31edt

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31edt divides the tritave into equal parts of 61.353 cents, corresponding to the non-octave third tone scale of [[39edo]] where each degree gets ~.185 cents flatter than the corresponding degree of 39edo. It supports the same higher-limit meantone temperament as 12 edt with better intonation of triads. It also contains a flat version of the BP nonatonic scale and the fair Sigma and false Father.scales.

=<span style="background-color: #ffffff;">Intervals</span>= 

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis]]1\31 tritave- approx. <span style="font-size: 1.1em;">61.35¢ - Third tone</span></span>=== 
<span style="background-color: #ffffff;">A single step of 31-edt is about 6</span><span style="background-color: #ffffff;">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.</span>

===<span style="background-color: #ffffff;">[[#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</span>=== 
<span style="background-color: #ffffff;">The difference between a major and minor third and the thing to a 'half step'; in</span>
<span style="background-color: #ffffff;">macromeantone, it is exactly analogus to the </span>//<span style="background-color: #ffffff;">chromatic semitone</span>//<span style="background-color: #ffffff;">, the interval that distinguishes major and minor intervals of the same generic interval class (eg. thirds). </span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| 15-tone ([[xenharmonic/Maximal evenness|ME]] or quasi-equal) || [[xenharmonic/1L 14s|1L 14s]] || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 3 ||   ||   ||
|| 16-tone || [[xenharmonic/15L 1s|15L 1s]] || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 1 ||

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-3\31 octave - approx. 116.13¢- Major Semitone or Diatonic Semitone or Large Major Second]]3\31 tritave - approx. 184.06¢- Whole tone or Large Minor Second</span>=== 

<span style="background-color: #ffffff;">A small whole tone only ~1.6 cents wide of 10:9 which is an interval sometimes called melodically dull; in macromeantone, it is exactly analogus to the </span>//<span style="background-color: #ffffff;">diatonic semitone</span>//<span style="background-color: #ffffff;"> which appears in the diatonic scale between, for instance, the major third and perfect fourth, and the major seventh and octave. </span>
====<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-3\31 octave - approx. 116.13¢- Major Semitone or Diatonic Semitone or Large Major Second-MOS Scales generated by 3\31:]]MOS Scales generated by 3\31:</span>==== 
||~ 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 ||
|| nonatonic || [[xenharmonic/1L 8s|1L 8s]] || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 7 ||   ||   ||   ||   ||   ||   ||
|| decatonic (quasi-equal) || [[xenharmonic/9L 1s|9L 1s]] || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 4 ||   ||   ||   ||
|| 11-tone || [[xenharmonic/10L 1s|10L 1s]] || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 1 ||
|| 21-tone (silimlar to Blackjack) || [[xenharmonic/11L 10s|11L 10s]] || 2 ||   || 1 || 2 ||   || 1 || 2 ||   || 1 || 2 ||   || 1 || 2 ||   || 1 || 2 ||   || 1 || 2 ||   || 1 || 2 ||   || 1 || 2 ||   || 1 || 2 ||   || 1 || 1 ||

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-4\31 octave - approx. 154.84¢ - Neutral Tone or Neutral Second]]4\31 tritave - approx. 245.41¢ - Classical hemifourth or Neutral Second</span>=== 
<span style="background-color: #ffffff;">Exactly one half of the minor third and twice the minor semitone, 4\31 stands in for 15:13 (247.74¢). Although 31 is not extremely accurate with 5 or 13, it is notable that the inaccuracies of these harmonics cancel out so much, leaving the interval that distinguishes them (15/13) only about 2.3¢ off.</span>
====<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-4\31 octave - approx. 154.84¢ - Neutral Tone or Neutral Second-MOS Scales generated by 4\31:]]MOS Scales generated by 4\31:</span>==== 
||~ 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 ||
|| heptatonic || [[xenharmonic/1L 6s|1L 6s]] || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   ||
|| octatonic (quasi-equal) || [[xenharmonic/7L 1s|7L 1s]] || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   || 3 ||   ||   ||
|| 15-tone || [[xenharmonic/8L 7s|8L 7s]] || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 3 ||   ||   ||
|| 23-tone || [[xenharmonic/8L 15s|8L 15s]] || 1 || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 2 ||   ||

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-5\31 octave - approx. 193.55¢ - Whole Tone or Major Second]]5\31 tritave - approx. 306.77¢ - <span style="font-size: 1.1em;">Sesquitone or Major Second</span></span>=== 
<span style="background-color: #ffffff;">At ~8.8 cents flat of a just 6:5, 5\31 is considered a "sesquitone". Two of this sesquitone make a near-just 10:7 tritone. Because it is fairly close to no intelligibly small integer ratio but 6/5, 5\31 can function as a semi-stabilized harmonic ninth.</span>
====<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-5\31 octave - approx. 193.55¢ - Whole Tone or Major Second-MOS Scales generated by 5\31:]]MOS Scales generated by 5\31:</span>==== 
||~ 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 ||
|| hexatonic (quasi-equal) || [[xenharmonic/1L 5s|1L 5s]] || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 6 ||   ||   ||   ||   ||   ||
|| heptatonic || [[xenharmonic/6L 1s|6L 1s]] || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 1 ||
|| 13-tone || [[xenharmonic/6L 7s|6L 7s]] || 4 ||   ||   ||   || 1 || 4 ||   ||   ||   || 1 || 4 ||   ||   ||   || 1 || 4 ||   ||   ||   || 1 || 4 ||   ||   ||   || 1 || 4 ||   ||   ||   || 1 || 1 ||
|| 19-tone || [[xenharmonic/6L 13s|6L 13s]] || 3 ||   ||   || 1 || 1 || 3 ||   ||   || 1 || 1 || 3 ||   ||   || 1 || 1 || 3 ||   ||   || 1 || 1 || 3 ||   ||   || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 ||
|| 25-tone || [[xenharmonic/6L 19s|6L 19s]] || 2 ||   || 1 || 1 || 1 || 2 ||   || 1 || 1 || 1 || 2 ||   || 1 || 1 || 1 || 2 ||   || 1 || 1 || 1 || 2 ||   || 1 || 1 || 1 || 2 ||   || 1 || 1 || 1 || 1 ||

