List of superparticular intervals: Difference between revisions

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Wikispaces>Andrew_Heathwaite
**Imported revision 258818696 - Original comment: **
Wikispaces>keenanpepper
**Imported revision 269487212 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-27 17:37:25 UTC</tt>.<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-28 04:07:29 UTC</tt>.<br>
: The original revision id was <tt>258818696</tt>.<br>
: The original revision id was <tt>269487212</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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See also: [[Gallery of Just Intervals]]. Many of the names below come from [[http://www.huygens-fokker.org/docs/intervals.html|here]].
See also: [[Gallery of Just Intervals]]. Many of the names below come from [[http://www.huygens-fokker.org/docs/intervals.html|here]].


||~ Ratio ||~ Cents Value ||~ Factorization ||~ Prime Limit ||~ Name(s) ||
||~ Ratio ||~ Cents Value ||~ Factorization ||~ Name(s) ||
|| [[2_1|2/1]] || 1200.000 || 2/1 || 2 || (perfect) unison, unity, perfect prime, tonic, duple ||
||||||||~ 2-limit ||
|| [[3_2|3/2]] || 701.995 || 3/2 || 3 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente ||
|| [[2_1|2/1]] || 1200.000 || 2/1 || (perfect) unison, unity, perfect prime, tonic, duple ||
|| [[4_3|4/3]] || 498.045 || 2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/3 || 3 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
||||||||~ 3-limit ||
|| [[5_4|5/4]] || 386.314 || 5/2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || 5 || (classic) (5-limit) major third, 5th harmonic (octave reduced) ||
|| [[3_2|3/2]] || 701.995 || 3/2 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente ||
|| [[6_5|6/5]] || 315.641 || (2*3)/5 || 5 || (classic) (5-limit) minor third ||
|| [[4_3|4/3]] || 498.045 || 2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/3 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
|| [[7_6|7/6]] || 266.871 || 7/(2*3) || 7 || (septimal) subminor third, septimal minor third, augmented second ||
|| [[9_8|9/8]] || 203.910 || 3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt; || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) ||
|| [[8_7|8/7]] || 231.174 || 2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/7 || 7 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
||||||||~ 5-limit ||
|| [[9_8|9/8]] || 203.910 || 3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt; || 3 || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) ||
|| [[5_4|5/4]] || 386.314 || 5/2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || (classic) (5-limit) major third, 5th harmonic (octave reduced) ||
|| [[10_9|10/9]] || 182.404 || (2*5)/3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || 5 || classic (whole) tone, classic major second, minor whole tone ||
|| [[6_5|6/5]] || 315.641 || (2*3)/5 || (classic) (5-limit) minor third ||
|| [[11_10|11/10]] || 165.004 || 11/(2*5) || 11 || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
|| [[10_9|10/9]] || 182.404 || (2*5)/3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || classic (whole) tone, classic major second, minor whole tone ||
|| [[12_11|12/11]] || 150.637 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)/11 || 11 || (small) (undecimal) neutral second, 3/4-tone ||
|| [[16_15|16/15]] || 111.713 || 2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(3*5) || minor diatonic semitone, 15th subharmonic ||
|| [[13_12|13/12]] || 138.573 || 13/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3) || 13 || tridecimal 2/3-tone ||
|| [[25_24|25/24]] || 70.672 || 5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3) || chroma, (classic) chromatic semitone, Zarlinian semitone ||
|| [[14_13|14/13]] || 128.298 || (2*7)/13 || 13 || 2/3-tone, trienthird ||
|| [[81_80|81/80]] || 21.506 || 3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5) || syntonic comma, Didymus comma ||
|| [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || 7 || septimal diatonic semitone ||
||||||||~ 7-limit ||
|| [[16_15|16/15]] || 111.713 || 2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(3*5) || 5 || minor diatonic semitone, 15th subharmonic ||
|| [[7_6|7/6]] || 266.871 || 7/(2*3) || (septimal) subminor third, septimal minor third, augmented second ||
|| [[17_16|17/16]] || 104.955 || 17/2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt; || 17 || 17th harmonic (octave reduced) ||
|| [[8_7|8/7]] || 231.174 || 2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/7 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
|| [[18_17|18/17]] || 98.955 || (2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/17 || 17 || Arabic lute index finger ||
|| [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || septimal diatonic semitone ||
|| [[19_18|19/18]] || 93.603 || 19/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 19 || undevicesimal semitone ||
|| [[21_20|21/20]] || 84.467 || (3*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) || minor semitone, large septimal chromatic semitone ||
|| [[20_19|20/19]] || 88.801 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/19 || 19 || small undevicesimal semitone ||
|| [[28_27|28/27]] || 62.961 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt; || septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone ||
|| [[21_20|21/20]] || 84.467 || (3*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) || 7 || minor semitone, large septimal chromatic semitone ||
|| [[36_35|36/35]] || 48.770 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(5*7) || septimal quarter tone, septimal diesis ||
|| [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || 11 || undecimal minor semitone ||
|| [[49_48|49/48]] || 35.697 || 7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3) || large septimal diesis, slendro diesis, septimal 1/6-tone ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) || 23 ||  ||
|| [[50_49|50/49]] || 34.976 || (2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
|| [[24_23|24/23]] || 73.681 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)/23 || 23 ||  ||
|| [[64_63|64/63]] || 27.264 || 2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7) || septimal comma, Archytas' comma ||
|| [[25_24|25/24]] || 70.672 || 5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3) || 5 || chroma, (classic) chromatic semitone, Zarlinian semitone ||
|| [[126_125|126/125]] || 13.795 || (2*3^2*7)/5^3 || starling comma ||
|| [[26_25|26/25]] || 67.900 || (2*13)/5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || 13 || tridecimal 1/3-tone ||
|| [[225_224|225/224]] || 7.7115 || (3^2*5^2)/(2^5*7) || marvel comma ||
|| [[27_26|27/26]] || 65.337 || 3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/(2*13) || 13 || tridecimal comma ||
|| [[2401_2400|2401/2400]] || 0.72120 || 7^4/(2^5*3*5^2) || breedsma ||
|| [[28_27|28/27]] || 62.961 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt; || 7 || septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone ||
|| [[4375_4374|4375/4374]] || 0.39576 || (5^4*7)/(2*3^7) || ragisma ||
|| [[29_28|29/28]] || 60.751 || 29/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7) || 29 ||  ||
||||||||~ 11-limit ||
|| [[30_29|30/29]] || 58.692 || (2*3*5)/29 || 29 ||  ||
|| [[11_10|11/10]] || 165.004 || 11/(2*5) || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
|| [[31_30|31/30]] || 56.767 || 31/(2*3*5) || 31 ||  ||
|| [[12_11|12/11]] || 150.637 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)/11 || (small) (undecimal) neutral second, 3/4-tone ||
|| [[32_31|32/31]] || 54.964 || 2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;/31 || 31 || 31st subharmonic ||
|| [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || undecimal minor semitone ||
|| [[33_32|33/32]] || 53.273 || (3*11)/2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt; || 11 || unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
|| [[33_32|33/32]] || 53.273 || (3*11)/2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt; || unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
|| [[34_33|34/33]] || 51.682 || (2*17)/(3*33) || 17 ||  ||
|| [[45_44|45/44]] || 38.906 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11) || 1/5-tone ||
|| [[35_34|35/34]] || 50.184 || (5*7)/(2*17) || 17 || septendecimal 1/4-tone ||
|| [[55_54|55/54]] || 31.767 || (5*11)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;) ||  ||
|| [[36_35|36/35]] || 48.770 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(5*7) || 7 || septimal quarter tone, septimal diesis ||
|| [[56_55|56/55]] || 31.194 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)/(5*11) ||   ||
|| [[37_36|37/36]] || 47.434 || 37/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 37 ||  ||
|| [[99_98|99/98]] || 17.576 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||   ||
|| [[38_37|38/37]] || 46.169 || (2*19)/37 || 37 ||  ||
|| [[100_99|100/99]] || 17.399 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11) || Ptolemy's comma ||
|| [[39_38|39/38]] || 44.970 || (3*13)/(2*19) || 19 ||   ||
|| [[121_120|121/120]] || 14.376 || 11^2/(2^3*3*5) ||   ||
|| [[40_39|40/39]] || 43.831 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)/(3*13) || 13 || tridecimal minor diesis ||
|| [[176_175|176/175]] || 9.8646 || (2^4*11)/(5^2*7) ||  ||
|| [[41_40|41/40]] || 42.749 || 41/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5) || 41 ||  ||
|| [[243_242|243/242]] || 7.1391 || 2^5/(2*11^2) ||  ||
|| [[42_41|42/41]] || 41.719 || (2*3*7)/41 || 41 |||
|| [[385_384|385/384]] || 4.5026 || (5*7*11)/(2^7*3) || keenanisma ||
|| [[43_42|43/42]] || 40.737 || 43/(2*3*7) || 43 ||  ||
|| [[441_440|441/440]] || 3.9302 || (3^2*7^2)/(2^3*5*11) ||  ||
|| [[44_43|44/43]] || 39.800 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/43 || 43 ||  ||
|| [[540_539|540/539]] || 3.2090 || (2^2*3^3*5)/(7^2*11) ||  ||
|| [[45_44|45/44]] || 38.906 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11) || 11 || 1/5-tone ||
|| [[3025_3024|3025/3024]] || 0.57240 || (5^2*11^2)/(2^4*3^3*7) ||  ||
|| [[46_45|46/45]] || 38.051 || (2*23)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) || 23 ||  ||
|| [[9801_9800|9801/9800]] || 0.17665 || (3^4*11^2)/(2^3*5^2*7^2) ||   ||
|| [[47_46|47/46]] || 37.232 || 47/(2*23) || 47 ||  ||
||||||||~ 13-limit (incomplete) ||
|| [[48_47|48/47]] || 36.448 || (2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)/47 || 47 ||   ||
|| [[13_12|13/12]] || 138.573 || 13/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3) || tridecimal 2/3-tone ||
|| [[49_48|49/48]] || 35.697 || 7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3) || 7 || large septimal diesis, slendro diesis, septimal 1/6-tone ||
|| [[14_13|14/13]] || 128.298 || (2*7)/13 || 2/3-tone, trienthird ||
|| [[50_49|50/49]] || 34.976 || (2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || 7 || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
|| [[26_25|26/25]] || 67.900 || (2*13)/5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; || tridecimal 1/3-tone ||
|| [[51_50|51/50]] || 34.283 || (3*17)/(2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 17 || 17th-partial chroma ||
|| [[27_26|27/26]] || 65.337 || 3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/(2*13) || tridecimal comma ||
|| [[52_51|52/51]] || 33.617 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)/(3*17) || 17 ||  ||
|| [[40_39|40/39]] || 43.831 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)/(3*13) || tridecimal minor diesis ||
|| [[53_52|53/52]] || 32.977 || 53/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13) || 53 ||   ||
|| [[65_64|65/64]] || 26.841 || (5*13)/2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt; || 13th-partial chroma ||
|| [[54_53|54/53]] || 32.360 || (2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/53 || 53 ||  ||
|| [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) ||  ||
|| [[55_54|55/54]] || 31.767 || (5*11)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;) || 11 ||  ||
|| [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) ||  ||
|| [[56_55|56/55]] || 31.194 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)/(5*11) || 11 ||  ||
|| [[91_90|91/90]] || 19.130 || (7*13)/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) ||   ||
|| [[57_56|57/56]] || 30.642 || (3*19)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7) || 19 ||  ||
||||||||~ 17-limit (incomplete) ||
|| [[58_57|58/57]] || 30.109 || (2*29)/(3*19) || 29 ||  ||
|| [[17_16|17/16]] || 104.955 || 17/2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt; || 17th harmonic (octave reduced) ||
|| [[59_58|59/58]] || 29.594 || 59/(2*29) || 59 ||  ||
|| [[18_17|18/17]] || 98.955 || (2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/17 || Arabic lute index finger ||
|| [[60_59|60/59]] || 29.097 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)/59 || 59 ||  ||
|| [[34_33|34/33]] || 51.682 || (2*17)/(3*33) ||   ||
|| [[61_60|61/60]] || 28.616 || 61/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5) || 61 ||  ||
|| [[35_34|35/34]] || 50.184 || (5*7)/(2*17) || septendecimal 1/4-tone ||
|| [[62_61|62/61]] || 28.151 || (2*31)/61 || 61 ||  ||
|| [[51_50|51/50]] || 34.283 || (3*17)/(2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 17th-partial chroma ||
|| [[63_62|63/62]] || 27.700 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/(2*31) || 31 ||  ||
|| [[52_51|52/51]] || 33.617 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)/(3*17) ||  ||
|| [[64_63|64/63]] || 27.264 || 2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7) || 7 || septimal comma, Archytas' comma ||
|| [[85_84|85/84]] || 20.488 || (5*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7) ||   ||
|| [[65_64|65/64]] || 26.841 || (5*13)/2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt; || 13 || 13th-partial chroma ||
||||||||~ 19-limit (incomplete) ||
