18 ||  ||  ||  ||  ||  ||  ||  ||= 3 1 3 3 1 3 1 3 || 466.667 || 933.333 || 200.000 || 666.667 ||  ||
||  ||  ||  || 12\31 ||  ||  ||  ||  ||  ||  ||= 5 2 5 5 2 5 2 5 || 464.516 || 929.032 || 193.549 || 658.065 ||  ||
||  || 5\13 ||  ||  ||  ||  ||  ||  ||  ||  ||= 2 1 2 2 1 2 1 2 || 461.538 || 923.077 || 184.615 || 646.154 ||  ||
||  ||  ||  || 13\34 ||  ||  ||  ||  ||  ||  ||= 5 3 5 5 3 5 3 5 || 458.824 || 917.647 || 176.471 || 635.294 ||  ||
||  ||  ||  ||  ||  || 34\89 ||  ||  ||  ||  ||= 13 8 13 13 8 13 8 13 || 458.427 ||  ||  ||  || Golden father ||
||  ||  ||  ||  || 21\55 ||  ||  ||  ||  ||  ||= 8 5 8 8 5 8 5 8 || 458.182 ||  ||  ||  ||  ||
||  ||  || 8\21 ||  ||  ||  ||  ||  ||  ||  ||= 3 2 3 3 2 3 2 3 || 457.143 || 914.286 || 171.429 || 628.571 ||  ||
||  ||  ||  || 11\29 ||  ||  ||  ||  ||  ||  ||= 4 3 4 4 3 4 3 4 || 455.172 || 910.345 || 165.517 || 620.690 ||  ||
|| 3\8 ||  ||  ||  ||  ||  ||  ||  ||  ||  ||= 1 1 1 1 1 1 1 1 || 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>
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<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]].
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        &lt;td style="text-align: center;"&gt;scale&lt;br /&gt;
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        &lt;td&gt;g in cents&lt;br /&gt;
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        &lt;td&gt;2g&lt;br /&gt;
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        &lt;td&gt;3g&lt;br /&gt;
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        &lt;td&gt;4g&lt;br /&gt;
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        &lt;td&gt;Comments&lt;br /&gt;
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        &lt;td&gt;2\5&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;1 0 1 1 0 1 0 1&lt;br /&gt;
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        &lt;td&gt;480.000&lt;br /&gt;
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        &lt;td&gt;960.000&lt;br /&gt;
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        &lt;td&gt;240.000&lt;br /&gt;
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        &lt;td&gt;720.000&lt;br /&gt;
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        &lt;td&gt;21\53&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;10 1 10 10 1 10 1 10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;475.472&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;950.943&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;226.415&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.887&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Vulture/Buzzard is around here&lt;br /&gt;
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    &lt;/tr&gt;
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        &lt;td&gt;19\48&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;9 1 9 9 1 9 1 9&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;8 1 8 8 1 8 1 8&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;7 1 7 7 1 7 1 7&lt;br /&gt;
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        &lt;td&gt;473.684&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;6 1 6 6 1 6 1 6&lt;br /&gt;
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        &lt;td&gt;472.727&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;5 1 5 5 1 5 1 5&lt;br /&gt;
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        &lt;td&gt;471.429&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;4 1 4 4 1 4 1 4&lt;br /&gt;
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        &lt;td&gt;469.565&lt;br /&gt;
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        &lt;td&gt;939.130&lt;br /&gt;
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        &lt;td&gt;208.696&lt;br /&gt;
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        &lt;td&gt;678.261&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;3 1 3 3 1 3 1 3&lt;br /&gt;
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        &lt;td&gt;466.667&lt;br /&gt;
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        &lt;td&gt;933.333&lt;br /&gt;
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        &lt;td&gt;200.000&lt;br /&gt;
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        &lt;td&gt;666.667&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;2 1 2 2 1 2 1 2&lt;br /&gt;
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        &lt;td&gt;461.538&lt;br /&gt;
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        &lt;td&gt;923.077&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;184.615&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;646.154&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;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;5 3 5 5 3 5 3 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;458.824&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;917.647&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;176.471&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;635.294&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;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;13 8 13 13 8 13 8 13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;458.427&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;Golden father&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;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;8 5 8 8 5 8 5 8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;458.182&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;/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;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;3 2 3 3 2 3 2 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;457.143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;914.286&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;171.429&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;628.571&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;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 style="text-align: center;"&gt;4 3 4 4 3 4 3 4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;455.172&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;910.345&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165.517&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;620.690&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&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1 1 1 1 1 1 1 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;450.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;900.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;150.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600.000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&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]]
Retrieved from "https://en.xen.wiki/w/5L_3s"