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second]]6\31 tritave - approx. 368.12¢ - Supermajor Second</span>=== 
<span style="background-color: #ffffff;">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 </span><span style="background-color: #ffffff;">21:17 (365.825¢). In </span><span style="background-color: #ffffff;">macro</span><span style="background-color: #ffffff;">meantone, it is a diminished third, eg. C to Ebb.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| pentatonic (quasi-equal) || [[xenharmonic/1L 4s|1L 4s]] || 6 ||   ||   ||   ||   ||   || 6 ||   ||   ||   ||   ||   || 6 ||   ||   ||   ||   ||   || 6 ||   ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   ||
|| hexatonic || [[xenharmonic/5L 1s|5L 1s]] || 6 ||   ||   ||   ||   ||   || 6 ||   ||   ||   ||   ||   || 6 ||   ||   ||   ||   ||   || 6 ||   ||   ||   ||   ||   || 6 ||   ||   ||   ||   ||   || 1 ||
|| 11-tone || [[xenharmonic/5L 6s|5L 6s]] || 5 ||   ||   ||   ||   || 1 || 5 ||   ||   ||   ||   || 1 || 5 ||   ||   ||   ||   || 1 || 5 ||   ||   ||   ||   || 1 || 5 ||   ||   ||   ||   || 1 || 1 ||
|| 16-tone || [[xenharmonic/5L 11s|5L 11s]] || 4 ||   ||   ||   || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 1 ||
|| 21-tone || [[xenharmonic/5L 16s|5L 16s]] || 3 ||   ||   || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 3 ||   ||   || 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 ||

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third]]7\31 octave - approx. 429.47¢ - Subminor Third</span>=== 
<span style="background-color: #ffffff;">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#.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| pentatonic || [[xenharmonic/4L 1s|4L 1s]] || 7 ||   ||   ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   || 3 ||   ||   ||
|| nonatonic (quasi-equal; similar to Orwell[9]) || [[xenharmonic/4L 5s|4L 5s]] || 4 ||   ||   ||   || 3 ||   ||   || 4 ||   ||   ||   || 3 ||   ||   || 4 ||   ||   ||   || 3 ||   ||   || 4 ||   ||   ||   || 3 ||   ||   || 3 ||   ||   ||
|| 13-tone (similar to Orwell[13]) || [[xenharmonic/9L 4s|9L 4s]] || 1 || 3 ||   ||   || 3 ||   ||   || 1 || 3 ||   ||   || 3 ||   ||   || 1 || 3 ||   ||   || 3 ||   ||   || 1 || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   ||
|| 22-tone (similar to Orwell[22]) || [[xenharmonic/9L 13s|9L 13s]] || 1 || 1 || 2 ||   || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 2 ||   || 1 || 1 || 2 ||   || 1 || 2 ||   || 1 || 2 ||   ||

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third]]8\31 octave - approx. 490.83¢ - Minor Third</span>=== 
<span style="background-color: #ffffff;">A 4:3 ~1.3 syntonic comma flat. Exactly twice a neutral second, four times a minor semitone, and half of a large tritone.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| tetratonic (quasi-equal) || [[xenharmonic/3L 1s|3L 1s]] || 8 ||   ||   ||   ||   ||   ||   ||   || 8 ||   ||   ||   ||   ||   ||   ||   || 8 ||   ||   ||   ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   ||
|| heptatonic || [[xenharmonic/4L 3s|4L 3s]] || 1 || 7 ||   ||   ||   ||   ||   ||   || 1 || 7 ||   ||   ||   ||   ||   ||   || 1 || 7 ||   ||   ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   ||
|| 11-tone || [[xenharmonic/4L 7s|4L 7s]] || 1 || 1 || 6 ||   ||   ||   ||   ||   || 1 || 1 || 6 ||   ||   ||   ||   ||   || 1 || 1 || 6 ||   ||   ||   ||   ||   || 1 || 6 ||   ||   ||   ||   ||   ||
|| 15-tone || [[xenharmonic/4L 11s|4L 11s]] || 1 || 1 || 1 || 5 ||   ||   ||   ||   || 1 || 1 || 1 || 5 ||   ||   ||   ||   || 1 || 1 || 1 || 5 ||   ||   ||   ||   || 1 || 1 || 5 ||   ||   ||   ||   ||
|| 19-tone || [[xenharmonic/4L 15s|4L 15s]] || 1 || 1 || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 1 || 4 ||   ||   ||   ||
|| 23-tone || [[xenharmonic/4L 19s|4L 19s]] || 1 || 1 || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 1 || 3 ||   ||   ||
|| 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 ||   ||