|| [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) || 13 ||  ||
|| [[19_18|19/18]] || 93.603 || 19/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || undevicesimal semitone ||
|| [[67_66|67/66]] || 26.034 || 67/(2*3*11) || 67 ||   ||
|| [[20_19|20/19]] || 88.801 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/19 || small undevicesimal semitone ||
|| [[68_67|68/67]] || 25.648 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/67 || 67 ||  ||
|| [[39_38|39/38]] || 44.970 || (3*13)/(2*19) ||  ||
|| [[69_68|69/68]] || 25.274 || (3*23)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) || 23 ||  ||
|| [[57_56|57/56]] || 30.642 || (3*19)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7) ||  ||
|| [[70_69|70/69]] || 24.910 || (2*5*7)/(3*23) || 23 ||  ||
|| [[76_75|76/75]] || 22.931 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| [[71_70|71/70]] || 24.557 || 71/(2*5*7) || 71 ||   ||
|| [[77_76|77/76]] || 22.631 || (7*11)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19) ||  ||
|| [[72_71|72/71]] || 24.213 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/71 || 71 ||  ||
|| [[96_95|96/95]] || 18.128 || (2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)/(5*19) ||  ||
|| [[73_72|73/72]] || 23.879 || 73/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 73 ||  ||
||||||||~ 23-limit (incomplete) ||
|| [[74_73|74/73]] || 23.555 || (2*37)/73 || 73 ||  ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) ||  ||
|| [[75_74|75/74]] || 23.238 || (3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2*37) || 37 ||   ||
|| [[24_23|24/23]] || 73.681 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)/23 ||  ||
|| [[76_75|76/75]] || 22.931 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 19 ||  ||
|| [[46_45|46/45]] || 38.051 || (2*23)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) ||   ||
|| [[77_76|77/76]] || 22.631 || (7*11)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19) || 19 ||  ||
|| [[69_68|69/68]] || 25.274 || (3*23)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||   ||
|| [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) || 13 ||  ||
|| [[70_69|70/69]] || 24.910 || (2*5*7)/(3*23) ||  ||
|| [[79_78|79/78]] || 22.054 || 79/(2*3*13) || 79 ||  ||
|| [[92_91|92/91]] || 18.921 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)/(7*13) ||  ||
|| [[80_79|80/79]] || 21.777 || (2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5)/79 || 79 ||  ||
||||||||~ 29-limit (incomplete) ||
|| [[81_80|81/80]] || 21.506 || 3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5) || 5 || syntonic comma, Didymus comma ||
|| [[29_28|29/28]] || 60.751 || 29/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7) ||  ||
|| [[82_81|82/81]] || 21.242 || (2*41)/3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt; || 41 ||  ||
|| [[30_29|30/29]] || 58.692 || (2*3*5)/29 ||  ||
|| [[83_82|83/82]] || 20.985 || 83/(2*41) || 83 ||  ||
|| [[58_57|58/57]] || 30.109 || (2*29)/(3*19) ||  ||
|| [[84_83|84/83]] || 20.734 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7)/83 || 83 ||   ||
|| [[88_87|88/87]] || 19.786 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)/(3*29) ||  ||
|| [[85_84|85/84]] || 20.488 || (5*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3) || 17 ||  ||
||||||||~ 31-limit (incomplete) ||
|| [[86_85|86/85]] || 20.249 || (2*43)/(5*17) || 43 ||  ||
|| [[31_30|31/30]] || 56.767 || 31/(2*3*5) ||  ||
|| [[87_86|87/86]] || 20.014 || (3*29)/(2*43) || 43 ||   ||
|| [[32_31|32/31]] || 54.964 || 2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;/31 || 31st subharmonic ||
|| [[88_87|88/87]] || 19.786 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)/(3*29) || 29 ||  ||
|| [[63_62|63/62]] || 27.700 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/(2*31) ||  ||
|| [[89_88|89/88]] || 19.562 || 89/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11) || 89 ||  ||
|| [[93_92|93/92]] || 18.716 || (3*31)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23) ||   ||
|| [[90_89|90/89]] || 19.344 || (2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/89 || 89 ||  ||
||||||||~ 37-limit (incomplete) ||
|| [[91_90|91/90]] || 19.130 || (7*13)/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) || 13 ||  ||
|| [[37_36|37/36]] || 47.434 || 37/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| [[92_91|92/91]] || 18.921 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)/(7*13) || 23 ||   ||
|| [[38_37|38/37]] || 46.169 || (2*19)/37 ||  ||
|| [[93_92|93/92]] || 18.716 || (3*31)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23) || 31 ||  ||
|| [[75_74|75/74]] || 23.238 || (3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2*37) ||  ||
|| [[94_93|94/93]] || 18.516 || (2*47)/(3*31) || 47 ||   ||
||||||||~ 41-limit (incomplete) ||
|| [[95_94|95/94]] || 18.320 || (5*19)/(2*47) || 47 ||  ||
|| [[41_40|41/40]] || 42.749 || 41/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5) ||  ||
|| [[96_95|96/95]] || 18.128 || (2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)/(5*19) || 19 ||   ||
|| [[42_41|42/41]] || 41.719 || (2*3*7)/41 ||  ||
|| [[97_96|97/96]] || 17.940 || 97/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3) || 97 ||  ||
|| [[82_81|82/81]] || 21.242 || (2*41)/3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt; ||   ||
|| [[98_97|98/97]] || 17.756 || (2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/97 || 97 ||  ||
||||||||~ 43-limit (incomplete) ||
|| [[99_98|99/98]] || 17.576 || (3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 11 ||  ||
|| [[43_42|43/42]] || 40.737 || 43/(2*3*7) ||  ||
|| [[100_99|100/99]] || 17.399 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11) || 11 || Ptolemy's comma ||
|| [[44_43|44/43]] || 39.800 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/43 ||  ||
|| [[101_100|101/100]] || 17.226 || 101/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) || 101 ||  ||</pre></div>
|| [[86_85|86/85]] || 20.249 || (2*43)/(5*17) ||  ||
|| [[87_86|87/86]] || 20.014 || (3*29)/(2*43) ||  ||
||||||||~ 47-limit (incomplete) ||
|| [[47_46|47/46]] || 37.232 || 47/(2*23) ||  ||
|| [[48_47|48/47]] || 36.448 || (2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)/47 ||  ||
|| [[94_93|94/93]] || 18.516 || (2*47)/(3*31) ||   ||
|| [[95_94|95/94]] || 18.320 || (5*19)/(2*47) ||   ||
||||||||~ 53-limit (incomplete) ||
|| [[53_52|53/52]] || 32.977 || 53/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13) ||  ||
|| [[54_53|54/53]] || 32.360 || (2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/53 ||  ||
||||||||~ 59-limit (incomplete) ||
|| [[59_58|59/58]] || 29.594 || 59/(2*29) ||  ||
|| [[60_59|60/59]] || 29.097 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)/59 ||  ||
||||||||~ 61-limit (incomplete) ||
|| [[61_60|61/60]] || 28.616 || 61/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5) ||  ||
|| [[62_61|62/61]] || 28.151 || (2*31)/61 ||  ||
||||||||~ 67-limit (incomplete) ||
|| [[67_66|67/66]] || 26.034 || 67/(2*3*11) ||  ||
|| [[68_67|68/67]] || 25.648 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/67 ||  ||
||||||||~ 71-limit (incomplete) ||
|| [[71_70|71/70]] || 24.557 || 71/(2*5*7) ||  ||
|| [[72_71|72/71]] || 24.213 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/71 ||  ||
||||||||~ 73-limit (incomplete) ||
|| [[73_72|73/72]] || 23.879 || 73/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||
|| [[74_73|74/73]] || 23.555 || (2*37)/73 ||  ||
||||||||~ 79-limit (incomplete) ||
|| [[79_78|79/78]] || 22.054 || 79/(2*3*13) ||  ||
|| [[80_79|80/79]] || 21.777 || (2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5)/79 ||  ||
||||||||~ 83-limit (incomplete) ||
|| [[83_82|83/82]] || 20.985 || 83/(2*41) ||  ||
|| [[84_83|84/83]] || 20.734 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7)/83 ||  ||
||||||||~ 89-limit (incomplete) ||
|| [[89_88|89/88]] || 19.562 || 89/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11) ||  ||
|| [[90_89|90/89]] || 19.344 || (2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/89 ||  ||
||||||||~ 97-limit (incomplete) ||
|| [[97_96|97/96]] || 17.940 || 97/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3) ||  ||
|| [[98_97|98/97]] || 17.756 || (2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/97 ||  ||
||||||||~ 101-limit (incomplete) ||
|| [[101_100|101/100]] || 17.226 || 101/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||  ||</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;List of Superparticular Intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="List of Superparticular Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #800080;"&gt;List of Superparticular Intervals&lt;/span&gt;&lt;/h1&gt;
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;List of Superparticular Intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="List of Superparticular Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #800080;"&gt;List of Superparticular Intervals&lt;/span&gt;&lt;/h1&gt;
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         &lt;th&gt;Factorization&lt;br /&gt;
         &lt;th&gt;Factorization&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
         &lt;th&gt;Prime Limit&lt;br /&gt;
         &lt;th&gt;Name(s)&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
         &lt;th&gt;Name(s)&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;th colspan="4"&gt;2-limit&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2/1&lt;br /&gt;
         &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(perfect) unison, unity, perfect prime, tonic, duple&lt;br /&gt;
         &lt;td&gt;(perfect) unison, unity, perfect prime, tonic, duple&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;3-limit&lt;br /&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
Line 157: Line 199:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3/2&lt;br /&gt;
         &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/perfect%20fifth"&gt;perfect fifth&lt;/a&gt;, 3rd harmonic (octave reduced), diapente&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/perfect%20fifth"&gt;perfect fifth&lt;/a&gt;, 3rd harmonic (octave reduced), diapente&lt;br /&gt;
Line 170: Line 210:
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/3&lt;br /&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3&lt;br /&gt;
         &lt;td&gt;perfect fourth, 3rd subharmonic (octave reduced), diatessaron&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;perfect fourth, 3rd subharmonic (octave reduced), diatessaron&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.910&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
         &lt;td&gt;(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;5-limit&lt;br /&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
Line 181: Line 233:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5/2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;5/2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(classic) (5-limit) major third, 5th harmonic (octave reduced)&lt;br /&gt;
         &lt;td&gt;(classic) (5-limit) major third, 5th harmonic (octave reduced)&lt;br /&gt;
Line 194: Line 244:
         &lt;td&gt;(2*3)/5&lt;br /&gt;
         &lt;td&gt;(2*3)/5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;(classic) (5-limit) minor third&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;182.404&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2*5)/3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;classic (whole) tone, classic major second, minor whole tone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(classic) (5-limit) minor third&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.713&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(3*5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;minor diatonic semitone, 15th subharmonic&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/25_24"&gt;25/24&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;70.672&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
         &lt;td&gt;chroma, (classic) chromatic semitone, Zarlinian semitone&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21.506&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;syntonic comma, Didymus comma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;7-limit&lt;br /&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
Line 205: Line 297:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7/(2*3)&lt;br /&gt;
         &lt;td&gt;7/(2*3)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(septimal) subminor third, septimal minor third, augmented second&lt;br /&gt;
         &lt;td&gt;(septimal) subminor third, septimal minor third, augmented second&lt;br /&gt;
Line 217: Line 307:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/7&lt;br /&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic&lt;br /&gt;
         &lt;td&gt;(septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic&lt;br /&gt;
Line 224: Line 312:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;203.910&lt;br /&gt;
         &lt;td&gt;119.443&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3*5)/(2*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3&lt;br /&gt;
         &lt;td&gt;septimal diatonic semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/21_20"&gt;21/20&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;182.404&lt;br /&gt;
         &lt;td&gt;84.467&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*5)/3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;minor semitone, large septimal chromatic semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;classic (whole) tone, classic major second, minor whole tone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;165.004&lt;br /&gt;
         &lt;td&gt;62.961&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11/(2*5)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(large) (undecimal) neutral second, 4/5-tone, Ptolemy's second&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/12_11"&gt;12/11&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;150.637&lt;br /&gt;
