Xenharmonic Wiki

4L 4s: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>JosephRuhf
**Imported revision 385876448 - Original comment: **
→Scale tree: replace with template (- golden diminished)
 
(27 intermediate revisions by 14 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Name = tetrawood; diminished
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-25 20:09:23 UTC</tt>.<br>
| Periods = 4
: The original revision id was <tt>385876448</tt>.<br>
| nLargeSteps = 4
: The revision comment was: <tt></tt><br>
| nSmallSteps = 4
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 1
<h4>Original Wikitext content:</h4>
| Collapsed = 0
<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">The minimum harmonic entropy scale with this [[MOSScales|MOS]] pattern is [[Jubilismic clan|diminished]][8], basically the familiar [[Octatonic scale|octatonic scale]] of 12edo.
| Pattern = LsLsLsLs
}}
{{MOS intro}}


There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)
The minimum harmonic entropy scale with this mos pattern is [[Diminished]][8], the familiar [[octatonic scale]] of 12edo.
||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\4 ||  ||  ||  ||  || 0 ||=  ||
||  ||  ||  ||  || 1\24 || 50 ||  ||
||  ||  ||  || 1\20 ||  || 60 ||= L/s=4:
generators smaller than this are "impractical" ||
||  ||  || 1\16 ||  ||  || 75 ||= L/s=3:
generators smaller than this may be considered "impractical" ||
||  || 1\12 ||  ||  ||  || 100 ||= Diminished is around here
Optimum rank range (L/s=2/1) for MOS ||
||  ||  ||  || 3\32 ||  || 112.5 ||=  ||
||  ||  ||  ||  || 5\52 || 115.38 ||= Golden diminished ||
||  ||  || 2\20 ||  ||  || 120 ||=  ||
|| 1\8 ||  ||  ||  ||  || 150 ||=  ||</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;4L 4s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The minimum harmonic entropy scale with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern is &lt;a class="wiki_link" href="/Jubilismic%20clan"&gt;diminished&lt;/a&gt;[8], basically the familiar &lt;a class="wiki_link" href="/Octatonic%20scale"&gt;octatonic scale&lt;/a&gt; of 12edo.&lt;br /&gt;
&lt;br /&gt;
There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)&lt;br /&gt;


In addition to the true mos form, LsLsLsLs, there are four near-mos forms – LLsLsLss, LLsLssLs, LLssLLss, and LLssLsLs – in which the period and its multiples are the only intervals with more than two varieties. The near-mos forms are only proper if the dark generator is larger than 1\12 (100{{c}}).


&lt;table class="wiki_table"&gt;
== Intervals ==
    &lt;tr&gt;
{{MOS intervals}}
        &lt;th colspan="5"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0\4&lt;br /&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\24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;50&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;1\20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;60&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;1\16&lt;br /&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;75&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;1\12&lt;br /&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;100&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Diminished is around here&lt;br /&gt;
Optimum rank range (L/s=2/1) for MOS&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\32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;115.38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Golden diminished&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\20&lt;br /&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;1\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;150&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 mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum
| 6/5 = [[Fourfives]]↑
| 13/8 = Unnamed golden tuning
| 2/1 = [[Diminished]]
| 13/5 = Unnamed golden tuning
| 6/1 = [[Quadritikleismic]]↓
}}
 
[[Category:Tetrawood| ]] <!-- main article -->
[[Category:8-tone scales]]
Retrieved from "https://en.xen.wiki/w/4L_4s"