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third]]9\31 octave - approx. 348.39¢ - Neutral Third</span>=== 
<span style="background-color: #ffffff;">A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for </span>[[xenharmonic/mohajira|mohajira temperament]]<span style="background-color: #ffffff;">), 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 </span>[[xenharmonic/13-limit|13-limit]]<span style="background-color: #ffffff;"> 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.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| tetratonic || [[xenharmonic/3L 1s|3L 1s]] || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 4 ||   ||   ||   ||
|| heptatonic (quasi-equal) || [[xenharmonic/3L 4s|3L 4s]] || 5 ||   ||   ||   ||   || 4 ||   ||   ||   || 5 ||   ||   ||   ||   || 4 ||   ||   ||   || 5 ||   ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   ||
|| 10-tone || [[xenharmonic/7L 3s|7L 3s]] || 1 || 4 ||   ||   ||   || 4 ||   ||   ||   || 1 || 4 ||   ||   ||   || 4 ||   ||   ||   || 1 || 4 ||   ||   ||   || 4 ||   ||   ||   || 4 ||   ||   ||   ||
|| 17-tone || [[xenharmonic/7L 10s|7L 10s]] || 1 || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 1 || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 1 || 1 || 3 ||   ||   || 1 || 3 ||   ||   || 1 || 3 ||   ||   ||
|| 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 ||   ||


===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third]]10\31 octave - approx. 387.10¢ - Major Third</span>=== 
<span style="background-color: #ffffff;">A near-just major 3rd (compare with 5:4 = 386.31¢). Has led to the characterization of 31-edo as "smooth". Generates </span>[[xenharmonic/Wuerschmidt family|wurshmidt/worshmidt temperaments]]<span style="background-color: #ffffff;">.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| tritonic (quasi-equal) || [[xenharmonic/1L 2s|1L 2s]] || 10 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 10 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 11 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| tetratonic || [[xenharmonic/3L 1s|3L 1s]] || 10 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 10 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 10 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 ||
|| heptatonic || [[xenharmonic/3L 4s|3L 4s]] || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 ||
|| 10-tone || [[xenharmonic/3L 7s|3L 7s]] || 8 ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 8 ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 8 ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 ||
|| 13-tone || [[xenharmonic/3L 10s|3L 10s]] || 7 ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 7 ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 7 ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 ||
|| 16-tone || [[xenharmonic/3L 13s|3L 13s]] || 6 ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 6 ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 6 ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 ||
|| 19-tone || [[xenharmonic/3L 16s|3L 16s]] || 5 ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 5 ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 5 ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 22-tone || [[xenharmonic/3L 19s|3L 19s]] || 4 ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 25-tone || [[xenharmonic/3L 22s|3L 22s]] || 3 ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 3 ||   ||   || 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 ||

===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third]]11\31 octave - approx. 425.806¢ - Supermajor Third</span>=== 
<span style="background-color: #ffffff;">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 </span>[[xenharmonic/23-limit|23-limit]]<span style="background-color: #ffffff;">, 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 </span>[[xenharmonic/17edo|17edo]]<span style="background-color: #ffffff;">. Generates </span>[[xenharmonic/Meantone family|squares temperament]]<span style="background-color: #ffffff;">.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| tritonic || [[xenharmonic/2L 1s|2L 1s]] || 11 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 11 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 9 ||   ||   ||   ||   ||   ||   ||   ||   ||
|| pentatonic || [[xenharmonic/3L 2s|3L 2s]] || 2 ||   || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 2 ||   || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 9 ||   ||   ||   ||   ||   ||   ||   ||   ||
|| octatonic || [[xenharmonic/3L 5s|3L 5s]] || 2 ||   || 2 ||   || 7 ||   ||   ||   ||   ||   ||   || 2 ||   || 2 ||   || 7 ||   ||   ||   ||   ||   ||   || 2 ||   || 7 ||   ||   ||   ||   ||   ||   ||
|| 11-tone || [[xenharmonic/3L 8s|3L 8s]] || 2 ||   || 2 ||   || 2 ||   || 5 ||   ||   ||   ||   || 2 ||   || 2 ||   || 2 ||   || 5 ||   ||   ||   ||   || 2 ||   || 2 ||   || 5 ||   ||   ||   ||   ||
|| 14-tone (quasi-equal) || [[xenharmonic/3L 11s|3L 11s]] || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 3 ||   ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 3 ||   ||   || 2 ||   || 2 ||   || 2 ||   || 3 ||   ||   ||
|| 17-tone || [[xenharmonic/3L 14s|3L 14s]] || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 1 || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 ||   || 2 || 1 ||   || 2 ||   || 2 ||   || 2 ||   || 1 ||


===<span style="background-color: #ffffff;">[[#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</span>=== 
<span style="background-color: #ffffff;">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 </span>[[xenharmonic/17-limit|17-limit]]<span style="background-color: #ffffff;">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 </span>[[xenharmonic/semisept|semisept]]<span style="background-color: #ffffff;"> temperament.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| tritonic || [[xenharmonic/2L 1s|2L 1s]] || 12 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 12 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   ||
|| pentatonic || [[xenharmonic/3L 2s|3L 2s]] || 5 ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   || 7 ||   ||   ||   ||   ||   ||   ||
|| octatonic || [[xenharmonic/5L 3s|5L 3s]] || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 2 ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 2 ||   || 5 ||   ||   ||   ||   || 2 ||   ||
|| 13-tone (quasi-equal) || [[xenharmonic/5L 8s|5L 8s]] || 3 ||   ||   || 2 ||   || 3 ||   ||   || 2 ||   || 2 ||   || 3 ||   ||   || 2 ||   || 3 ||   ||   || 2 ||   || 2 ||   || 3 ||   ||   || 2 ||   || 2 ||   ||
|| 18-tone || [[xenharmonic/13L 5s|13L 5s]] || 1 || 2 ||   || 2 ||   || 1 || 2 ||   || 2 ||   || 2 ||   || 1 || 2 ||   || 2 ||   || 1 || 2 ||   || 2 ||   || 2 ||   || 1 || 2 ||   || 2 ||   || 2 ||   ||


