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31edt: Difference between revisions

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**Imported revision 596368930 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 596565200 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>2016-10-21 15:50:49 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-22 22:17:18 UTC</tt>.<br>
: The original revision id was <tt>596368930</tt>.<br>
: The original revision id was <tt>596565200</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis]]1\31 tritave- approx. &lt;span style="font-size: 1.1em;"&gt;61.35¢ - Third tone&lt;/span&gt;&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis]]1\31 tritave- approx. &lt;span style="font-size: 1.1em;"&gt;61.35¢ - Third tone&lt;/span&gt;&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;A single step of 31-edt is about 6&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;1.35¢. Intervals around this size are called //third tones//. In 31 it is equivalent to the difference between one tritave and three stacked major thirds (C to E, to G#, to B#, but B# ≠ C), or four minor thirds (C to Eb to Gb to Bbb to Dbb ≠ C). The third tone is a defining sound of 31edt; when it does not appear directly in a scale, it often shows up as the difference between two or more intervals of a similar size.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;A single step of 31-edt is about 61.35¢. Intervals around this size are called //third tones//. In 31 it is equivalent to the difference between one tritave and three stacked major thirds (C to E, to G#, to B#, but B# ≠ C), or four minor thirds (C to Eb to Gb to Bbb to Dbb ≠ C). The third tone is a defining sound of 31edt; when it does not appear directly in a scale, it often shows up as the difference between two or more intervals of a similar size.&lt;/span&gt;


===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second]]2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second]]2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;The difference between a major and minor third and the thing to a 'half step'; in&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;The difference between a major and minor third and the thing to a 'half step'; in macromeantone, it is exactly analogus to the &lt;/span&gt;//&lt;span style="background-color: #ffffff;"&gt;chromatic semitone&lt;/span&gt;//&lt;span style="background-color: #ffffff;"&gt;, the interval that distinguishes major and minor intervals of the same generic interval class (eg. thirds).&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;macromeantone, it is exactly analogus to the &lt;/span&gt;//&lt;span style="background-color: #ffffff;"&gt;chromatic semitone&lt;/span&gt;//&lt;span style="background-color: #ffffff;"&gt;, the interval that distinguishes major and minor intervals of the same generic interval class (eg. thirds). &lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second-MOS Scales generated by 2\31:]]MOS Scales generated by 2\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second-MOS Scales generated by 2\31:]]MOS Scales generated by 2\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second]]6\31 tritave - approx. 368.12¢ - Supermajor Second&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second]]6\31 tritave - approx. 368.12¢ - Supermajor Second&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;Exactly one half of a narrow fourth, twice a tone, or thrice a two-third tone. In 17-limit tonal music, 6\31 closely represents &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;21:17 (365.825¢). In &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;macro&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;meantone, it is a diminished third, eg. C to Ebb.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;Exactly one half of a narrow fourth, twice a tone, or thrice a two-third tone. In 17-limit tonal music, 6\31 closely represents 21:17 (365.825¢). In macromeantone, it is a diminished third, eg. C to Ebb.&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:]]MOS Scales generated by 6\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:]]MOS Scales generated by 6\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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|| 26-tone || [[xenharmonic/5L 21s|5L 21s]] || 2 ||  || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 ||
|| 26-tone || [[xenharmonic/5L 21s|5L 21s]] || 2 ||  || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 ||


===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third]]7\31 octave - approx. 429.47¢ - Subminor Third&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third]]7\31 tritave - approx. 429.47¢ - Subminor Third&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;Exactly one half of a superfourth. In 7-limit tonal music, 7\31 stands in for 9:7 (435.08¢). In macromeantone temperament, it is an augmented 2nd, eg. C to D#.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;Exactly one half of a superfourth. In 7-limit tonal music, 7\31 stands in for 9:7 (435.08¢). In macromeantone temperament, it is an augmented 2nd, eg. C to D#.&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:]]MOS Scales generated by 7\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:]]MOS Scales generated by 7\31:&lt;/span&gt;====  
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===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third]]8\31 octave - approx. 490.83¢ - Minor Third&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third]]8\31 octave - approx. 490.83¢ - Minor Third&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;A 4:3 ~1.3 syntonic comma flat. Exactly twice a neutral second, four times a minor semitone, and half of a large tritone.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;A 4:3 ~1.3 syntonic comma flat. Exactly twice a neutral second, four times a minor semitone, and half of a large tritone. Generates a Fair Sigma scale&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:]]MOS Scales generated by 8\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:]]MOS Scales generated by 8\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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|| 27-tone || [[xenharmonic/4L 23s|4L 23s]] || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 2 ||  ||
|| 27-tone || [[xenharmonic/4L 23s|4L 23s]] || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 2 ||  ||


