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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
There are two notable [[Harmonic_Entropy|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.
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>2015-11-05 12:56:26 UTC</tt>.<br>
: The original revision id was <tt>565336805</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 [[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.
Scales of this form are always [[Rothenberg_propriety|proper]], because there is only one small step.
||||||||||||~ [[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 ||
||  ||  ||  ||  ||  ||  || 163.97 ||= pi pi pi pi pi pi pi 1 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
||  ||  || 3\22 ||  ||  ||  || 163.64 ||= 3 3 3 3 3 3 3 1 ||= L/s = 3 ||
||=  ||=  ||=  ||=  ||=  ||=  ||= 162.87 ||= e e e e e e e e 1 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
||  ||  ||  ||  || 8\59 ||  || 162,71 ||= &lt;span style="display: block; text-align: center;"&gt;8 8 8 8 8 8 8 3&lt;/span&gt; ||  ||
||  ||  ||  ||  ||  || 13\96 || 162.5 ||= &lt;span style="display: block; text-align: center;"&gt;13 13 13 13 13 13 13 5&lt;/span&gt; ||  ||
||  ||  ||  || 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 ||
||  ||  ||  ||  ||  ||  || 158.37 ||= &lt;span style="background-color: #ffffff;"&gt;√3 √3 √3 √3 √3 √3 √3 1&lt;/span&gt; ||  ||
||  ||  ||  || 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 ||=  ||
||  ||  ||  ||  ||  || (11\84) || 157.14 ||= &lt;span style="display: block; text-align: center;"&gt;11 11 11 11 11 11 11 7 &lt;/span&gt;&lt;span style="display: block; text-align: center;"&gt;pi pi pi pi pi pi pi 2&lt;/span&gt; ||  ||
||  ||  || 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;