===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth]]13\31 octave - approx. 503.23¢ - Perfect Fourth</span>=== 
<span style="background-color: #ffffff;">A slightly wide perfect fourth (compare to 4:3 = 498.04¢). As such, it functions marvelously as a generator for </span>[[xenharmonic/meantone|meantone]]<span style="background-color: #ffffff;"> temperament.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| tritonic || [[xenharmonic/2L 1s|2L 1s]] || 13 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 13 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 5 ||   ||   ||   ||   ||
|| pentatonic || [[xenharmonic/2L 3s|2L 3s]] || 8 ||   ||   ||   ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 8 ||   ||   ||   ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   ||
|| heptatonic || [[xenharmonic/5L 2s|5L 2s]] || 3 ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 3 ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   || 5 ||   ||   ||   ||   ||
|| 12-tone (quasi-equal) || [[xenharmonic/7L 5s|7L 5s]] || 3 ||   ||   || 3 ||   ||   || 2 ||   || 3 ||   ||   || 2 ||   || 3 ||   ||   || 3 ||   ||   || 2 ||   || 3 ||   ||   || 2 ||   || 3 ||   ||   || 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 ||   ||


===<span style="background-color: #ffffff;">[[#Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth]]14\31 octave - approx. 541.94¢ - Superfourth</span>=== 
<span style="background-color: #ffffff;">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 </span>[[xenharmonic/Starling temperaments|casablanca temperament]]<span style="background-color: #ffffff;">.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| tritonic || [[xenharmonic/2L 1s|2L 1s]] || 14 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 14 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 3 ||   ||   ||
|| pentatonic || [[xenharmonic/2L 3s|2L 3s]] || 11 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 3 ||   ||   || 11 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 3 ||   ||   || 3 ||   ||   ||
|| heptatonic || [[xenharmonic/2L 5s|2L 5s]] || 8 ||   ||   ||   ||   ||   ||   ||   || 3 ||   ||   || 3 ||   ||   || 8 ||   ||   ||   ||   ||   ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   ||
|| nonatonic || [[xenharmonic/2L 7s|2L 7s]] || 5 ||   ||   ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 5 ||   ||   ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   ||
|| 11-tone (quasi-equal) || [[xenharmonic/9L 2s|9L 2s]] || 2 ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 2 ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   || 3 ||   ||   ||
|| 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 ||


===<span style="background-color: #ffffff;">[[#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</span>=== 
<span style="background-color: #ffffff;">In 7-limit tonal music, functions quite well as 7:5 (582.51¢). Exactly thrice a whole tone. Generates </span>[[xenharmonic/tritonic|tritonic]]<span style="background-color: #ffffff;"> temperament.</span>
====<span style="background-color: #ffffff;">[[#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:</span>==== 
||~ 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 ||
|| tritonic || [[xenharmonic/2L 1s|2L 1s]] || 15 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 15 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 ||
|| pentatonic || [[xenharmonic/2L 3s|2L 3s]] || 14 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 14 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 ||
|| heptatonic || [[xenharmonic/2L 5s|2L 5s]] || 13 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 13 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 ||
|| nonatonic || [[xenharmonic/2L 7s|2L 7s]] || 12 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 12 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 ||
|| 11-tone || [[xenharmonic/2L 9s|2L 9s]] || 11 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 11 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 ||
|| 13-tone || [[xenharmonic/2L 11s|2L 11s]] || 10 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 10 ||   ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 15-tone || [[xenharmonic/2L 13s|2L 13s]] || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 9 ||   ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 17-tone || [[xenharmonic/2L 15s|2L 15s]] || 8 ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 8 ||   ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 19-tone || [[xenharmonic/2L 17s|2L 17s]] || 7 ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 7 ||   ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 21-tone || [[xenharmonic/2L 19s|2L 19s]] || 6 ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 6 ||   ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 23-tone || [[xenharmonic/2L 21s|2L 21s]] || 5 ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 5 ||   ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 25-tone || [[xenharmonic/2L 23s|2L 23s]] || 4 ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 4 ||   ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 27-tone || [[xenharmonic/2L 25s|2L 25s]] || 3 ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 3 ||   ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||
|| 29-tone || [[xenharmonic/2L 27s|2L 27s]] || 2 ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||   || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 ||

Original HTML content:

<html><head><title>31edt</title></head><body>31edt divides the tritave into equal parts of 61.353 cents, corresponding to the non-octave third tone scale of <a class="wiki_link" href="/39edo">39edo</a> where each degree gets ~.185 cents flatter than the corresponding degree of 39edo. It supports the same higher-limit meantone temperament as 12 edt with better intonation of triads. It also contains a flat version of the BP nonatonic scale and the fair Sigma and false Father.scales.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="background-color: #ffffff;">Intervals</span></h1>
 <br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="Intervals--1\31 tritave- approx. 61.35¢ - Third tone"></a><!-- ws:end:WikiTextHeadingRule:2 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:60:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis&quot;/&gt; --><a name="Intervals-Selected just intervals by error-1\31 octave - approx. 38.71¢ - Diesis"></a><!-- ws:end:WikiTextAnchorRule:60 -->1\31 tritave- approx. <span style="font-size: 1.1em;">61.35¢ - Third tone</span></span></h3>
 <span style="background-color: #ffffff;">A single step of 31-edt is about 6</span><span style="background-color: #ffffff;">1.35¢. Intervals around this size are called <em>third tones</em>. 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.</span><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="Intervals--2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second"></a><!-- ws:end:WikiTextHeadingRule:4 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:61:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second&quot;/&gt; --><a name="Intervals-Selected just intervals by error-2\31 octave - approx. 77.42¢ - Minor Semitone or Chromatic Semitone or Small Minor Second"></a><!-- ws:end:WikiTextAnchorRule:61 -->2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second</span></h3>
 <span style="background-color: #ffffff;">The difference between a major and minor third and the thing to a 'half step'; in</span><br />
<span style="background-color: #ffffff;">macromeantone, it is exactly analogus to the </span><em><span style="background-color: #ffffff;">chromatic semitone</span></em><span style="background-color: #ffffff;">, the interval that distinguishes major and minor intervals of the same generic interval class (eg. thirds). </span><br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h4&gt; --><h4 id="toc3"><a name="Intervals--2\31 tritave - approx. 122.71¢ - Two-third tone or Small Minor Second-MOS Scales generated by 2\31:"></a><!-- ws:end:WikiTextHeadingRule:6 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:62:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&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:&quot; title=&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:&quot;/&gt; --><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:"></a><!-- ws:end:WikiTextAnchorRule:62 -->MOS Scales generated by 2\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>15-tone (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Maximal%20evenness">ME</a> or quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%2014s">1L 14s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>16-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/15L%201s">15L 1s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Intervals--3\31 tritave - approx. 184.06¢- Whole tone or Large Minor Second"></a><!-- ws:end:WikiTextHeadingRule:8 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:63:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-3\31 octave - approx. 116.13¢- Major Semitone or Diatonic Semitone or Large Major Second&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-3\31 octave - approx. 116.13¢- Major Semitone or Diatonic Semitone or Large Major Second&quot;/&gt; --><a name="Intervals-Selected just intervals by error-3\31 octave - approx. 116.13¢- Major Semitone or Diatonic Semitone or Large Major Second"></a><!-- ws:end:WikiTextAnchorRule:63 -->3\31 tritave - approx. 184.06¢- Whole tone or Large Minor Second</span></h3>
 <br />
<span style="background-color: #ffffff;">A small whole tone only ~1.6 cents wide of 10:9 which is an interval sometimes called melodically dull; in macromeantone, it is exactly analogus to the </span><em><span style="background-color: #ffffff;">diatonic semitone</span></em><span style="background-color: #ffffff;"> which appears in the diatonic scale between, for instance, the major third and perfect fourth, and the major seventh and octave. </span><br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h4&gt; --><h4 id="toc5"><a name="Intervals--3\31 tritave - approx. 184.06¢- Whole tone or Large Minor Second-MOS Scales generated by 3\31:"></a><!-- ws:end:WikiTextHeadingRule:10 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:64:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-3\31 octave - approx. 116.13¢- Major Semitone or Diatonic Semitone or Large Major Second-MOS Scales generated by 3\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-3\31 octave - approx. 116.13¢- Major Semitone or Diatonic Semitone or Large Major Second-MOS Scales generated by 3\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-3\31 octave - approx. 116.13¢- Major Semitone or Diatonic Semitone or Large Major Second-MOS Scales generated by 3\31:"></a><!-- ws:end:WikiTextAnchorRule:64 -->MOS Scales generated by 3\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>nonatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%208s">1L 8s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>decatonic (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%201s">9L 1s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/10L%201s">10L 1s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>21-tone (silimlar to Blackjack)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/11L%2010s">11L 10s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Intervals--4\31 tritave - approx. 245.41¢ - Classical hemifourth or Neutral Second"></a><!-- ws:end:WikiTextHeadingRule:12 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:65:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-4\31 octave - approx. 154.84¢ - Neutral Tone or Neutral Second&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-4\31 octave - approx. 154.84¢ - Neutral Tone or Neutral Second&quot;/&gt; --><a name="Intervals-Selected just intervals by error-4\31 octave - approx. 154.84¢ - Neutral Tone or Neutral Second"></a><!-- ws:end:WikiTextAnchorRule:65 -->4\31 tritave - approx. 245.41¢ - Classical hemifourth or Neutral Second</span></h3>
 <span style="background-color: #ffffff;">Exactly one half of the minor third and twice the minor semitone, 4\31 stands in for 15:13 (247.74¢). Although 31 is not extremely accurate with 5 or 13, it is notable that the inaccuracies of these harmonics cancel out so much, leaving the interval that distinguishes them (15/13) only about 2.3¢ off.</span><br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h4&gt; --><h4 id="toc7"><a name="Intervals--4\31 tritave - approx. 245.41¢ - Classical hemifourth or Neutral Second-MOS Scales generated by 4\31:"></a><!-- ws:end:WikiTextHeadingRule:14 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:66:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-4\31 octave - approx. 154.84¢ - Neutral Tone or Neutral Second-MOS Scales generated by 4\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-4\31 octave - approx. 154.84¢ - Neutral Tone or Neutral Second-MOS Scales generated by 4\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-4\31 octave - approx. 154.84¢ - Neutral Tone or Neutral Second-MOS Scales generated by 4\31:"></a><!-- ws:end:WikiTextAnchorRule:66 -->MOS Scales generated by 4\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>heptatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%206s">1L 6s</a><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>octatonic (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%201s">7L 1s</a><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%207s">8L 7s</a><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%2015s">8L 15s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Intervals--5\31 tritave - approx. 306.77¢ - Sesquitone or Major Second"></a><!-- ws:end:WikiTextHeadingRule:16 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:67:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-5\31 octave - approx. 193.55¢ - Whole Tone or Major Second&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-5\31 octave - approx. 193.55¢ - Whole Tone or Major Second&quot;/&gt; --><a name="Intervals-Selected just intervals by error-5\31 octave - approx. 193.55¢ - Whole Tone or Major Second"></a><!-- ws:end:WikiTextAnchorRule:67 -->5\31 tritave - approx. 306.77¢ - <span style="font-size: 1.1em;">Sesquitone or Major Second</span></span></h3>
 <span style="background-color: #ffffff;">At ~8.8 cents flat of a just 6:5, 5\31 is considered a &quot;sesquitone&quot;. Two of this sesquitone make a near-just 10:7 tritone. Because it is fairly close to no intelligibly small integer ratio but 6/5, 5\31 can function as a semi-stabilized harmonic ninth.</span><br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h4&gt; --><h4 id="toc9"><a name="Intervals--5\31 tritave - approx. 306.77¢ - Sesquitone or Major Second-MOS Scales generated by 5\31:"></a><!-- ws:end:WikiTextHeadingRule:18 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:68:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-5\31 octave - approx. 193.55¢ - Whole Tone or Major Second-MOS Scales generated by 5\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-5\31 octave - approx. 193.55¢ - Whole Tone or Major Second-MOS Scales generated by 5\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-5\31 octave - approx. 193.55¢ - Whole Tone or Major Second-MOS Scales generated by 5\31:"></a><!-- ws:end:WikiTextAnchorRule:68 -->MOS Scales generated by 5\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>hexatonic (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%205s">1L 5s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>heptatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%201s">6L 1s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>13-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%207s">6L 7s</a><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>19-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%2013s">6L 13s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>25-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/6L%2019s">6L 19s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Intervals--6\31 tritave - approx. 368.12¢ - Supermajor Second"></a><!-- ws:end:WikiTextHeadingRule:20 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:69:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second&quot;/&gt; --><a name="Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second"></a><!-- ws:end:WikiTextAnchorRule:69 -->6\31 tritave - approx. 368.12¢ - Supermajor Second</span></h3>