         &lt;td&gt;48.770&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)/11&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(5*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;septimal quarter tone, septimal diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(small) (undecimal) neutral second, 3/4-tone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/13_12"&gt;13/12&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;138.573&lt;br /&gt;
         &lt;td&gt;35.697&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;large septimal diesis, slendro diesis, septimal 1/6-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;tridecimal 2/3-tone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/14_13"&gt;14/13&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;128.298&lt;br /&gt;
         &lt;td&gt;34.976&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*7)/13&lt;br /&gt;
         &lt;td&gt;(2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2/3-tone, trienthird&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;119.443&lt;br /&gt;
         &lt;td&gt;27.264&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*5)/(2*7)&lt;br /&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;septimal comma, Archytas' comma&lt;br /&gt;
&lt;/td&gt;
         &lt;td&gt;septimal diatonic semitone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/16_15"&gt;16/15&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/126_125"&gt;126/125&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;111.713&lt;br /&gt;
         &lt;td&gt;13.795&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(3*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;(2*3^2*7)/5^3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;minor diatonic semitone, 15th subharmonic&lt;br /&gt;
         &lt;td&gt;starling comma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/17_16"&gt;17/16&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/225_224"&gt;225/224&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;104.955&lt;br /&gt;
         &lt;td&gt;7.7115&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17/2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3^2*5^2)/(2^5*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17&lt;br /&gt;
         &lt;td&gt;marvel comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17th harmonic (octave reduced)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/18_17"&gt;18/17&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/2401_2400"&gt;2401/2400&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;98.955&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/17&lt;br /&gt;
         &lt;td&gt;0.72120&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17&lt;br /&gt;
         &lt;td&gt;7^4/(2^5*3*5^2)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Arabic lute index finger&lt;br /&gt;
         &lt;td&gt;breedsma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/19_18"&gt;19/18&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/4375_4374"&gt;4375/4374&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;93.603&lt;br /&gt;
         &lt;td&gt;0.39576&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(5^4*7)/(2*3^7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;ragisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;undevicesimal semitone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/20_19"&gt;20/19&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;11-limit&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;88.801&lt;br /&gt;
         &lt;td&gt;165.004&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/19&lt;br /&gt;
         &lt;td&gt;11/(2*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;(large) (undecimal) neutral second, 4/5-tone, Ptolemy's second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;small undevicesimal semitone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/21_20"&gt;21/20&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/12_11"&gt;12/11&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;84.467&lt;br /&gt;
         &lt;td&gt;150.637&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)/11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;(small) (undecimal) neutral second, 3/4-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;minor semitone, large septimal chromatic semitone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 385: Line 451:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*11)/(3*7)&lt;br /&gt;
         &lt;td&gt;(2*11)/(3*7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;undecimal minor semitone&lt;br /&gt;
         &lt;td&gt;undecimal minor semitone&lt;br /&gt;
Line 392: Line 456:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/23_22"&gt;23/22&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/33_32"&gt;33/32&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;53.273&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(3*11)/2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;76.956&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/45_44"&gt;45/44&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;23/(2*11)&lt;br /&gt;
         &lt;td&gt;38.906&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;23&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;1/5-tone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/24_23"&gt;24/23&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/55_54"&gt;55/54&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;73.681&lt;br /&gt;
         &lt;td&gt;31.767&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)/23&lt;br /&gt;
         &lt;td&gt;(5*11)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 416: Line 486:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/25_24"&gt;25/24&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/56_55"&gt;56/55&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;70.672&lt;br /&gt;
         &lt;td&gt;31.194&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)/(5*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;chroma, (classic) chromatic semitone, Zarlinian semitone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/26_25"&gt;26/25&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/99_98"&gt;99/98&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;67.900&lt;br /&gt;
         &lt;td&gt;17.576&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*13)/5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;tridecimal 1/3-tone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/27_26"&gt;27/26&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/100_99"&gt;100/99&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;65.337&lt;br /&gt;
         &lt;td&gt;17.399&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/(2*13)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;Ptolemy's comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;tridecimal comma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/121_120"&gt;121/120&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;62.961&lt;br /&gt;
         &lt;td&gt;14.376&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;11^2/(2^3*3*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/29_28"&gt;29/28&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/176_175"&gt;176/175&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;60.751&lt;br /&gt;
         &lt;td&gt;9.8646&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;29/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
         &lt;td&gt;(2^4*11)/(5^2*7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 476: Line 536:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/30_29"&gt;30/29&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/243_242"&gt;243/242&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;58.692&lt;br /&gt;
         &lt;td&gt;7.1391&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3*5)/29&lt;br /&gt;
         &lt;td&gt;2^5/(2*11^2)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 488: Line 546:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/31_30"&gt;31/30&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/385_384"&gt;385/384&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;56.767&lt;br /&gt;
         &lt;td&gt;4.5026&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;31/(2*3*5)&lt;br /&gt;
         &lt;td&gt;(5*7*11)/(2^7*3)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;31&lt;br /&gt;
         &lt;td&gt;keenanisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/32_31"&gt;32/31&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/441_440"&gt;441/440&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;54.964&lt;br /&gt;
         &lt;td&gt;3.9302&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;/31&lt;br /&gt;
         &lt;td&gt;(3^2*7^2)/(2^3*5*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;31&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31st subharmonic&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/33_32"&gt;33/32&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/540_539"&gt;540/539&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;53.273&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*11)/2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;3.2090&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;(2^2*3^3*5)/(7^2*11)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/34_33"&gt;34/33&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/3025_3024"&gt;3025/3024&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;51.682&lt;br /&gt;
         &lt;td&gt;0.57240&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*17)/(3*33)&lt;br /&gt;
         &lt;td&gt;(5^2*11^2)/(2^4*3^3*7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 536: Line 586:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/35_34"&gt;35/34&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/9801_9800"&gt;9801/9800&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;50.184&lt;br /&gt;
         &lt;td&gt;0.17665&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*7)/(2*17)&lt;br /&gt;
         &lt;td&gt;(3^4*11^2)/(2^3*5^2*7^2)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;septendecimal 1/4-tone&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;13-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/13_12"&gt;13/12&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;48.770&lt;br /&gt;
         &lt;td&gt;138.573&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(5*7)&lt;br /&gt;
         &lt;td&gt;13/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;tridecimal 2/3-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;septimal quarter tone, septimal diesis&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/37_36"&gt;37/36&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/14_13"&gt;14/13&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;47.434&lt;br /&gt;
         &lt;td&gt;128.298&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;37/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(2*7)/13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;37&lt;br /&gt;
         &lt;td&gt;2/3-tone, trienthird&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/38_37"&gt;38/37&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/26_25"&gt;26/25&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;46.169&lt;br /&gt;
         &lt;td&gt;67.900&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*19)/37&lt;br /&gt;
         &lt;td&gt;(2*13)/5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;37&lt;br /&gt;
         &lt;td&gt;tridecimal 1/3-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/39_38"&gt;39/38&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/27_26"&gt;27/26&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;44.970&lt;br /&gt;
         &lt;td&gt;65.337&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*13)/(2*19)&lt;br /&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;/(2*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;tridecimal comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 601: Line 645:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)/(3*13)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)/(3*13)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;tridecimal minor diesis&lt;br /&gt;
         &lt;td&gt;tridecimal minor diesis&lt;br /&gt;
Line 608: Line 650:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/41_40"&gt;41/40&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/65_64"&gt;65/64&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;42.749&lt;br /&gt;
         &lt;td&gt;26.841&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;41/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;(5*13)/2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;41&lt;br /&gt;
         &lt;td&gt;13th-partial chroma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/42_41"&gt;42/41&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/66_65"&gt;66/65&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;41.719&lt;br /&gt;
         &lt;td&gt;26.432&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3*7)/41&lt;br /&gt;
         &lt;td&gt;(2*3*11)/(5*13)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 632: Line 670:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/43_42"&gt;43/42&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/78_77"&gt;78/77&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;40.737&lt;br /&gt;
         &lt;td&gt;22.339&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;43/(2*3*7)&lt;br /&gt;
         &lt;td&gt;(2*3*13)/(7*11)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 644: Line 680:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/44_43"&gt;44/43&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/91_90"&gt;91/90&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;39.800&lt;br /&gt;