===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third]]9\31 octave - approx. 348.39¢ - Neutral Third&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third]]9\31 tritave - approx. 552.18¢ - Neutral Third&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for &lt;/span&gt;[[xenharmonic/mohajira|mohajira temperament]]&lt;span style="background-color: #ffffff;"&gt;), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a &lt;/span&gt;[[xenharmonic/13-limit|13-limit]]&lt;span style="background-color: #ffffff;"&gt; interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more "major-like" than "minor-like"). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;A neutral 3rd, about 1¢ away from 11:8 (551.32¢). 9\31 is half a perfect fifth (making it a suitable generator for macro&lt;/span&gt;mohajira temperament&lt;span style="background-color: #ffffff;"&gt;), and also a very small tritone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 18/13 (563.38¢), suggesting a &lt;/span&gt;[[xenharmonic/13-limit|13-limit]]&lt;span style="background-color: #ffffff;"&gt; interpretation for 31edt. However, its close proximity to 11/8 makes it hard to hear it as 18/13, which in JI has a different quality (and, as a neutral third, is more "major-like" than "minor-like")..&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:]]MOS Scales generated by 9\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:]]MOS Scales generated by 9\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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|| 24-tone || [[xenharmonic/7L 17s|7L 17s]] || 1 || 1 || 1 || 2 ||  || 1 || 1 || 2 ||  || 1 || 1 || 1 || 2 ||  || 1 || 1 || 2 ||  || 1 || 1 || 1 || 2 ||  || 1 || 1 || 2 ||  || 1 || 1 || 2 ||  ||
|| 24-tone || [[xenharmonic/7L 17s|7L 17s]] || 1 || 1 || 1 || 2 ||  || 1 || 1 || 2 ||  || 1 || 1 || 1 || 2 ||  || 1 || 1 || 2 ||  || 1 || 1 || 1 || 2 ||  || 1 || 1 || 2 ||  || 1 || 1 || 2 ||  ||


===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third]]10\31 octave - approx. 387.10¢ - Major Third&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third]]10\31 tritave - approx. 613.53¢ - Major Third&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;A near-just major 3rd (compare with 5:4 = 386.31¢). Has led to the characterization of 31-edo as "smooth". Generates &lt;/span&gt;[[xenharmonic/Wuerschmidt family|wurshmidt/worshmidt temperaments]]&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;A near-enough-just greater septimal (compare with 10:7 = 617.49¢). Generates &lt;/span&gt;[[Wuerschmidt family|wurshmidt/worshmidt temperaments]]&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:]]MOS Scales generated by 10\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:]]MOS Scales generated by 10\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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|| 28-tone || [[xenharmonic/3L 25s|3L 25s]] || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 28-tone || [[xenharmonic/3L 25s|3L 25s]] || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||  || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||