 <span style="background-color: #ffffff;">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 </span><span style="background-color: #ffffff;">21:17 (365.825¢). In </span><span style="background-color: #ffffff;">macro</span><span style="background-color: #ffffff;">meantone, it is a diminished third, eg. C to Ebb.</span><br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h4&gt; --><h4 id="toc11"><a name="Intervals--6\31 tritave - approx. 368.12¢ - Supermajor Second-MOS Scales generated by 6\31:"></a><!-- ws:end:WikiTextHeadingRule:22 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:70:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-6\31 octave - approx. 232.26¢ - Supermajor Second-MOS Scales generated by 6\31:"></a><!-- ws:end:WikiTextAnchorRule:70 -->MOS Scales generated by 6\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>pentatonic (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%204s">1L 4s</a><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>hexatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%201s">5L 1s</a><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>11-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%206s">5L 6s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>16-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%2011s">5L 11s</a><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>21-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%2016s">5L 16s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>26-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%2021s">5L 21s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Intervals--7\31 octave - approx. 429.47¢ - Subminor Third"></a><!-- ws:end:WikiTextHeadingRule:24 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:71:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third&quot;/&gt; --><a name="Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third"></a><!-- ws:end:WikiTextAnchorRule:71 -->7\31 octave - approx. 429.47¢ - Subminor Third</span></h3>
 <span style="background-color: #ffffff;">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#.</span><br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h4&gt; --><h4 id="toc13"><a name="Intervals--7\31 octave - approx. 429.47¢ - Subminor Third-MOS Scales generated by 7\31:"></a><!-- ws:end:WikiTextHeadingRule:26 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:72:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:"></a><!-- ws:end:WikiTextAnchorRule:72 -->MOS Scales generated by 7\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>pentatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%201s">4L 1s</a><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>nonatonic (quasi-equal; similar to Orwell[9])<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%205s">4L 5s</a><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13-tone (similar to Orwell[13])<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%204s">9L 4s</a><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>22-tone (similar to Orwell[22])<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%2013s">9L 13s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Intervals--8\31 octave - approx. 490.83¢ - Minor Third"></a><!-- ws:end:WikiTextHeadingRule:28 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:73:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third&quot;/&gt; --><a name="Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third"></a><!-- ws:end:WikiTextAnchorRule:73 -->8\31 octave - approx. 490.83¢ - Minor Third</span></h3>
 <span style="background-color: #ffffff;">A 4:3 ~1.3 syntonic comma flat. Exactly twice a neutral second, four times a minor semitone, and half of a large tritone.</span><br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h4&gt; --><h4 id="toc15"><a name="Intervals--8\31 octave - approx. 490.83¢ - Minor Third-MOS Scales generated by 8\31:"></a><!-- ws:end:WikiTextHeadingRule:30 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:74:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:"></a><!-- ws:end:WikiTextAnchorRule:74 -->MOS Scales generated by 8\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>tetratonic (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%201s">3L 1s</a><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>heptatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%203s">4L 3s</a><br />
</td>
        <td>1<br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%207s">4L 7s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>15-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%2011s">4L 11s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%2015s">4L 15s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>23-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%2019s">4L 19s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4L%2023s">4L 23s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Intervals--9\31 octave - approx. 348.39¢ - Neutral Third"></a><!-- ws:end:WikiTextHeadingRule:32 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:75:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third&quot;/&gt; --><a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third"></a><!-- ws:end:WikiTextAnchorRule:75 -->9\31 octave - approx. 348.39¢ - Neutral Third</span></h3>
 <span style="background-color: #ffffff;">A neutral 3rd, about 1¢ away from 11:9 (347.41¢). 9\31 is half a perfect fifth (making it a suitable generator for </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/mohajira">mohajira temperament</a><span style="background-color: #ffffff;">), 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 </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/13-limit">13-limit</a><span style="background-color: #ffffff;"> 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 &quot;major-like&quot; than &quot;minor-like&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.</span><br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h4&gt; --><h4 id="toc17"><a name="Intervals--9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:"></a><!-- ws:end:WikiTextHeadingRule:34 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:76:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:"></a><!-- ws:end:WikiTextAnchorRule:76 -->MOS Scales generated by 9\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>tetratonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%201s">3L 1s</a><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>heptatonic (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%204s">3L 4s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%203s">7L 3s</a><br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%2010s">7L 10s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>24-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%2017s">7L 17s</a><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h3&gt; --><h3 id="toc18"><a name="Intervals--10\31 octave - approx. 387.10¢ - Major Third"></a><!-- ws:end:WikiTextHeadingRule:36 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:77:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third&quot;/&gt; --><a name="Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third"></a><!-- ws:end:WikiTextAnchorRule:77 -->10\31 octave - approx. 387.10¢ - Major Third</span></h3>
 <span style="background-color: #ffffff;">A near-just major 3rd (compare with 5:4 = 386.31¢). Has led to the characterization of 31-edo as &quot;smooth&quot;. Generates </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Wuerschmidt%20family">wurshmidt/worshmidt temperaments</a><span style="background-color: #ffffff;">.</span><br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h4&gt; --><h4 id="toc19"><a name="Intervals--10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:"></a><!-- ws:end:WikiTextHeadingRule:38 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:78:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:"></a><!-- ws:end:WikiTextAnchorRule:78 -->MOS Scales generated by 10\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>tritonic (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1L%202s">1L 2s</a><br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>tetratonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%201s">3L 1s</a><br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>heptatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%204s">3L 4s</a><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>10-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%207s">3L 7s</a><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>13-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2010s">3L 10s</a><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>16-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2013s">3L 13s</a><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>19-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2016s">3L 16s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>22-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2019s">3L 19s</a><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>25-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2022s">3L 22s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>28-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2025s">3L 25s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h3&gt; --><h3 id="toc20"><a name="Intervals--11\31 octave - approx. 425.806¢ - Supermajor Third"></a><!-- ws:end:WikiTextHeadingRule:40 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:79:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third&quot;/&gt; --><a name="Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third"></a><!-- ws:end:WikiTextAnchorRule:79 -->11\31 octave - approx. 425.806¢ - Supermajor Third</span></h3>