         &lt;td&gt;19.130&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/43&lt;br /&gt;
         &lt;td&gt;(7*13)/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 656: Line 690:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/45_44"&gt;45/44&lt;/a&gt;&lt;br /&gt;
         &lt;th colspan="4"&gt;17-limit (incomplete)&lt;br /&gt;
&lt;/td&gt;
&lt;/th&gt;
        &lt;td&gt;38.906&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/5-tone&lt;br /&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/46_45"&gt;46/45&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/17_16"&gt;17/16&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;38.051&lt;br /&gt;
         &lt;td&gt;104.955&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*23)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;17/2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;23&lt;br /&gt;
         &lt;td&gt;17th harmonic (octave reduced)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/47_46"&gt;47/46&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/18_17"&gt;18/17&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;37.232&lt;br /&gt;
         &lt;td&gt;98.955&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;47/(2*23)&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;47&lt;br /&gt;
         &lt;td&gt;Arabic lute index finger&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/48_47"&gt;48/47&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/34_33"&gt;34/33&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;36.448&lt;br /&gt;
         &lt;td&gt;51.682&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)/47&lt;br /&gt;
         &lt;td&gt;(2*17)/(3*33)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 704: Line 724:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/35_34"&gt;35/34&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;35.697&lt;br /&gt;
         &lt;td&gt;50.184&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;(5*7)/(2*17)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;septendecimal 1/4-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;large septimal diesis, slendro diesis, septimal 1/6-tone&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;34.976&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 733: Line 739:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*17)/(2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(3*17)/(2*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17th-partial chroma&lt;br /&gt;
         &lt;td&gt;17th-partial chroma&lt;br /&gt;
Line 745: Line 749:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)/(3*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)/(3*17)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 752: Line 754:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/53_52"&gt;53/52&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/85_84"&gt;85/84&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;32.977&lt;br /&gt;
         &lt;td&gt;20.488&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;53/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
         &lt;td&gt;(5*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;53&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 764: Line 764:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/54_53"&gt;54/53&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;19-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/19_18"&gt;19/18&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;32.360&lt;br /&gt;
         &lt;td&gt;93.603&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/53&lt;br /&gt;
         &lt;td&gt;19/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;53&lt;br /&gt;
         &lt;td&gt;undevicesimal semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/55_54"&gt;55/54&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/20_19"&gt;20/19&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;31.767&lt;br /&gt;
         &lt;td&gt;88.801&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*11)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/19&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;small undevicesimal semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/56_55"&gt;56/55&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/39_38"&gt;39/38&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;31.194&lt;br /&gt;
         &lt;td&gt;44.970&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)/(5*11)&lt;br /&gt;
         &lt;td&gt;(3*13)/(2*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 806: Line 804:
         &lt;td&gt;(3*19)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)&lt;br /&gt;
         &lt;td&gt;(3*19)/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/76_75"&gt;76/75&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;22.931&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 812: Line 818:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/58_57"&gt;58/57&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/77_76"&gt;77/76&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;30.109&lt;br /&gt;
         &lt;td&gt;22.631&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*29)/(3*19)&lt;br /&gt;
         &lt;td&gt;(7*11)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 824: Line 828:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/59_58"&gt;59/58&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/96_95"&gt;96/95&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;29.594&lt;br /&gt;
         &lt;td&gt;18.128&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;59/(2*29)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)/(5*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;59&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 836: Line 838:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/60_59"&gt;60/59&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;23-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/23_22"&gt;23/22&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;29.097&lt;br /&gt;
         &lt;td&gt;76.956&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)/59&lt;br /&gt;
         &lt;td&gt;23/(2*11)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;59&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 848: Line 852:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/61_60"&gt;61/60&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/24_23"&gt;24/23&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;28.616&lt;br /&gt;
         &lt;td&gt;73.681&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;61/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3)/23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;61&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 860: Line 862:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/62_61"&gt;62/61&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/46_45"&gt;46/45&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;28.151&lt;br /&gt;
         &lt;td&gt;38.051&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*31)/61&lt;br /&gt;
         &lt;td&gt;(2*23)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;61&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 872: Line 872:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/63_62"&gt;63/62&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/69_68"&gt;69/68&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;27.700&lt;br /&gt;
         &lt;td&gt;25.274&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/(2*31)&lt;br /&gt;
         &lt;td&gt;(3*23)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 884: Line 882:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/70_69"&gt;70/69&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;27.264&lt;br /&gt;
         &lt;td&gt;24.910&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
         &lt;td&gt;(2*5*7)/(3*23)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;septimal comma, Archytas' comma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/65_64"&gt;65/64&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/92_91"&gt;92/91&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;26.841&lt;br /&gt;
         &lt;td&gt;18.921&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*13)/2&lt;span style="vertical-align: super;"&gt;6&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)/(7*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13th-partial chroma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/66_65"&gt;66/65&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;29-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/29_28"&gt;29/28&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;26.432&lt;br /&gt;
         &lt;td&gt;60.751&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3*11)/(5*13)&lt;br /&gt;
         &lt;td&gt;29/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 920: Line 916:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/67_66"&gt;67/66&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/30_29"&gt;30/29&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;26.034&lt;br /&gt;
         &lt;td&gt;58.692&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;67/(2*3*11)&lt;br /&gt;
         &lt;td&gt;(2*3*5)/29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;67&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 932: Line 926:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/68_67"&gt;68/67&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/58_57"&gt;58/57&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;25.648&lt;br /&gt;
         &lt;td&gt;30.109&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/67&lt;br /&gt;
         &lt;td&gt;(2*29)/(3*19)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;67&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 944: Line 936:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/69_68"&gt;69/68&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/88_87"&gt;88/87&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;25.274&lt;br /&gt;
         &lt;td&gt;19.786&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*23)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)/(3*29)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 956: Line 946:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/70_69"&gt;70/69&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;31-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/31_30"&gt;31/30&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;24.910&lt;br /&gt;
         &lt;td&gt;56.767&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*5*7)/(3*23)&lt;br /&gt;
         &lt;td&gt;31/(2*3*5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 968: Line 960:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/71_70"&gt;71/70&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/32_31"&gt;32/31&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;54.964&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;/31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31st subharmonic&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;24.557&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/63_62"&gt;63/62&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;71/(2*5*7)&lt;br /&gt;
         &lt;td&gt;27.700&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;71&lt;br /&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7)/(2*31)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 980: Line 980:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/72_71"&gt;72/71&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/93_92"&gt;93/92&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;24.213&lt;br /&gt;
         &lt;td&gt;18.716&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/71&lt;br /&gt;
         &lt;td&gt;(3*31)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;71&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 992: Line 990:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/73_72"&gt;73/72&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;37-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/37_36"&gt;37/36&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;23.879&lt;br /&gt;
         &lt;td&gt;47.434&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;73/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;37/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;73&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,004: Line 1,004:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/74_73"&gt;74/73&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/38_37"&gt;38/37&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;23.555&lt;br /&gt;
         &lt;td&gt;46.169&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*37)/73&lt;br /&gt;
         &lt;td&gt;(2*19)/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;73&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,022: Line 1,020:
         &lt;td&gt;(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2*37)&lt;br /&gt;