===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third]]11\31 octave - approx. 425.806¢ - Supermajor Third&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third]]11\31 tritave - approx. 674.89¢ - Supermajor Third&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;11\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. In meantone temperament, it is a diminished fourth, eg. C to Fb. It is notable as closely approximating an interval of the &lt;/span&gt;[[xenharmonic/23-limit|23-limit]]&lt;span style="background-color: #ffffff;"&gt;, suggesting the possibility of treating 16\31 (619.35¢) as a flat version of 23/16 (628.27¢). It is perhaps also notable for being close to 6\17, the bright major third of the ever-popular &lt;/span&gt;[[xenharmonic/17edo|17edo]]&lt;span style="background-color: #ffffff;"&gt;. Generates &lt;/span&gt;[[xenharmonic/Meantone family|squares temperament]]&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;11\31 functions as 126:85 (681.47¢). In metameantone temperament, it is a diminished fourth, eg. C to Fb. It is notable as closely approximating the 9/16edo Armodue sixth. Generates the Unfair Mu scale&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:]]MOS Scales generated by 11\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:]]MOS Scales generated by 11\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth]]12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth]]12\31 tritave - approx. 736.52¢ - Narrow Fourth or Subfourth&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the &lt;/span&gt;[[xenharmonic/17-limit|17-limit]]&lt;span style="background-color: #ffffff;"&gt;interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates &lt;/span&gt;[[xenharmonic/semisept|semisept]]&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 32:21 (729.22¢). It is also quite close to the &lt;/span&gt;[[xenharmonic/17-limit|17-limit]] &lt;span style="background-color: #ffffff;"&gt;interval 26/17 (735.57¢) and 19\31edo (735.48¢). However, although 31edt offers up a reasonable approximation of the 17th harmonic (18\31), no such approximation of the 13th comes with it to help make this identity clear. Generates &lt;/span&gt;[[xenharmonic/semisept|f]]alse Father&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:]]MOS Scales generated by 12\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:]]MOS Scales generated by 12\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth]]13\31 octave - approx. 503.23¢ - Perfect Fourth&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth]]13\31 tritave - approx. 797.54¢ - Perfect Fourth&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;A slightly wide perfect fourth (compare to 4:3 = 498.04¢). As such, it functions marvelously as a generator for &lt;/span&gt;[[xenharmonic/meantone|meantone]]&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;A slightly narrow perfect fourth (compare to 27:17 = 800.91¢). As such, it functions marvelously as a generator for macro&lt;/span&gt;meantone&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:]]MOS Scales generated by 13\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:]]MOS Scales generated by 13\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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|| 19-tone || [[xenharmonic/12L 7s|12L 7s]] || 1 || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 2 ||  ||
|| 19-tone || [[xenharmonic/12L 7s|12L 7s]] || 1 || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 2 ||  ||


&lt;span style="background-color: #ffffff; font-size: 1.1em;"&gt;**14\31 octave - approx. 541.94¢ - Superfourth**&lt;/span&gt;
&lt;span style="background-color: #ffffff; font-size: 1.1em;"&gt;**14\31 tritave - approx. 858.95¢ - Superfourth**&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;Exactly twice a subminor third. Functions as both the 11:8 (551.32¢) and 15:11 (536.95¢) undecimal superfourths (121/120 is tempered out). Thus it makes possible a symmetrical tempered version of an 8:11:15 triad. As 11/8, 14\31 is about 9¢ flat; however, it fits nicely with the also-flat 9/8, allowing a near-just 11/9. Nonetheless, most 11-limit chords in 31edo have a somewhat unstable quality which distinguishes them from their just counterparts. Generates &lt;/span&gt;[[xenharmonic/Starling temperaments|casablanca temperament]]&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;Exactly twice a subminor third, this interval functions as both the 28:17 (863.86¢) septendecimal and 23:14 (859.44¢) vicesmotertial superfourths (392/391 is tempered out). Thus it makes possible a symmetrical tempered version of a 17:28:46 triad. As either, 14\31 is flat (about 5¢ or about .5¢); however, it fits nicely with the sharp 17, allowing a even-nearer-just 28/27.&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:]]MOS Scales generated by 14\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:]]MOS Scales generated by 14\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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|| 20-tone || [[xenharmonic/11L 9s|11L 9s]] || 2 ||  || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 ||
|| 20-tone || [[xenharmonic/11L 9s|11L 9s]] || 2 ||  || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 || 2 ||  || 1 ||