 
{| class="wikitable"
&lt;table class="wiki_table"&gt;
|-
    &lt;tr&gt;
! colspan="6" | [[generator|Generator]]
        &lt;th colspan="6"&gt;&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;&lt;br /&gt;
! | [[cent|Cent]]s
&lt;/th&gt;
! | Scale in [[EDO|EDO]] steps
        &lt;th&gt;&lt;a class="wiki_link" href="/Cent"&gt;Cent&lt;/a&gt;s&lt;br /&gt;
! | Comments
&lt;/th&gt;
|-
        &lt;th&gt;Scale in &lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt; steps&lt;br /&gt;
| | 1\7
&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;
| | 171.43
&lt;/td&gt;
| style="text-align:center;" | 1 1 1 1 1 1 1 0
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 4\29
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 165.52
&lt;/td&gt;
| style="text-align:center;" | 4 4 4 4 4 4 4 1
        &lt;td&gt;171.43&lt;br /&gt;
| style="text-align:center;" | L/s = 4
&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;
| | 163.97
&lt;/td&gt;
| style="text-align:center;" | pi pi pi pi pi pi pi 1
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;4\29&lt;br /&gt;
| | 3\22
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 163.64
&lt;/td&gt;
| style="text-align:center;" | 3 3 3 3 3 3 3 1
        &lt;td&gt;165.52&lt;br /&gt;
| style="text-align:center;" | L/s = 3
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;4 4 4 4 4 4 4 1&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
| style="text-align:center;" |
        &lt;td style="text-align: center;"&gt;L/s = 4&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
| style="text-align:center;" |
    &lt;/tr&gt;
| style="text-align:center;" |
    &lt;tr&gt;
| style="text-align:center;" |
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | 162.87
&lt;/td&gt;
| style="text-align:center;" | e e e e e e e e 1
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
&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;
| | 8\59
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 162,71
&lt;/td&gt;
| style="text-align:center;" | <span style="display: block; text-align: center;">8 8 8 8 8 8 8 3</span>
        &lt;td&gt;163.97&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;pi pi pi pi pi pi pi 1&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;
| | 13\96
        &lt;td&gt;&lt;br /&gt;
| | 162.5
&lt;/td&gt;
| style="text-align:center;" | <span style="display: block; text-align: center;">13 13 13 13 13 13 13 5</span>
        &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;
| | 5\37
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 162.16
&lt;/td&gt;
| style="text-align:center;" | 5 5 5 5 5 5 5 2
        &lt;td&gt;163.64&lt;br /&gt;
| style="text-align:center;" | Porcupine is in this general region
&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;
| | 7\52
    &lt;tr&gt;
| |
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| | 161.54
&lt;/td&gt;
| style="text-align:center;" | 7 7 7 7 7 7 7 3
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | 2\15
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
| | 160
&lt;/td&gt;
| style="text-align:center;" | 2 2 2 2 2 2 2 1
        &lt;td style="text-align: center;"&gt;162.87&lt;br /&gt;
| style="text-align:center;" | Optimum rank range (L/s=2/1) porcupine
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;e e e e e e e e 1&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;
| | 158.37
&lt;/td&gt;
| style="text-align:center;" | <span style="background-color: #ffffff;">√3 √3 √3 √3 √3 √3 √3 1</span>
        &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\38
        &lt;td&gt;8\59&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 157.89
&lt;/td&gt;
| style="text-align:center;" | 5 5 5 5 5 5 5 3
        &lt;td&gt;162,71&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;8 8 8 8 8 8 8 3&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| | 13\99
        &lt;td&gt;&lt;br /&gt;
| | 157.58
&lt;/td&gt;
| style="text-align:center;" | 13 13 13 13 13 13 13 8
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | Golden porcupine / golden hemikleismic
&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;
| | 8\61
&lt;/td&gt;
| |
        &lt;td&gt;13\96&lt;br /&gt;
| | 157.38
&lt;/td&gt;
| style="text-align:center;" | 8 8 8 8 8 8 8 5
        &lt;td&gt;162.5&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;13 13 13 13 13 13 13 5&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| | (11\84)
        &lt;td&gt;&lt;br /&gt;
| | 157.14
&lt;/td&gt;
| style="text-align:center;" | <span style="display: block; text-align: center;">11 11 11 11 11 11 11 7 </span><span style="display: block; text-align: center;">pi pi pi pi pi pi pi 2</span>
        &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;
| | 3\23
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 156.52
&lt;/td&gt;
| style="text-align:center;" | 3 3 3 3 3 3 3 2
        &lt;td&gt;162.16&lt;br /&gt;
| style="text-align:center;" |
&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;
| | 10\77
        &lt;td&gt;&lt;br /&gt;
| | 155.84
&lt;/td&gt;
| style="text-align:center;" | 10 10 10 10 10 10 10 7
        &lt;td&gt;&lt;br /&gt;
| style="text-align:center;" | Greeley is around here
&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;
| | 7\54
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 155.56
&lt;/td&gt;
| style="text-align:center;" | 7 7 7 7 7 7 7 5
        &lt;td&gt;161.54&lt;br /&gt;
| style="text-align:center;" |
&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;
| | 4\31
    &lt;/tr&gt;
| |
    &lt;tr&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | 154.84
&lt;/td&gt;
| style="text-align:center;" | 4 4 4 4 4 4 4 3
        &lt;td&gt;2\15&lt;br /&gt;
| style="text-align:center;" |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | 1\8
&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;
| | 150
&lt;/td&gt;
| style="text-align:center;" | 1 1 1 1 1 1 1 1
        &lt;td&gt;160&lt;br /&gt;
| style="text-align:center;" |
&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;&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;158.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff;"&gt;√3 √3 √3 √3 √3 √3 √3 1&lt;/span&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;&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;&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\84)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;11 11 11 11 11 11 11 7 &lt;/span&gt;&lt;span style="display: block; text-align: center;"&gt;pi pi pi pi pi pi pi 2&lt;/span&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;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>

Revision as of 00:00, 17 July 2018

There are two notable harmonic entropy minima with this MOS pattern. The first 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 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.

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

Generator Cents 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
163.97 pi pi pi pi pi pi pi 1 L/s = pi
3\22 163.64 3 3 3 3 3 3 3 1 L/s = 3
162.87 e e e e e e e e 1 L/s = e
8\59 162,71 8 8 8 8 8 8 8 3
13\96 162.5 13 13 13 13 13 13 13 5
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
158.37 √3 √3 √3 √3 √3 √3 √3 1
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
(11\84) 157.14 11 11 11 11 11 11 11 7 pi pi pi pi pi pi pi 2
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
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