         &lt;td&gt;(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(2*37)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;37&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;41-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/41_40"&gt;41/40&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;42.749&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;41/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,028: Line 1,038:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/76_75"&gt;76/75&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/42_41"&gt;42/41&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;41.719&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2*3*7)/41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;22.931&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/82_81"&gt;82/81&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)/(3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;21.242&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;(2*41)/3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,040: Line 1,058:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/77_76"&gt;77/76&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;43-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/43_42"&gt;43/42&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;40.737&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;43/(2*3*7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;22.631&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/44_43"&gt;44/43&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(7*11)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*19)&lt;br /&gt;
         &lt;td&gt;39.800&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/43&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,052: Line 1,082:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/78_77"&gt;78/77&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/86_85"&gt;86/85&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20.249&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2*43)/(5*17)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;22.339&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/87_86"&gt;87/86&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3*13)/(7*11)&lt;br /&gt;
         &lt;td&gt;20.014&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13&lt;br /&gt;
         &lt;td&gt;(3*29)/(2*43)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,064: Line 1,102:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/79_78"&gt;79/78&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;47-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/47_46"&gt;47/46&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;37.232&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;47/(2*23)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;22.054&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/48_47"&gt;48/47&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;79/(2*3*13)&lt;br /&gt;
         &lt;td&gt;36.448&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;79&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*3)/47&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,076: Line 1,126:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/80_79"&gt;80/79&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/94_93"&gt;94/93&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18.516&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(2*47)/(3*31)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;21.777&lt;br /&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/95_94"&gt;95/94&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5)/79&lt;br /&gt;
         &lt;td&gt;18.320&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;79&lt;br /&gt;
         &lt;td&gt;(5*19)/(2*47)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,088: Line 1,146:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;53-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/53_52"&gt;53/52&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;21.506&lt;br /&gt;
         &lt;td&gt;32.977&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;53/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13)&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;syntonic comma, Didymus comma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/82_81"&gt;82/81&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/54_53"&gt;54/53&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;21.242&lt;br /&gt;
         &lt;td&gt;32.360&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*41)/3&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,112: Line 1,170:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/83_82"&gt;83/82&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;59-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/59_58"&gt;59/58&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;20.985&lt;br /&gt;
         &lt;td&gt;29.594&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;83/(2*41)&lt;br /&gt;
         &lt;td&gt;59/(2*29)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;83&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,124: Line 1,184:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/84_83"&gt;84/83&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/60_59"&gt;60/59&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;20.734&lt;br /&gt;
         &lt;td&gt;29.097&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7)/83&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)/59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;83&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,136: Line 1,194:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/85_84"&gt;85/84&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;61-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/61_60"&gt;61/60&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;20.488&lt;br /&gt;
         &lt;td&gt;28.616&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;61/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,148: Line 1,208:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/86_85"&gt;86/85&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/62_61"&gt;62/61&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;20.249&lt;br /&gt;
         &lt;td&gt;28.151&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*43)/(5*17)&lt;br /&gt;
         &lt;td&gt;(2*31)/61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,160: Line 1,218:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/87_86"&gt;87/86&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;67-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/67_66"&gt;67/66&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;20.014&lt;br /&gt;
         &lt;td&gt;26.034&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*29)/(2*43)&lt;br /&gt;
         &lt;td&gt;67/(2*3*11)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,172: Line 1,232:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/88_87"&gt;88/87&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/68_67"&gt;68/67&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19.786&lt;br /&gt;
         &lt;td&gt;25.648&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)/(3*29)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/67&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,184: Line 1,242:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/89_88"&gt;89/88&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;71-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/71_70"&gt;71/70&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19.562&lt;br /&gt;
         &lt;td&gt;24.557&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;89/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)&lt;br /&gt;
         &lt;td&gt;71/(2*5*7)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;89&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,196: Line 1,256:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/90_89"&gt;90/89&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/72_71"&gt;72/71&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19.344&lt;br /&gt;
         &lt;td&gt;24.213&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/89&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;89&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,208: Line 1,266:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/91_90"&gt;91/90&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;73-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/73_72"&gt;73/72&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;19.130&lt;br /&gt;
         &lt;td&gt;23.879&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(7*13)/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)&lt;br /&gt;
         &lt;td&gt;73/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,220: Line 1,280:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/92_91"&gt;92/91&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/74_73"&gt;74/73&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;18.921&lt;br /&gt;
         &lt;td&gt;23.555&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)/(7*13)&lt;br /&gt;
         &lt;td&gt;(2*37)/73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,232: Line 1,290:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/93_92"&gt;93/92&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;79-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/79_78"&gt;79/78&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;18.716&lt;br /&gt;
         &lt;td&gt;22.054&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3*31)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)&lt;br /&gt;
         &lt;td&gt;79/(2*3*13)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,244: Line 1,304:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/94_93"&gt;94/93&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/80_79"&gt;80/79&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;18.516&lt;br /&gt;
         &lt;td&gt;21.777&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*47)/(3*31)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*5)/79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,256: Line 1,314:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/95_94"&gt;95/94&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;83-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/83_82"&gt;83/82&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;18.320&lt;br /&gt;
         &lt;td&gt;20.985&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(5*19)/(2*47)&lt;br /&gt;
         &lt;td&gt;83/(2*41)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,268: Line 1,328:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/96_95"&gt;96/95&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/84_83"&gt;84/83&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;18.128&lt;br /&gt;
         &lt;td&gt;20.734&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)/(5*19)&lt;br /&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7)/83&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,280: Line 1,338:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/97_96"&gt;97/96&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;89-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/89_88"&gt;89/88&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17.940&lt;br /&gt;
         &lt;td&gt;19.562&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;97/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)&lt;br /&gt;
         &lt;td&gt;89/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*11)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;97&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,292: Line 1,352:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/98_97"&gt;98/97&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/90_89"&gt;90/89&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17.756&lt;br /&gt;
         &lt;td&gt;19.344&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/97&lt;br /&gt;
         &lt;td&gt;(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5)/89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;97&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,304: Line 1,362:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/99_98"&gt;99/98&lt;/a&gt;&lt;br /&gt;
        &lt;th colspan="4"&gt;97-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/97_96"&gt;97/96&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17.576&lt;br /&gt;
         &lt;td&gt;17.940&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)/(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;97/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
Line 1,316: Line 1,376:
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/100_99"&gt;100/99&lt;/a&gt;&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="/98_97"&gt;98/97&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;17.399&lt;br /&gt;
         &lt;td&gt;17.756&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*11)&lt;br /&gt;
         &lt;td&gt;(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)/97&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ptolemy's comma&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="4"&gt;101-limit (incomplete)&lt;br /&gt;
&lt;/th&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
Line 1,333: Line 1,395:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;101/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
         &lt;td&gt;101/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;101&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;

Revision as of 04:07, 28 October 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author keenanpepper and made on 2011-10-28 04:07:29 UTC.
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=<span style="color: #800080;">List of Superparticular Intervals</span>= 

[[Superparticular]] numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in [[Just Intonation]] and [[OverToneSeries|Harmonic Series]] music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio [[21_20|21/20]]. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common [[comma]]s are superparticular ratios.

In addition to names and cents values, the list below includes the factorization of each superparticular ratio as well as the largest prime involved. This is relevant when considering which intervals are characteristic of which [[harmonic limit]]s. [[36_35|36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-limit.

See also: [[Gallery of Just Intervals]]. Many of the names below come from [[http://www.huygens-fokker.org/docs/intervals.html|here]].