===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth]]15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&lt;/span&gt;===  
===&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth]]15\31 octave - approx. 920.3¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&lt;/span&gt;===  
&lt;span style="background-color: #ffffff;"&gt;In 7-limit tonal music, functions quite well as 7:5 (582.51¢). Exactly thrice a whole tone. Generates &lt;/span&gt;[[xenharmonic/tritonic|tritonic]]&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;
&lt;span style="background-color: #ffffff;"&gt;In 23-limit tonal music, functions quite well as 46:27 (922.41¢). Exactly thrice a whole tone. Generates Super-[[Arcturus]] temperament.&lt;/span&gt;
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:]]MOS Scales generated by 15\31:&lt;/span&gt;====  
====&lt;span style="background-color: #ffffff;"&gt;[[#Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:]]MOS Scales generated by 15\31:&lt;/span&gt;====  
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
||~ number of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 ||
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  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="Intervals--1\31 tritave- approx. 61.35¢ - Third tone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:58:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:58 --&gt;1\31 tritave- approx. &lt;span style="font-size: 1.1em;"&gt;61.35¢ - Third tone&lt;/span&gt;&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="Intervals--1\31 tritave- approx. 61.35¢ - Third tone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:58:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:58 --&gt;1\31 tritave- approx. &lt;span style="font-size: 1.1em;"&gt;61.35¢ - Third tone&lt;/span&gt;&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;A single step of 31-edt is about 6&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;1.35¢. Intervals around this size are called &lt;em&gt;third tones&lt;/em&gt;. In 31 it is equivalent to the difference between one tritave and three stacked major thirds (C to E, to G#, to B#, but B# ≠ C), or four minor thirds (C to Eb to Gb to Bbb to Dbb ≠ C). The third tone is a defining sound of 31edt; when it does not appear directly in a scale, it often shows up as the difference between two or more intervals of a similar size.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;A single step of 31-edt is about 61.35¢. Intervals around this size are called &lt;em&gt;third tones&lt;/em&gt;. In 31 it is equivalent to the difference between one tritave and three stacked major thirds (C to E, to G#, to B#, but B# ≠ C), or four minor thirds (C to Eb to Gb to Bbb to Dbb ≠ C). The third tone is a defining sound of 31edt; when it does not appear directly in a scale, it often shows up as the difference between two or more intervals of a similar size.&lt;/span&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="Intervals--2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:59:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:59 --&gt;2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="Intervals--2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:59:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:59 --&gt;2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;The difference between a major and minor third and the thing to a 'half step'; in&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;The difference between a major and minor third and the thing to a 'half step'; in macromeantone, it is exactly analogus to the &lt;/span&gt;&lt;em&gt;&lt;span style="background-color: #ffffff;"&gt;chromatic semitone&lt;/span&gt;&lt;/em&gt;&lt;span style="background-color: #ffffff;"&gt;, the interval that distinguishes major and minor intervals of the same generic interval class (eg. thirds).&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: #ffffff;"&gt;macromeantone, it is exactly analogus to the &lt;/span&gt;&lt;em&gt;&lt;span style="background-color: #ffffff;"&gt;chromatic semitone&lt;/span&gt;&lt;/em&gt;&lt;span style="background-color: #ffffff;"&gt;, the interval that distinguishes major and minor intervals of the same generic interval class (eg. thirds). &lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc3"&gt;&lt;a name="Intervals--2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second-MOS Scales generated by 2\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:60:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second-MOS Scales generated by 2\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second-MOS Scales generated by 2\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second-MOS Scales generated by 2\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:60 --&gt;MOS Scales generated by 2\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc3"&gt;&lt;a name="Intervals--2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second-MOS Scales generated by 2\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:60:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second-MOS Scales generated by 2\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second-MOS Scales generated by 2\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second-MOS Scales generated by 2\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:60 --&gt;MOS Scales generated by 2\31:&lt;/span&gt;&lt;/h4&gt;
   
   
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&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Intervals--6\31 tritave - approx. 368.12¢ - Supermajor Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:67:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:67 --&gt;6\31 tritave - approx. 368.12¢ - Supermajor Second&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Intervals--6\31 tritave - approx. 368.12¢ - Supermajor Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:67:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:67 --&gt;6\31 tritave - approx. 368.12¢ - Supermajor Second&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;Exactly one half of a narrow fourth, twice a tone, or thrice a two-third tone. In 17-limit tonal music, 6\31 closely represents &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;21:17 (365.825¢). In &lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;macro&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;meantone, it is a diminished third, eg. C to Ebb.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;Exactly one half of a narrow fourth, twice a tone, or thrice a two-third tone. In 17-limit tonal music, 6\31 closely represents 21:17 (365.825¢). In macromeantone, it is a diminished third, eg. C to Ebb.&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc11"&gt;&lt;a name="Intervals--6\31 tritave - approx. 368.12¢ - Supermajor Second-MOS Scales generated by 6\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:68:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:68 --&gt;MOS Scales generated by 6\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc11"&gt;&lt;a name="Intervals--6\31 tritave - approx. 368.12¢ - Supermajor Second-MOS Scales generated by 6\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:68:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:68 --&gt;MOS Scales generated by 6\31:&lt;/span&gt;&lt;/h4&gt;
   
