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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
There are two notable harmonic entropy minima with this [[MOSScales|MOS]] pattern. The first is [[Tetracot_family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7|roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic_pairs#Roulette|roulette]]. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.)
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-04 15:39:59 UTC</tt>.<br>
: The original revision id was <tt>565207855</tt>.<br>
: 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 [[Tetracot family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic pairs#Roulette|roulette]]. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.)


The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.
The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.
Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step.
||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 1\7 ||  ||  ||  ||  ||  || 171.43 ||=  ||
||  ||  ||  ||  ||  || 6\41 || 175.61 ||= Enipucrop is between here and 1\7 ||
||  ||  ||  ||  || 5\34 ||  || 176.47 ||= Tetracot is around here ||
||  ||  ||  || 4\27 ||  ||  || 177.78 ||=  ||
||  ||  || 3\20 ||  ||  ||  || 180 ||=  ||
||  ||  ||  ||  ||  ||  || 180.815 ||  ||
||  ||  ||  ||  || 8\53 ||  || 181.13 ||=  ||
||  ||  ||  ||  ||  ||  || 1200/(5+phi) ||= Unnamed golden temperament (discussed in [[http://launch.groups.yahoo.com/group/tuning/message/100254|this thread]]) ||
||  ||  ||  || 5\33 ||  ||  || 181.82 ||=  ||
||  ||  ||  ||  ||  ||  || 182.44 ||  ||
||  ||  ||  ||  || 7\46 ||  || 182.61 ||  ||
||  || 2\13 ||  ||  ||  ||  || 184.62 ||= Optimum rank range glacial (L/s=2/1) ||
||  ||  ||  || 5\32 ||  ||  || 187.5 ||  ||
||  ||  ||  ||  ||  ||  || 188.03 ||  ||
||  ||  ||  ||  || 8\51 ||  || 188.235 ||  ||
||  ||  ||  ||  ||  ||  || 188.45 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
||  ||  || 3\19 ||  ||  ||  || 189.47 ||= L/s = 3 ||
||  ||  ||  ||  ||  ||  || 189.92 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
||  ||  ||  || 4\25 ||  ||  || 192 ||= L/s = 4 ||
||  ||  ||  ||  || 5\31 ||  || 193.55 ||= Luna/hemithird/roulette is around here ||
|| 1\6 ||  ||  ||  ||  ||  || 200 ||=  ||</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;6L 1s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There are two notable harmonic entropy 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="/Tetracot%20family"&gt;tetracot&lt;/a&gt;, in which four generators make a 3/2, and the second is known as &lt;a class="wiki_link" href="/roulette7"&gt;roulette7&lt;/a&gt;, the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament &lt;a class="wiki_link" href="/Chromatic%20pairs#Roulette"&gt;roulette&lt;/a&gt;. (Other temperaments like &amp;quot;luna&amp;quot;, &amp;quot;hemithird&amp;quot;, and &amp;quot;hemiwürschmidt&amp;quot; have very similar 7-note MOSes.)&lt;br /&gt;
&lt;br /&gt;
The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.&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;


Scales of this form are always [[Rothenberg_propriety|proper]], because there is only one small step.


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;th colspan="6"&gt;Generator&lt;br /&gt;
! colspan="6" | Generator
&lt;/th&gt;
! | Cents
        &lt;th&gt;Cents&lt;br /&gt;
! | Comments
&lt;/th&gt;
|-
        &lt;th&gt;Comments&lt;br /&gt;
| | 1\7
&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;
| | 171.43
&lt;/td&gt;
| style="text-align:center;" |
        &lt;td&gt;&lt;br /&gt;
|-
&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;
| | 6\41
&lt;/td&gt;
| | 175.61
        &lt;td&gt;171.43&lt;br /&gt;
| style="text-align:center;" | Enipucrop is between here and 1\7
&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;
| | 5\34
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 176.47
&lt;/td&gt;
| style="text-align:center;" | Tetracot is around here
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 4\27
&lt;/td&gt;
| |
        &lt;td&gt;6\41&lt;br /&gt;
| |
&lt;/td&gt;
| | 177.78
        &lt;td&gt;175.61&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;Enipucrop is between here and 1\7&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| | 3\20
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 180
&lt;/td&gt;
| style="text-align:center;" |
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;5\34&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 180.815
        &lt;td&gt;176.47&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;Tetracot is around here&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 8\53
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 181.13
&lt;/td&gt;
| style="text-align:center;" |
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;4\27&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 1200/(5+phi)
        &lt;td&gt;177.78&lt;br /&gt;
| style="text-align:center;" | Unnamed golden temperament (discussed in [http://launch.groups.yahoo.com/group/tuning/message/100254 this thread])
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| | 5\33
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 181.82
&lt;/td&gt;
| style="text-align:center;" |
        &lt;td&gt;3\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;&lt;br /&gt;
| |
&lt;/td&gt;
| | 182.44
        &lt;td&gt;180&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;
| | 7\46
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 182.61
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 2\13
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 184.62
        &lt;td&gt;180.815&lt;br /&gt;
| style="text-align:center;" | Optimum rank range glacial (L/s=2/1)
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| | 5\32
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 187.5
&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\53&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 188.03
        &lt;td&gt;181.13&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;
| | 8\51
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 188.235
&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;
| | 188.45
        &lt;td&gt;1200/(5+phi)&lt;br /&gt;
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;Unnamed golden temperament (discussed in &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100254" rel="nofollow"&gt;this thread&lt;/a&gt;)&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| | 3\19
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 189.47
&lt;/td&gt;
| style="text-align:center;" | L/s = 3
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;5\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;
| | 189.92
        &lt;td&gt;181.82&lt;br /&gt;
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| | 4\25
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 192
&lt;/td&gt;
| style="text-align:center;" | L/s = 4
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 5\31
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 193.55
        &lt;td&gt;182.44&lt;br /&gt;
| style="text-align:center;" | Luna/hemithird/roulette is around here
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 1\6
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 200
&lt;/td&gt;
| style="text-align:center;" |
        &lt;td&gt;&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;182.61&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;2\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;184.62&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Optimum rank range glacial (L/s=2/1)&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\32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;187.5&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;188.03&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;8\51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;188.235&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;188.45&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;3\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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189.47&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189.92&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;&lt;br /&gt;
&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\25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;192&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;193.55&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Luna/hemithird/roulette is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1\6&lt;br /&gt;
&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;200&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>
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