||~ Ratio ||~ Cents Value ||~ Factorization ||~ Name(s) ||
||||||||~ 2-limit ||
|| [[2_1|2/1]] || 1200.000 || 2/1 || (perfect) unison, unity, perfect prime, tonic, duple ||
||||||||~ 3-limit ||
|| [[3_2|3/2]] || 701.995 || 3/2 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente ||
|| [[4_3|4/3]] || 498.045 || 2<span style="vertical-align: super;">2</span>/3 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
|| [[9_8|9/8]] || 203.910 || 3<span style="vertical-align: super;">2</span>/2<span style="vertical-align: super;">3</span> || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) ||
||||||||~ 5-limit ||
|| [[5_4|5/4]] || 386.314 || 5/2<span style="vertical-align: super;">2</span> || (classic) (5-limit) major third, 5th harmonic (octave reduced) ||
|| [[6_5|6/5]] || 315.641 || (2*3)/5 || (classic) (5-limit) minor third ||
|| [[10_9|10/9]] || 182.404 || (2*5)/3<span style="vertical-align: super;">2</span> || classic (whole) tone, classic major second, minor whole tone ||
|| [[16_15|16/15]] || 111.713 || 2<span style="vertical-align: super;">4</span>/(3*5) || minor diatonic semitone, 15th subharmonic ||
|| [[25_24|25/24]] || 70.672 || 5<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3) || chroma, (classic) chromatic semitone, Zarlinian semitone ||
|| [[81_80|81/80]] || 21.506 || 3<span style="vertical-align: super;">4</span>/(2<span style="vertical-align: super;">4</span>*5) || syntonic comma, Didymus comma ||
||||||||~ 7-limit ||
|| [[7_6|7/6]] || 266.871 || 7/(2*3) || (septimal) subminor third, septimal minor third, augmented second ||
|| [[8_7|8/7]] || 231.174 || 2<span style="vertical-align: super;">3</span>/7 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
|| [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || septimal diatonic semitone ||
|| [[21_20|21/20]] || 84.467 || (3*7)/(2<span style="vertical-align: super;">2</span>*5) || minor semitone, large septimal chromatic semitone ||
|| [[28_27|28/27]] || 62.961 || (2<span style="vertical-align: super;">2</span>*7)/3<span style="vertical-align: super;">3</span> || septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone ||
|| [[36_35|36/35]] || 48.770 || (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>)/(5*7) || septimal quarter tone, septimal diesis ||
|| [[49_48|49/48]] || 35.697 || 7<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">4</span>*3) || large septimal diesis, slendro diesis, septimal 1/6-tone ||
|| [[50_49|50/49]] || 34.976 || (2*5<span style="vertical-align: super;">2</span>)/7<span style="vertical-align: super;">2</span> || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
|| [[64_63|64/63]] || 27.264 || 2<span style="vertical-align: super;">6</span>/(3<span style="vertical-align: super;">2</span>*7) || septimal comma, Archytas' comma ||
|| [[126_125|126/125]] || 13.795 || (2*3^2*7)/5^3 || starling comma ||
|| [[225_224|225/224]] || 7.7115 || (3^2*5^2)/(2^5*7) || marvel comma ||
|| [[2401_2400|2401/2400]] || 0.72120 || 7^4/(2^5*3*5^2) || breedsma ||
|| [[4375_4374|4375/4374]] || 0.39576 || (5^4*7)/(2*3^7) || ragisma ||
||||||||~ 11-limit ||
|| [[11_10|11/10]] || 165.004 || 11/(2*5) || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
|| [[12_11|12/11]] || 150.637 || (2<span style="vertical-align: super;">2</span>*3)/11 || (small) (undecimal) neutral second, 3/4-tone ||
|| [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || undecimal minor semitone ||
|| [[33_32|33/32]] || 53.273 || (3*11)/2<span style="vertical-align: super;">5</span> || unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
|| [[45_44|45/44]] || 38.906 || (3<span style="vertical-align: super;">2</span>*5)/(2<span style="vertical-align: super;">2</span>*11) || 1/5-tone ||
|| [[55_54|55/54]] || 31.767 || (5*11)/(2*3<span style="vertical-align: super;">3</span>) ||   ||
|| [[56_55|56/55]] || 31.194 || (2<span style="vertical-align: super;">3</span>*7)/(5*11) ||   ||
|| [[99_98|99/98]] || 17.576 || (3<span style="vertical-align: super;">2</span>*11)/(2*7<span style="vertical-align: super;">2</span>) ||   ||
|| [[100_99|100/99]] || 17.399 || (2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)/(3<span style="vertical-align: super;">2</span>*11) || Ptolemy's comma ||
|| [[121_120|121/120]] || 14.376 || 11^2/(2^3*3*5) ||   ||
|| [[176_175|176/175]] || 9.8646 || (2^4*11)/(5^2*7) ||   ||
|| [[243_242|243/242]] || 7.1391 || 2^5/(2*11^2) ||   ||
|| [[385_384|385/384]] || 4.5026 || (5*7*11)/(2^7*3) || keenanisma ||
|| [[441_440|441/440]] || 3.9302 || (3^2*7^2)/(2^3*5*11) ||   ||
|| [[540_539|540/539]] || 3.2090 || (2^2*3^3*5)/(7^2*11) ||   ||
|| [[3025_3024|3025/3024]] || 0.57240 || (5^2*11^2)/(2^4*3^3*7) ||   ||
|| [[9801_9800|9801/9800]] || 0.17665 || (3^4*11^2)/(2^3*5^2*7^2) ||   ||
||||||||~ 13-limit (incomplete) ||
|| [[13_12|13/12]] || 138.573 || 13/(2<span style="vertical-align: super;">2</span>*3) || tridecimal 2/3-tone ||
|| [[14_13|14/13]] || 128.298 || (2*7)/13 || 2/3-tone, trienthird ||
|| [[26_25|26/25]] || 67.900 || (2*13)/5<span style="vertical-align: super;">2</span> || tridecimal 1/3-tone ||
|| [[27_26|27/26]] || 65.337 || 3<span style="vertical-align: super;">3</span>/(2*13) || tridecimal comma ||
|| [[40_39|40/39]] || 43.831 || (2<span style="vertical-align: super;">3</span>*5)/(3*13) || tridecimal minor diesis ||
|| [[65_64|65/64]] || 26.841 || (5*13)/2<span style="vertical-align: super;">6</span> || 13th-partial chroma ||
|| [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) ||   ||
|| [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) ||   ||
|| [[91_90|91/90]] || 19.130 || (7*13)/(2*3<span style="vertical-align: super;">2</span>*5) ||   ||
||||||||~ 17-limit (incomplete) ||
|| [[17_16|17/16]] || 104.955 || 17/2<span style="vertical-align: super;">4</span> || 17th harmonic (octave reduced) ||
|| [[18_17|18/17]] || 98.955 || (2*3<span style="vertical-align: super;">2</span>)/17 || Arabic lute index finger ||
|| [[34_33|34/33]] || 51.682 || (2*17)/(3*33) ||   ||
|| [[35_34|35/34]] || 50.184 || (5*7)/(2*17) || septendecimal 1/4-tone ||
|| [[51_50|51/50]] || 34.283 || (3*17)/(2*5<span style="vertical-align: super;">2</span>) || 17th-partial chroma ||
|| [[52_51|52/51]] || 33.617 || (2<span style="vertical-align: super;">2</span>*13)/(3*17) ||   ||
|| [[85_84|85/84]] || 20.488 || (5*17)/(2<span style="vertical-align: super;">2</span>*3*7) ||   ||
||||||||~ 19-limit (incomplete) ||
|| [[19_18|19/18]] || 93.603 || 19/(2*3<span style="vertical-align: super;">2</span>) || undevicesimal semitone ||
|| [[20_19|20/19]] || 88.801 || (2<span style="vertical-align: super;">2</span>*5)/19 || small undevicesimal semitone ||
|| [[39_38|39/38]] || 44.970 || (3*13)/(2*19) ||   ||
|| [[57_56|57/56]] || 30.642 || (3*19)/(2<span style="vertical-align: super;">3</span>*7) ||   ||
|| [[76_75|76/75]] || 22.931 || (2<span style="vertical-align: super;">2</span>*19)/(3*5<span style="vertical-align: super;">2</span>) ||   ||
|| [[77_76|77/76]] || 22.631 || (7*11)/(2<span style="vertical-align: super;">2</span>*19) ||   ||
|| [[96_95|96/95]] || 18.128 || (2<span style="vertical-align: super;">5</span>*3)/(5*19) ||   ||
||||||||~ 23-limit (incomplete) ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) ||   ||
|| [[24_23|24/23]] || 73.681 || (2<span style="vertical-align: super;">3</span>*3)/23 ||   ||
|| [[46_45|46/45]] || 38.051 || (2*23)/(3<span style="vertical-align: super;">2</span>*5) ||   ||
|| [[69_68|69/68]] || 25.274 || (3*23)/(2<span style="vertical-align: super;">2</span>*17) ||   ||
|| [[70_69|70/69]] || 24.910 || (2*5*7)/(3*23) ||   ||
|| [[92_91|92/91]] || 18.921 || (2<span style="vertical-align: super;">2</span>*23)/(7*13) ||   ||
||||||||~ 29-limit (incomplete) ||
|| [[29_28|29/28]] || 60.751 || 29/(2<span style="vertical-align: super;">2</span>*7) ||   ||
|| [[30_29|30/29]] || 58.692 || (2*3*5)/29 ||   ||
|| [[58_57|58/57]] || 30.109 || (2*29)/(3*19) ||   ||
|| [[88_87|88/87]] || 19.786 || (2<span style="vertical-align: super;">3</span>*11)/(3*29) ||   ||
||||||||~ 31-limit (incomplete) ||
|| [[31_30|31/30]] || 56.767 || 31/(2*3*5) ||   ||
|| [[32_31|32/31]] || 54.964 || 2<span style="vertical-align: super;">5</span>/31 || 31st subharmonic ||
|| [[63_62|63/62]] || 27.700 || (3<span style="vertical-align: super;">2</span>*7)/(2*31) ||   ||
|| [[93_92|93/92]] || 18.716 || (3*31)/(2<span style="vertical-align: super;">2</span>*23) ||   ||
||||||||~ 37-limit (incomplete) ||
|| [[37_36|37/36]] || 47.434 || 37/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>) ||   ||
|| [[38_37|38/37]] || 46.169 || (2*19)/37 ||   ||
|| [[75_74|75/74]] || 23.238 || (3*5<span style="vertical-align: super;">2</span>)/(2*37) ||   ||
||||||||~ 41-limit (incomplete) ||
|| [[41_40|41/40]] || 42.749 || 41/(2<span style="vertical-align: super;">3</span>*5) ||   ||
|| [[42_41|42/41]] || 41.719 || (2*3*7)/41 ||   ||
|| [[82_81|82/81]] || 21.242 || (2*41)/3<span style="vertical-align: super;">4</span> ||   ||
||||||||~ 43-limit (incomplete) ||
|| [[43_42|43/42]] || 40.737 || 43/(2*3*7) ||   ||
|| [[44_43|44/43]] || 39.800 || (2<span style="vertical-align: super;">2</span>*11)/43 ||   ||
|| [[86_85|86/85]] || 20.249 || (2*43)/(5*17) ||   ||
|| [[87_86|87/86]] || 20.014 || (3*29)/(2*43) ||   ||
||||||||~ 47-limit (incomplete) ||
|| [[47_46|47/46]] || 37.232 || 47/(2*23) ||   ||
|| [[48_47|48/47]] || 36.448 || (2<span style="vertical-align: super;">4</span>*3)/47 ||   ||
|| [[94_93|94/93]] || 18.516 || (2*47)/(3*31) ||   ||
|| [[95_94|95/94]] || 18.320 || (5*19)/(2*47) ||   ||
||||||||~ 53-limit (incomplete) ||
|| [[53_52|53/52]] || 32.977 || 53/(2<span style="vertical-align: super;">2</span>*13) ||   ||
|| [[54_53|54/53]] || 32.360 || (2*3<span style="vertical-align: super;">3</span>)/53 ||   ||
||||||||~ 59-limit (incomplete) ||
|| [[59_58|59/58]] || 29.594 || 59/(2*29) ||   ||
|| [[60_59|60/59]] || 29.097 || (2<span style="vertical-align: super;">2</span>*3*5)/59 ||   ||
||||||||~ 61-limit (incomplete) ||