   
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&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Intervals--7\31 octave - approx. 429.47¢ - Subminor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:69:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:69 --&gt;7\31 octave - approx. 429.47¢ - Subminor Third&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Intervals--7\31 tritave - approx. 429.47¢ - Subminor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:69:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:69 --&gt;7\31 tritave - approx. 429.47¢ - Subminor Third&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;Exactly one half of a superfourth. In 7-limit tonal music, 7\31 stands in for 9:7 (435.08¢). In macromeantone temperament, it is an augmented 2nd, eg. C to D#.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;Exactly one half of a superfourth. In 7-limit tonal music, 7\31 stands in for 9:7 (435.08¢). In macromeantone temperament, it is an augmented 2nd, eg. C to D#.&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc13"&gt;&lt;a name="Intervals--7\31 octave - approx. 429.47¢ - Subminor Third-MOS Scales generated by 7\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:70:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:70 --&gt;MOS Scales generated by 7\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc13"&gt;&lt;a name="Intervals--7\31 tritave - approx. 429.47¢ - Subminor Third-MOS Scales generated by 7\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:70:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:70 --&gt;MOS Scales generated by 7\31:&lt;/span&gt;&lt;/h4&gt;
   
   


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&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Intervals--8\31 octave - approx. 490.83¢ - Minor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:71:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:71 --&gt;8\31 octave - approx. 490.83¢ - Minor Third&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Intervals--8\31 octave - approx. 490.83¢ - Minor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:71:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:71 --&gt;8\31 octave - approx. 490.83¢ - Minor Third&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;A 4:3 ~1.3 syntonic comma flat. Exactly twice a neutral second, four times a minor semitone, and half of a large tritone.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;A 4:3 ~1.3 syntonic comma flat. Exactly twice a neutral second, four times a minor semitone, and half of a large tritone. Generates a Fair Sigma scale&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc15"&gt;&lt;a name="Intervals--8\31 octave - approx. 490.83¢ - Minor Third-MOS Scales generated by 8\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:72:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:72 --&gt;MOS Scales generated by 8\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc15"&gt;&lt;a name="Intervals--8\31 octave - approx. 490.83¢ - Minor Third-MOS Scales generated by 8\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:72:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:72 --&gt;MOS Scales generated by 8\31:&lt;/span&gt;&lt;/h4&gt;
   
   
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&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Intervals--9\31 octave - approx. 348.39¢ - Neutral Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:73:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:73 --&gt;9\31 octave - approx. 348.39¢ - Neutral Third&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Intervals--9\31 tritave - approx. 552.18¢ - Neutral Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:73:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:73 --&gt;9\31 tritave - approx. 552.18¢ - Neutral Third&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/mohajira"&gt;mohajira temperament&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt;), and also thrice a major semitone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 16/13 (359.47¢), suggesting a &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/13-limit"&gt;13-limit&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt; interpretation for 31edo. However, its close proximity to 11/9 makes it hard to hear it as 16/13, which in JI has a different quality (and, as a neutral third, is more &amp;quot;major-like&amp;quot; than &amp;quot;minor-like&amp;quot;). Also, its inversion, 22\31 (851.61¢) is wide of the 13th harmonic by about 11¢, while all the lower harmonics are either near-just or narrow. This means the errors can accumulate, for instance, with 13/9 (636.62¢) represented by 17\31 (658.06¢), a good 21.4¢ sharp.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;A neutral 3rd, about 1¢ away from 11:8 (551.32¢). 9\31 is half a perfect fifth (making it a suitable generator for macro&lt;/span&gt;mohajira temperament&lt;span style="background-color: #ffffff;"&gt;), and also a very small tritone. It is closer in quality to a minor third than a major third, but indeed, it is distinct. It is 11¢ shy of 18/13 (563.38¢), suggesting a &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/13-limit"&gt;13-limit&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt; interpretation for 31edt. However, its close proximity to 11/8 makes it hard to hear it as 18/13, which in JI has a different quality (and, as a neutral third, is more &amp;quot;major-like&amp;quot; than &amp;quot;minor-like&amp;quot;)..&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc17"&gt;&lt;a name="Intervals--9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:74:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:74 --&gt;MOS Scales generated by 9\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc17"&gt;&lt;a name="Intervals--9\31 tritave - approx. 552.18¢ - Neutral Third-MOS Scales generated by 9\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:74:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:74 --&gt;MOS Scales generated by 9\31:&lt;/span&gt;&lt;/h4&gt;
   
   


