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1L 8s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Periods = 1
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-25 20:46:26 UTC</tt>.<br>
| nLargeSteps = 1
: The original revision id was <tt>385887062</tt>.<br>
| nSmallSteps = 8
: The revision comment was: <tt></tt><br>
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Collapsed = 1
<h4>Original Wikitext content:</h4>
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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;white-space: pre-wrap ! important" class="old-revision-html">This MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&lt;L&lt;3 s=1) and Negri (3&lt;L&lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval of at least 3/28edo (L&lt;= 4 s=3).
}}
|| 0/1 ||  ||  ||  ||  || 0 ||=  ||
||  ||  ||  ||  || 1/13 || 92 4/13 ||=   ||
||  ||  ||  || 1/12 ||  || 100 ||= L/s=4:
generators smaller than this are "impractical" ||
||  ||  ||  ||  || 2/23 || 104.347826 ||=   ||
||  ||  || 1/11 ||  ||  || 109 1/11 ||= L/s=3:
generators smaller than this may be considered "impractical" ||
||  ||  ||  ||  || 3/32 || 112.5 ||=  ||
||  ||  ||  || 2/21 ||  || 114 2/7 ||=   ||
||  ||  ||  ||  || 3/31 || 116.129032 ||=   ||
||  || 1/10 ||  ||  ||  || 120 ||=   ||
||  ||  ||  ||  || 4/39 || 123 1/13 ||=  ||
||  ||  ||  || 3/29 ||  || 124.137931 ||=  ||
||  ||  ||  ||  || 5/48 || 125 ||=  ||
||  ||  || 2/19 ||  ||  || 126.315789 ||=  ||
||  ||  ||  ||  || 5/47 || 127.659574 ||=  ||
||  ||  ||  || 3/28 ||  || 128 4/7 ||=  ||
||  ||  ||  ||  || 4/37 || 129 27/37 ||=  ||
|| 1/9 ||  ||  ||  ||  || 133 1/3 ||=   ||</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;1L 8s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&amp;lt;L&amp;lt;3 s=1) and Negri (3&amp;lt;L&amp;lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval of at least 3/28edo (L&amp;lt;= 4 s=3).&lt;br /&gt;


{{MOS intro}}


&lt;table class="wiki_table"&gt;
This MOS represents temperaments like [[Miracle]] and [[Negri]]. Of all the temperaments it represents, the [[harmonic entropy]] minimum is the one where the scale is generated by an interval near [[28edo|3\28]] (around [[14/13]]).
    &lt;tr&gt;
        &lt;td&gt;0/1&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;0&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;1/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;92 4/13&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;1/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;100&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s=4:&lt;br /&gt;
generators smaller than this are &amp;quot;impractical&amp;quot;&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;2/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104.347826&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;1/11&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;109 1/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s=3:&lt;br /&gt;
generators smaller than this may be considered &amp;quot;impractical&amp;quot;&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;3/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112.5&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;2/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;114 2/7&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;3/31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.129032&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;1/10&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;120&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;4/39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;123 1/13&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;3/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;124.137931&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;5/48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;125&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;2/19&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;126.315789&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;5/47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;127.659574&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;3/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;128 4/7&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;4/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;129 27/37&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;1/9&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;133 1/3&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;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Modes ==
{{MOS modes}}
 
=== Degrees ===
{{MOS mode degrees}}
 
== Intervals ==
{{MOS intervals}}
 
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 1066.6667 cents (8\9) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 133.3333 cents (1\9)
 
{| class="wikitable center-all"
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
! Cents
! L
! s
! L/s
! Comments
|-
| 1\9 || || || || || || 133.333 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\46 || 130.435 || 6 || 5 || 1.200 ||
|-
| || || || || 4\37 || || 129.730 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\65 || 129.231 || 9 || 7 || 1.286 ||
|-
| || || || 3\28 || || || 128.571 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\75 || 128.000 || 11 || 8 || 1.375 ||
|-
| || || || || 5\47 || || 127.660 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\66 || 127.273 || 10 || 7 || 1.429 ||
|-
| || || 2\19 || || || || 126.316 || 3 || 2 || 1.500 || [[Negri]]
|-
| || || || || || 7\67 || 125.373 || 11 || 7 || 1.571 ||
|-
| || || || || 5\48 || || 125.000 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\77 || 124.675 || 13 || 8 || 1.625 || Golden negri (124.7656¢)
|-
| || || || 3\29 || || || 124.138 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\68 || 123.529 || 12 || 7 || 1.714 ||
|-
| || || || || 4\39 || || 123.077 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\49 || 122.449 || 9 || 5 || 1.800 ||
|-
| || 1\10 || || || || || 120.000 || 2 || 1 || 2.000 || Basic 1L 8s <br>(small steps larger than this are proper)
|-
| || || || || || 4\41 || 117.073 || 9 || 4 || 2.250 || [[Miracle]]
|-
| || || || || 3\31 || || 116.129 || 7 || 3 || 2.333 || Miracle/[[revelation]]
|-
| || || || || || 5\52 || 115.385 || 12 || 5 || 2.400 ||
|-
| || || || 2\21 || || || 114.286 || 5 || 2 || 2.500 ||
|-
| || || || || || 5\53 || 113.208 || 13 || 5 || 2.600 || Golden [[misneb]] (113.0153¢)
|-
| || || || || 3\32 || || 112.500 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\43 || 111.628 || 11 || 4 || 2.750 ||
|-
| || || 1\11 || || || || 109.091 || 3 || 1 || 3.000 ||
|-
| || || || || || 3\34 || 105.882 || 10 || 3 || 3.333 ||
|-
| || || || || 2\23 || || 104.348 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\35 || 102.857 || 11 || 3 || 3.667 ||
|-
| || || || 1\12 || || || 100.000 || 4 || 1 || 4.000 || [[Ripple]]
|-
| || || || || || 2\25 || 96.000 || 9 || 2 || 4.500 || [[Passion]]
|-
| || || || || 1\13 || || 92.308 || 5 || 1 || 5.000 ||
|-
| || || || || || 1\14 || 85.714 || 6 || 1 || 6.000 ||
|-
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
|}
 
{{todo|expand}}
[[Category:9-tone scales]]
Retrieved from "https://en.xen.wiki/w/1L_8s"