 <span style="background-color: #ffffff;">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 </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/23-limit">23-limit</a><span style="background-color: #ffffff;">, 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 </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a><span style="background-color: #ffffff;">. Generates </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">squares temperament</a><span style="background-color: #ffffff;">.</span><br />
<!-- ws:start:WikiTextHeadingRule:42:&lt;h4&gt; --><h4 id="toc21"><a name="Intervals--11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:"></a><!-- ws:end:WikiTextHeadingRule:42 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:80:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-11\31 octave - approx. 425.806¢ - Supermajor Third-MOS Scales generated by 11\31:"></a><!-- ws:end:WikiTextAnchorRule:80 -->MOS Scales generated by 11\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>tritonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%201s">2L 1s</a><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>pentatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%202s">3L 2s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>octatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%205s">3L 5s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%208s">3L 8s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14-tone (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2011s">3L 11s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>17-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%2014s">3L 14s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td>1<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:44:&lt;h3&gt; --><h3 id="toc22"><a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"></a><!-- ws:end:WikiTextHeadingRule:44 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:81:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth&quot;/&gt; --><a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth"></a><!-- ws:end:WikiTextAnchorRule:81 -->12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth</span></h3>
 <span style="background-color: #ffffff;">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 </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/17-limit">17-limit</a><span style="background-color: #ffffff;">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 </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/semisept">semisept</a><span style="background-color: #ffffff;"> temperament.</span><br />
<!-- ws:start:WikiTextHeadingRule:46:&lt;h4&gt; --><h4 id="toc23"><a name="Intervals--12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"></a><!-- ws:end:WikiTextHeadingRule:46 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:82:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&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:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-12\31 octave - approx. 464.52¢ - Narrow Fourth or Subfourth-MOS Scales generated by 12\31:"></a><!-- ws:end:WikiTextAnchorRule:82 -->MOS Scales generated by 12\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>tritonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%201s">2L 1s</a><br />
</td>
        <td>12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>pentatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3L%202s">3L 2s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>octatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%203s">5L 3s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>13-tone (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%208s">5L 8s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>18-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/13L%205s">13L 5s</a><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:48:&lt;h3&gt; --><h3 id="toc24"><a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth"></a><!-- ws:end:WikiTextHeadingRule:48 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:83:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth&quot;/&gt; --><a name="Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth"></a><!-- ws:end:WikiTextAnchorRule:83 -->13\31 octave - approx. 503.23¢ - Perfect Fourth</span></h3>
 <span style="background-color: #ffffff;">A slightly wide perfect fourth (compare to 4:3 = 498.04¢). As such, it functions marvelously as a generator for </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone">meantone</a><span style="background-color: #ffffff;"> temperament.</span><br />
<!-- ws:start:WikiTextHeadingRule:50:&lt;h4&gt; --><h4 id="toc25"><a name="Intervals--13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:"></a><!-- ws:end:WikiTextHeadingRule:50 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:84:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-13\31 octave - approx. 503.23¢ - Perfect Fourth-MOS Scales generated by 13\31:"></a><!-- ws:end:WikiTextAnchorRule:84 -->MOS Scales generated by 13\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>tritonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%201s">2L 1s</a><br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>pentatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>heptatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5L%202s">5L 2s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12-tone (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/7L%205s">7L 5s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>19-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/12L%207s">12L 7s</a><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc26"><a name="Intervals--14\31 octave - approx. 541.94¢ - Superfourth"></a><!-- ws:end:WikiTextHeadingRule:52 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:85:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth&quot;/&gt; --><a name="Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth"></a><!-- ws:end:WikiTextAnchorRule:85 -->14\31 octave - approx. 541.94¢ - Superfourth</span></h3>
 <span style="background-color: #ffffff;">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 </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Starling%20temperaments">casablanca temperament</a><span style="background-color: #ffffff;">.</span><br />
<!-- ws:start:WikiTextHeadingRule:54:&lt;h4&gt; --><h4 id="toc27"><a name="Intervals--14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:"></a><!-- ws:end:WikiTextHeadingRule:54 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:86:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:&quot;/&gt; --><a name="Intervals-Selected just intervals by error-14\31 octave - approx. 541.94¢ - Superfourth-MOS Scales generated by 14\31:"></a><!-- ws:end:WikiTextAnchorRule:86 -->MOS Scales generated by 14\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>tritonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%201s">2L 1s</a><br />
</td>
        <td>14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>pentatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>heptatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%205s">2L 5s</a><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>nonatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%207s">2L 7s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11-tone (quasi-equal)<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/9L%202s">9L 2s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>20-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/11L%209s">11L 9s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:56:&lt;h3&gt; --><h3 id="toc28"><a name="Intervals--15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth"></a><!-- ws:end:WikiTextHeadingRule:56 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:87:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&quot; title=&quot;Anchor: Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth&quot;/&gt; --><a name="Intervals-Selected just intervals by error-15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth"></a><!-- ws:end:WikiTextAnchorRule:87 -->15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth</span></h3>
 <span style="background-color: #ffffff;">In 7-limit tonal music, functions quite well as 7:5 (582.51¢). Exactly thrice a whole tone. Generates </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/tritonic">tritonic</a><span style="background-color: #ffffff;"> temperament.</span><br />
<!-- ws:start:WikiTextHeadingRule:58:&lt;h4&gt; --><h4 id="toc29"><a name="Intervals--15\31 octave - approx. 580.65¢ - Small Tritone or Augmented Fourth or Subdiminished Fifth-MOS Scales generated by 15\31:"></a><!-- ws:end:WikiTextHeadingRule:58 --><span style="background-color: #ffffff;"><!-- ws:start:WikiTextAnchorRule:88:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&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:&quot; title=&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:&quot;/&gt; --><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:"></a><!-- ws:end:WikiTextAnchorRule:88 -->MOS Scales generated by 15\31:</span></h4>
 