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&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="Intervals--10\31 octave - approx. 387.10¢ - Major Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:75:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:75 --&gt;10\31 octave - approx. 387.10¢ - Major Third&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="Intervals--10\31 tritave - approx. 613.53¢ - Major Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:75:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:75 --&gt;10\31 tritave - approx. 613.53¢ - Major Third&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;A near-just major 3rd (compare with 5:4 = 386.31¢). Has led to the characterization of 31-edo as &amp;quot;smooth&amp;quot;. Generates &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Wuerschmidt%20family"&gt;wurshmidt/worshmidt temperaments&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;A near-enough-just greater septimal (compare with 10:7 = 617.49¢). Generates &lt;/span&gt;&lt;a class="wiki_link" href="/Wuerschmidt%20family"&gt;wurshmidt/worshmidt temperaments&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc19"&gt;&lt;a name="Intervals--10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:76:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:76 --&gt;MOS Scales generated by 10\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc19"&gt;&lt;a name="Intervals--10\31 tritave - approx. 613.53¢ - Major Third-MOS Scales generated by 10\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:76:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:76 --&gt;MOS Scales generated by 10\31:&lt;/span&gt;&lt;/h4&gt;
   
   


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&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc20"&gt;&lt;a name="Intervals--11\31 octave - approx. 425.806¢ - Supermajor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:77:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:77 --&gt;11\31 octave - approx. 425.806¢ - Supermajor Third&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc20"&gt;&lt;a name="Intervals--11\31 tritave - approx. 674.89¢ - Supermajor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:77:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:77 --&gt;11\31 tritave - approx. 674.89¢ - Supermajor Third&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;11\31 functions as 14:11 (417.51¢), 23:18 (424.36¢), 32:25 (427.37¢), 9:7 (435.08¢) and others. In meantone temperament, it is a diminished fourth, eg. C to Fb. It is notable as closely approximating an interval of the &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/23-limit"&gt;23-limit&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt;, suggesting the possibility of treating 16\31 (619.35¢) as a flat version of 23/16 (628.27¢). It is perhaps also notable for being close to 6\17, the bright major third of the ever-popular &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo"&gt;17edo&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt;. Generates &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family"&gt;squares temperament&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;11\31 functions as 126:85 (681.47¢). In metameantone temperament, it is a diminished fourth, eg. C to Fb. It is notable as closely approximating the 9/16edo Armodue sixth. Generates the Unfair Mu scale&lt;/span&gt;&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc21"&gt;&lt;a name="Intervals--11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:78:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:78 --&gt;MOS Scales generated by 11\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc21"&gt;&lt;a name="Intervals--11\31 tritave - approx. 674.89¢ - Supermajor Third-MOS Scales generated by 11\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:78:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:78 --&gt;MOS Scales generated by 11\31:&lt;/span&gt;&lt;/h4&gt;
   
   


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&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc22"&gt;&lt;a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:79:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:79 --&gt;12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc22"&gt;&lt;a name="Intervals--12\31 tritave - approx. 736.52¢ - Narrow Fourth or Subfourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:79:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:79 --&gt;12\31 tritave - approx. 736.52¢ - Narrow Fourth or Subfourth&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 21:16 (470.78¢). It is also quite close to the &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit"&gt;17-limit&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt;interval 17/13 (464.43¢), although 31edo does not offer up reasonable approximations of the 17th or 13th harmonics to help make this identity clear. This interval and its inversion 19\31 (735.48¢, a superfifth) are notable for being the only intervals in the 31edo octave larger than the 3\31 diatonic semitone (and smaller than its inversion, 28\31) that are not 11-limit consonances. Generates &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/semisept"&gt;semisept&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;Exactly twice a supermajor second, thrice a neutral second, or four times a minor second. In the 7-limit, 12\31 functions as 32:21 (729.22¢). It is also quite close to the &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit"&gt;17-limit&lt;/a&gt; &lt;span style="background-color: #ffffff;"&gt;interval 26/17 (735.57¢) and 19\31edo (735.48¢). However, although 31edt offers up a reasonable approximation of the 17th harmonic (18\31), no such approximation of the 13th comes with it to help make this identity clear. Generates &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/semisept"&gt;f&lt;/a&gt;alse Father&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc23"&gt;&lt;a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:80:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:80 --&gt;MOS Scales generated by 12\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc23"&gt;&lt;a name="Intervals--12\31 tritave - approx. 736.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:80:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:80 --&gt;MOS Scales generated by 12\31:&lt;/span&gt;&lt;/h4&gt;
   
   


