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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>
{{MOS intro}}
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-11-29 12:42:48 UTC</tt>.<br>
== Name ==
: The original revision id was <tt>387367746</tt>.<br>
{{TAMNAMS name}}
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">There are two notable [[harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The first is [[Porcupine family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is [[Chromatic pairs#Greeley|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.


Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step.
== Scale properties ==
||||||||||||~ [[Generator]] ||~ [[Cent]]s ||~ Scale in [[EDO]] steps ||~ Comments ||
|| 1\7 ||  ||  ||  ||  ||  || 171.43 ||= 1 1 1 1 1 1 1 0 ||=   ||
||  ||  ||  || 4\29 ||  ||  || 165.52 ||= 4 4 4 4 4 4 4 1 ||= L/s = 4 ||
||  ||  || 3\22 ||  ||  ||  || 163.64 ||= 3 3 3 3 3 3 3 1 ||= L/s = 3 ||
||  ||  ||  || 5\37 ||  ||  || 162.16 ||= 5 5 5 5 5 5 5 2 ||= Porcupine is in this general region ||
||  ||  ||  ||  || 7\52 ||  || 161.54 ||= 7 7 7 7 7 7 7 3 ||=  ||
||  || 2\15 ||  ||  ||  ||  || 160 ||= 2 2 2 2 2 2 2 1 ||= Optimum rank range (L/s=2/1) porcupine ||
||  ||  ||  || 5\38 ||  ||  || 157.89 ||= 5 5 5 5 5 5 5 3 ||=  ||
||  ||  ||  ||  ||  || 13\99 || 157.58 ||= 13 13 13 13 13 13 13 8 ||= Golden porcupine / golden hemikleismic ||
||  ||  ||  ||  || 8\61 ||  || 157.38 ||= 8 8 8 8 8 8 8 5 ||=  ||
||  ||  || 3\23 ||  ||  ||  || 156.52 ||= 3 3 3 3 3 3 3 2 ||=  ||
||  ||  ||  ||  ||  || 10\77 || 155.84 ||= 10 10 10 10 10 10 10 7 ||= Greeley is around here ||
||  ||  ||  ||  || 7\54 ||  || 155.56 ||= 7 7 7 7 7 7 7 5 ||=  ||
||  ||  ||  || 4\31 ||  ||  || 154.84 ||= 4 4 4 4 4 4 4 3 ||=  ||
|| 1\8 ||  ||  ||  ||  ||  || 150 ||= 1 1 1 1 1 1 1 1 ||=  ||</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;7L 1s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There are two notable &lt;a class="wiki_link" href="/harmonic%20entropy"&gt;harmonic entropy&lt;/a&gt; minima with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern. The first is &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine&lt;/a&gt;, in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is &lt;a class="wiki_link" href="/Chromatic%20pairs#Greeley"&gt;greeley&lt;/a&gt;, in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.&lt;br /&gt;
&lt;br /&gt;
Scales of this form are always &lt;a class="wiki_link" href="/Rothenberg%20propriety"&gt;proper&lt;/a&gt;, because there is only one small step.&lt;br /&gt;


=== Intervals ===
{{MOS intervals}}


&lt;table class="wiki_table"&gt;
=== Generator chain ===
    &lt;tr&gt;
{{MOS genchain}}
        &lt;th colspan="6"&gt;&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;a class="wiki_link" href="/Cent"&gt;Cent&lt;/a&gt;s&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Scale in &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt; steps&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;1\7&lt;br /&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;171.43&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1 1 1 1 1 1 1 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;4\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;165.52&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4 4 4 4 4 4 4 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s = 4&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;3\22&lt;br /&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;163.64&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3 3 3 3 3 3 3 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s = 3&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;5\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;162.16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5 5 5 5 5 5 5 2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Porcupine is in this general region&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;7\52&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;161.54&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7 7 7 7 7 7 7 3&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;2\15&lt;br /&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;160&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2 2 2 2 2 2 2 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Optimum rank range (L/s=2/1) porcupine&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;5\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;157.89&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5 5 5 5 5 5 5 3&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;13\99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.58&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13 13 13 13 13 13 13 8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Golden porcupine / golden hemikleismic&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;8\61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8 8 8 8 8 8 8 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;3\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;156.52&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3 3 3 3 3 3 3 2&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;10\77&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;155.84&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10 10 10 10 10 10 10 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Greeley is around here&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;7\54&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;155.56&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7 7 7 7 7 7 7 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;4\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;154.84&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4 4 4 4 4 4 4 3&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;150&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 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}}
 
=== Proposed names ===
Mode names are from [[Porcupine Temperament Modal Harmony|Porcupine temperament modal harmony]]. Descriptive mode names are based on using {{dash|1, 4, 7}}, i.e. 3+3 triads as a basis for harmony.
{{MOS modes
| Mode names =
octopus $
mantis $
dolphin $
crab $
tuna $
salmon $
starfish $
whale $
| Table Headers=Name Origin
| Table Entries=
Bright quartal $
Dark quartal $
Bright major $
Middle major $
Dark major $
Bright minor $
Middle minor $
Dark minor $
}}
 
== Theory ==
=== Low harmonic entropy scales ===
There are three notable [[harmonic entropy]] minima with this [[mos]] pattern.
 
* The lowest accuracy one is [[porcupine]], in which two generators make a [[6/5]] and three make a [[4/3]]. The range of porcupine tunings is about 2\15 to 3\22.
* Less well-known and more accurate is [[greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like [[10/7]], [[11/7]], etc.
* Thirdly and finally, [[tempering out]] [[4000/3993|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered out results in an unusually high accuracy and efficient rank-2 temperament in the 2.3.11/5 subgroup for which interpretation as a rank-3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[square superparticular|equidistant from 11/10]] and offering many fruitful tempering opportunities. Note therefore that [[porkypine]] can be seen as a trivial tuning of [[4000/3993|pine]] tempering out {{nowrap|[[100/99]] {{=}} S10}} and {{nowrap|[[121/120]] {{=}} S11}}.
 
== Scale tree ==
{{MOS tuning spectrum
| 5/2 = General range of porcupine
| 2/1 = Optimum rank range for porcupine
| 13/8 = Golden porcupine/hemikleismic
| 10/7 = General range of greeley
}}
 
[[Category:8-tone scales]]
Retrieved from "https://en.xen.wiki/w/7L_1s"