<table class="wiki_table">
    <tr>
        <th>number of tones<br />
</th>
        <th>MOS class<br />
</th>
        <th>0<br />
</th>
        <th>1<br />
</th>
        <th>2<br />
</th>
        <th>3<br />
</th>
        <th>4<br />
</th>
        <th>5<br />
</th>
        <th>6<br />
</th>
        <th>7<br />
</th>
        <th>8<br />
</th>
        <th>9<br />
</th>
        <th>10<br />
</th>
        <th>11<br />
</th>
        <th>12<br />
</th>
        <th>13<br />
</th>
        <th>14<br />
</th>
        <th>15<br />
</th>
        <th>16<br />
</th>
        <th>17<br />
</th>
        <th>18<br />
</th>
        <th>19<br />
</th>
        <th>20<br />
</th>
        <th>21<br />
</th>
        <th>22<br />
</th>
        <th>23<br />
</th>
        <th>24<br />
</th>
        <th>25<br />
</th>
        <th>26<br />
</th>
        <th>27<br />
</th>
        <th>28<br />
</th>
        <th>29<br />
</th>
        <th>30<br />
</th>
    </tr>
    <tr>
        <td>tritonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%201s">2L 1s</a><br />
</td>
        <td>15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>pentatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%203s">2L 3s</a><br />
</td>
        <td>14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>heptatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%205s">2L 5s</a><br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>nonatonic<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%207s">2L 7s</a><br />
</td>
        <td>12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>11-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%209s">2L 9s</a><br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>13-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2011s">2L 11s</a><br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>10<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>15-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2013s">2L 13s</a><br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>9<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>17-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2015s">2L 15s</a><br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>19-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2017s">2L 17s</a><br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>7<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>21-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2019s">2L 19s</a><br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>6<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>23-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2021s">2L 21s</a><br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>25-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2023s">2L 23s</a><br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>4<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>27-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2025s">2L 25s</a><br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
    <tr>
        <td>29-tone<br />
</td>
        <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/2L%2027s">2L 27s</a><br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>2<br />
</td>
        <td><br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
        <td>1<br />
</td>
    </tr>
</table>

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