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&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc24"&gt;&lt;a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:81:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:81 --&gt;13\31 octave - approx. 503.23¢ - Perfect Fourth&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc24"&gt;&lt;a name="Intervals--13\31 tritave - approx. 797.54¢ - Perfect Fourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:81:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:81 --&gt;13\31 tritave - approx. 797.54¢ - Perfect Fourth&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;A slightly wide perfect fourth (compare to 4:3 = 498.04¢). As such, it functions marvelously as a generator for &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone"&gt;meantone&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;A slightly narrow perfect fourth (compare to 27:17 = 800.91¢). As such, it functions marvelously as a generator for macro&lt;/span&gt;meantone&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc25"&gt;&lt;a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:82:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:82 --&gt;MOS Scales generated by 13\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc25"&gt;&lt;a name="Intervals--13\31 tritave - approx. 797.54¢ - Perfect Fourth-MOS Scales generated by 13\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:82:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:82 --&gt;MOS Scales generated by 13\31:&lt;/span&gt;&lt;/h4&gt;
   
   


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&lt;span style="background-color: #ffffff; font-size: 1.1em;"&gt;&lt;strong&gt;14\31 octave - approx. 541.94¢ - Superfourth&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: #ffffff; font-size: 1.1em;"&gt;&lt;strong&gt;14\31 tritave - approx. 858.95¢ - Superfourth&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: #ffffff;"&gt;Exactly twice a subminor third. Functions as both the 11:8 (551.32¢) and 15:11 (536.95¢) undecimal superfourths (121/120 is tempered out). Thus it makes possible a symmetrical tempered version of an 8:11:15 triad. As 11/8, 14\31 is about 9¢ flat; however, it fits nicely with the also-flat 9/8, allowing a near-just 11/9. Nonetheless, most 11-limit chords in 31edo have a somewhat unstable quality which distinguishes them from their just counterparts. Generates &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20temperaments"&gt;casablanca temperament&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt;.&lt;/span&gt;&lt;br /&gt;
&lt;span style="background-color: #ffffff;"&gt;Exactly twice a subminor third, this interval functions as both the 28:17 (863.86¢) septendecimal and 23:14 (859.44¢) vicesmotertial superfourths (392/391 is tempered out). Thus it makes possible a symmetrical tempered version of a 17:28:46 triad. As either, 14\31 is flat (about 5¢ or about .5¢); however, it fits nicely with the sharp 17, allowing a even-nearer-just 28/27.&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc26"&gt;&lt;a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 14\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:83:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:83 --&gt;MOS Scales generated by 14\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc26"&gt;&lt;a name="Intervals--13\31 tritave - approx. 797.54¢ - Perfect Fourth-MOS Scales generated by 14\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:83:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:83 --&gt;MOS Scales generated by 14\31:&lt;/span&gt;&lt;/h4&gt;
   
   


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&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Intervals--15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:84:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:84 --&gt;15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&lt;/span&gt;&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Intervals--15\31 octave - approx. 920.3¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:84:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:84 --&gt;15\31 octave - approx. 920.3¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&lt;/span&gt;&lt;/h3&gt;
  &lt;span style="background-color: #ffffff;"&gt;In 7-limit tonal music, functions quite well as 7:5 (582.51¢). Exactly thrice a whole tone. Generates &lt;/span&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tritonic"&gt;tritonic&lt;/a&gt;&lt;span style="background-color: #ffffff;"&gt; temperament.&lt;/span&gt;&lt;br /&gt;
  &lt;span style="background-color: #ffffff;"&gt;In 23-limit tonal music, functions quite well as 46:27 (922.41¢). Exactly thrice a whole tone. Generates Super-&lt;a class="wiki_link" href="/Arcturus"&gt;Arcturus&lt;/a&gt; temperament.&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc28"&gt;&lt;a name="Intervals--15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:85:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:85 --&gt;MOS Scales generated by 15\31:&lt;/span&gt;&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc28"&gt;&lt;a name="Intervals--15\31 octave - approx. 920.3¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;&lt;span style="background-color: #ffffff;"&gt;&lt;!-- ws:start:WikiTextAnchorRule:85:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:&amp;quot; title=&amp;quot;Anchor: Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:&amp;quot;/&amp;gt; --&gt;&lt;a name="Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:85 --&gt;MOS Scales generated by 15\31:&lt;/span&gt;&lt;/h4&gt;
   
   


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