|| [[61_60|61/60]] || 28.616 || 61/(2<span style="vertical-align: super;">2</span>*3*5) ||   ||
|| [[62_61|62/61]] || 28.151 || (2*31)/61 ||   ||
||||||||~ 67-limit (incomplete) ||
|| [[67_66|67/66]] || 26.034 || 67/(2*3*11) ||   ||
|| [[68_67|68/67]] || 25.648 || (2<span style="vertical-align: super;">2</span>*17)/67 ||   ||
||||||||~ 71-limit (incomplete) ||
|| [[71_70|71/70]] || 24.557 || 71/(2*5*7) ||   ||
|| [[72_71|72/71]] || 24.213 || (2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>)/71 ||   ||
||||||||~ 73-limit (incomplete) ||
|| [[73_72|73/72]] || 23.879 || 73/(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>) ||   ||
|| [[74_73|74/73]] || 23.555 || (2*37)/73 ||   ||
||||||||~ 79-limit (incomplete) ||
|| [[79_78|79/78]] || 22.054 || 79/(2*3*13) ||   ||
|| [[80_79|80/79]] || 21.777 || (2<span style="vertical-align: super;">4</span>*5)/79 ||   ||
||||||||~ 83-limit (incomplete) ||
|| [[83_82|83/82]] || 20.985 || 83/(2*41) ||   ||
|| [[84_83|84/83]] || 20.734 || (2<span style="vertical-align: super;">2</span>*3*7)/83 ||   ||
||||||||~ 89-limit (incomplete) ||
|| [[89_88|89/88]] || 19.562 || 89/(2<span style="vertical-align: super;">3</span>*11) ||   ||
|| [[90_89|90/89]] || 19.344 || (2*3<span style="vertical-align: super;">2</span>*5)/89 ||   ||
||||||||~ 97-limit (incomplete) ||
|| [[97_96|97/96]] || 17.940 || 97/(2<span style="vertical-align: super;">5</span>*3) ||   ||
|| [[98_97|98/97]] || 17.756 || (2*7<span style="vertical-align: super;">2</span>)/97 ||   ||
||||||||~ 101-limit (incomplete) ||
|| [[101_100|101/100]] || 17.226 || 101/(2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>) ||   ||

Original HTML content:

<html><head><title>List of Superparticular Intervals</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="List of Superparticular Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #800080;">List of Superparticular Intervals</span></h1>
 <br />
<a class="wiki_link" href="/Superparticular">Superparticular</a> numbers are ratios of the form (n+1)/n, or 1+1/n, where n is a whole number other than 1. They appear frequently in <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a> and <a class="wiki_link" href="/OverToneSeries">Harmonic Series</a> music. Adjacent tones in the harmonic series are separated by superparticular intervals: for instance, the 20th and 21st by the superparticular ratio <a class="wiki_link" href="/21_20">21/20</a>. As the overtones get closer together, the superparticular intervals get smaller and smaller. Thus, an examination of the superparticular intervals is an examination of some of the simplest small intervals in rational tuning systems. Indeed, many but not all common <a class="wiki_link" href="/comma">comma</a>s are superparticular ratios.<br />
<br />
In addition to names and cents values, the list below includes the factorization of each superparticular ratio as well as the largest prime involved. This is relevant when considering which intervals are characteristic of which <a class="wiki_link" href="/harmonic%20limit">harmonic limit</a>s. <a class="wiki_link" href="/36_35">36/35</a>, for instance, is an interval of the <a class="wiki_link" href="/7-limit">7-limit</a>, as it factors to (2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-limit.<br />
<br />
See also: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a>. Many of the names below come from <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">here</a>.<br />
<br />


<table class="wiki_table">
    <tr>
        <th>Ratio<br />
</th>
        <th>Cents Value<br />
</th>
        <th>Factorization<br />
</th>
        <th>Name(s)<br />
</th>
    </tr>
    <tr>
        <th colspan="4">2-limit<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/2_1">2/1</a><br />
</td>
        <td>1200.000<br />
</td>
        <td>2/1<br />
</td>
        <td>(perfect) unison, unity, perfect prime, tonic, duple<br />
</td>
    </tr>
    <tr>
        <th colspan="4">3-limit<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/3_2">3/2</a><br />
</td>
        <td>701.995<br />
</td>
        <td>3/2<br />
</td>
        <td><a class="wiki_link" href="/perfect%20fifth">perfect fifth</a>, 3rd harmonic (octave reduced), diapente<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/4_3">4/3</a><br />
</td>
        <td>498.045<br />
</td>
        <td>2<span style="vertical-align: super;">2</span>/3<br />
</td>
        <td>perfect fourth, 3rd subharmonic (octave reduced), diatessaron<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9_8">9/8</a><br />
</td>
        <td>203.910<br />
</td>
        <td>3<span style="vertical-align: super;">2</span>/2<span style="vertical-align: super;">3</span><br />
</td>
        <td>(Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced)<br />
</td>
    </tr>
    <tr>
        <th colspan="4">5-limit<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/5_4">5/4</a><br />
</td>
        <td>386.314<br />
</td>
        <td>5/2<span style="vertical-align: super;">2</span><br />
</td>
        <td>(classic) (5-limit) major third, 5th harmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/6_5">6/5</a><br />
</td>
        <td>315.641<br />
</td>
        <td>(2*3)/5<br />
</td>
        <td>(classic) (5-limit) minor third<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/10_9">10/9</a><br />
</td>
        <td>182.404<br />
</td>
        <td>(2*5)/3<span style="vertical-align: super;">2</span><br />
</td>
        <td>classic (whole) tone, classic major second, minor whole tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_15">16/15</a><br />
</td>
        <td>111.713<br />
</td>
        <td>2<span style="vertical-align: super;">4</span>/(3*5)<br />
</td>
        <td>minor diatonic semitone, 15th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/25_24">25/24</a><br />
</td>
        <td>70.672<br />
</td>
        <td>5<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3)<br />
</td>
        <td>chroma, (classic) chromatic semitone, Zarlinian semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/81_80">81/80</a><br />
</td>
        <td>21.506<br />
</td>
        <td>3<span style="vertical-align: super;">4</span>/(2<span style="vertical-align: super;">4</span>*5)<br />
</td>
        <td>syntonic comma, Didymus comma<br />
</td>
    </tr>
    <tr>
        <th colspan="4">7-limit<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/7_6">7/6</a><br />
</td>
        <td>266.871<br />
</td>
        <td>7/(2*3)<br />
</td>
        <td>(septimal) subminor third, septimal minor third, augmented second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/8_7">8/7</a><br />
</td>
        <td>231.174<br />
</td>
        <td>2<span style="vertical-align: super;">3</span>/7<br />
</td>
        <td>(septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_14">15/14</a><br />
</td>
        <td>119.443<br />
</td>
        <td>(3*5)/(2*7)<br />
</td>
        <td>septimal diatonic semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/21_20">21/20</a><br />
</td>
        <td>84.467<br />
</td>
        <td>(3*7)/(2<span style="vertical-align: super;">2</span>*5)<br />
</td>
        <td>minor semitone, large septimal chromatic semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/28_27">28/27</a><br />
</td>
        <td>62.961<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*7)/3<span style="vertical-align: super;">3</span><br />
</td>
        <td>septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/36_35">36/35</a><br />
</td>
        <td>48.770<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>)/(5*7)<br />
</td>
        <td>septimal quarter tone, septimal diesis<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/49_48">49/48</a><br />
</td>
        <td>35.697<br />
</td>
        <td>7<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">4</span>*3)<br />
</td>
        <td>large septimal diesis, slendro diesis, septimal 1/6-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/50_49">50/49</a><br />
</td>
        <td>34.976<br />
</td>
        <td>(2*5<span style="vertical-align: super;">2</span>)/7<span style="vertical-align: super;">2</span><br />
</td>
        <td>septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/64_63">64/63</a><br />
</td>
        <td>27.264<br />
</td>
        <td>2<span style="vertical-align: super;">6</span>/(3<span style="vertical-align: super;">2</span>*7)<br />
</td>
        <td>septimal comma, Archytas' comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/126_125">126/125</a><br />
</td>
        <td>13.795<br />
</td>
        <td>(2*3^2*7)/5^3<br />
</td>
        <td>starling comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/225_224">225/224</a><br />
</td>
        <td>7.7115<br />
</td>
        <td>(3^2*5^2)/(2^5*7)<br />
</td>
        <td>marvel comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/2401_2400">2401/2400</a><br />
</td>
        <td>0.72120<br />
</td>
        <td>7^4/(2^5*3*5^2)<br />
</td>
        <td>breedsma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/4375_4374">4375/4374</a><br />
</td>
        <td>0.39576<br />
</td>
        <td>(5^4*7)/(2*3^7)<br />
</td>
        <td>ragisma<br />
</td>
    </tr>
    <tr>
        <th colspan="4">11-limit<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_10">11/10</a><br />
</td>
        <td>165.004<br />
</td>
        <td>11/(2*5)<br />
</td>
        <td>(large) (undecimal) neutral second, 4/5-tone, Ptolemy's second<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/12_11">12/11</a><br />
</td>
        <td>150.637<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*3)/11<br />
</td>
        <td>(small) (undecimal) neutral second, 3/4-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_21">22/21</a><br />
</td>
        <td>80.537<br />
</td>
        <td>(2*11)/(3*7)<br />
</td>
        <td>undecimal minor semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/33_32">33/32</a><br />
</td>
        <td>53.273<br />
</td>
        <td>(3*11)/2<span style="vertical-align: super;">5</span><br />
</td>
        <td>unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/45_44">45/44</a><br />
</td>
        <td>38.906<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*5)/(2<span style="vertical-align: super;">2</span>*11)<br />
</td>
        <td>1/5-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/55_54">55/54</a><br />
</td>
        <td>31.767<br />
</td>
        <td>(5*11)/(2*3<span style="vertical-align: super;">3</span>)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/56_55">56/55</a><br />
</td>
        <td>31.194<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*7)/(5*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/99_98">99/98</a><br />
</td>
        <td>17.576<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*11)/(2*7<span style="vertical-align: super;">2</span>)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/100_99">100/99</a><br />
</td>
        <td>17.399<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)/(3<span style="vertical-align: super;">2</span>*11)<br />
</td>
        <td>Ptolemy's comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/121_120">121/120</a><br />
</td>
        <td>14.376<br />
</td>
        <td>11^2/(2^3*3*5)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/176_175">176/175</a><br />
</td>
        <td>9.8646<br />
</td>
        <td>(2^4*11)/(5^2*7)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/243_242">243/242</a><br />
</td>
        <td>7.1391<br />
</td>
        <td>2^5/(2*11^2)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/385_384">385/384</a><br />
</td>
        <td>4.5026<br />
</td>
        <td>(5*7*11)/(2^7*3)<br />
</td>
        <td>keenanisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/441_440">441/440</a><br />
</td>
        <td>3.9302<br />
</td>
        <td>(3^2*7^2)/(2^3*5*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/540_539">540/539</a><br />
</td>
        <td>3.2090<br />
</td>
        <td>(2^2*3^3*5)/(7^2*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/3025_3024">3025/3024</a><br />
</td>
        <td>0.57240<br />
</td>
        <td>(5^2*11^2)/(2^4*3^3*7)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9801_9800">9801/9800</a><br />
</td>
        <td>0.17665<br />
</td>
        <td>(3^4*11^2)/(2^3*5^2*7^2)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">13-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/13_12">13/12</a><br />
</td>
        <td>138.573<br />
</td>
        <td>13/(2<span style="vertical-align: super;">2</span>*3)<br />
</td>
        <td>tridecimal 2/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_13">14/13</a><br />
</td>
        <td>128.298<br />
</td>
        <td>(2*7)/13<br />
</td>
        <td>2/3-tone, trienthird<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/26_25">26/25</a><br />
</td>
        <td>67.900<br />
</td>
        <td>(2*13)/5<span style="vertical-align: super;">2</span><br />
</td>
        <td>tridecimal 1/3-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/27_26">27/26</a><br />
</td>
        <td>65.337<br />
</td>
        <td>3<span style="vertical-align: super;">3</span>/(2*13)<br />
</td>
        <td>tridecimal comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/40_39">40/39</a><br />
</td>
        <td>43.831<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*5)/(3*13)<br />
</td>
        <td>tridecimal minor diesis<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/65_64">65/64</a><br />
</td>
        <td>26.841<br />
</td>
        <td>(5*13)/2<span style="vertical-align: super;">6</span><br />
</td>
        <td>13th-partial chroma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/66_65">66/65</a><br />
</td>
        <td>26.432<br />
</td>
        <td>(2*3*11)/(5*13)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/78_77">78/77</a><br />
</td>
        <td>22.339<br />
</td>
        <td>(2*3*13)/(7*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/91_90">91/90</a><br />
</td>
        <td>19.130<br />
</td>
        <td>(7*13)/(2*3<span style="vertical-align: super;">2</span>*5)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">17-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/17_16">17/16</a><br />
</td>
        <td>104.955<br />
</td>
        <td>17/2<span style="vertical-align: super;">4</span><br />
</td>
        <td>17th harmonic (octave reduced)<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_17">18/17</a><br />
</td>
        <td>98.955<br />
</td>
        <td>(2*3<span style="vertical-align: super;">2</span>)/17<br />
</td>
        <td>Arabic lute index finger<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/34_33">34/33</a><br />
</td>
        <td>51.682<br />
</td>
        <td>(2*17)/(3*33)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/35_34">35/34</a><br />
</td>
        <td>50.184<br />
</td>
        <td>(5*7)/(2*17)<br />
</td>
        <td>septendecimal 1/4-tone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/51_50">51/50</a><br />
</td>
        <td>34.283<br />
</td>
        <td>(3*17)/(2*5<span style="vertical-align: super;">2</span>)<br />
</td>
        <td>17th-partial chroma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/52_51">52/51</a><br />
</td>
        <td>33.617<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*13)/(3*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/85_84">85/84</a><br />
</td>
        <td>20.488<br />
</td>
        <td>(5*17)/(2<span style="vertical-align: super;">2</span>*3*7)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">19-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/19_18">19/18</a><br />
</td>
        <td>93.603<br />
</td>
        <td>19/(2*3<span style="vertical-align: super;">2</span>)<br />
</td>
        <td>undevicesimal semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/20_19">20/19</a><br />
</td>
        <td>88.801<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*5)/19<br />
</td>
        <td>small undevicesimal semitone<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/39_38">39/38</a><br />
</td>
        <td>44.970<br />
</td>
        <td>(3*13)/(2*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/57_56">57/56</a><br />
</td>
        <td>30.642<br />
</td>
        <td>(3*19)/(2<span style="vertical-align: super;">3</span>*7)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/76_75">76/75</a><br />
</td>
        <td>22.931<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*19)/(3*5<span style="vertical-align: super;">2</span>)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/77_76">77/76</a><br />
</td>
        <td>22.631<br />
</td>
        <td>(7*11)/(2<span style="vertical-align: super;">2</span>*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/96_95">96/95</a><br />
</td>
        <td>18.128<br />
</td>
        <td>(2<span style="vertical-align: super;">5</span>*3)/(5*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">23-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/23_22">23/22</a><br />
</td>
        <td>76.956<br />
</td>
        <td>23/(2*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/24_23">24/23</a><br />
</td>
        <td>73.681<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*3)/23<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/46_45">46/45</a><br />
</td>
        <td>38.051<br />
</td>
        <td>(2*23)/(3<span style="vertical-align: super;">2</span>*5)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/69_68">69/68</a><br />
</td>
        <td>25.274<br />
</td>
        <td>(3*23)/(2<span style="vertical-align: super;">2</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/70_69">70/69</a><br />
</td>
        <td>24.910<br />
</td>
        <td>(2*5*7)/(3*23)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/92_91">92/91</a><br />
</td>
        <td>18.921<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*23)/(7*13)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">29-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/29_28">29/28</a><br />
</td>
        <td>60.751<br />
</td>
        <td>29/(2<span style="vertical-align: super;">2</span>*7)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/30_29">30/29</a><br />
</td>
        <td>58.692<br />
</td>
        <td>(2*3*5)/29<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/58_57">58/57</a><br />
</td>
        <td>30.109<br />
</td>
        <td>(2*29)/(3*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/88_87">88/87</a><br />
</td>
        <td>19.786<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*11)/(3*29)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">31-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/31_30">31/30</a><br />
</td>
        <td>56.767<br />
</td>
        <td>31/(2*3*5)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/32_31">32/31</a><br />
</td>
        <td>54.964<br />
</td>
        <td>2<span style="vertical-align: super;">5</span>/31<br />
</td>
        <td>31st subharmonic<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/63_62">63/62</a><br />
</td>
        <td>27.700<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*7)/(2*31)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/93_92">93/92</a><br />
</td>
        <td>18.716<br />
</td>
        <td>(3*31)/(2<span style="vertical-align: super;">2</span>*23)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">37-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/37_36">37/36</a><br />
</td>
        <td>47.434<br />
</td>
        <td>37/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">2</span>)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/38_37">38/37</a><br />
</td>
        <td>46.169<br />
</td>
        <td>(2*19)/37<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/75_74">75/74</a><br />
</td>
        <td>23.238<br />
</td>
        <td>(3*5<span style="vertical-align: super;">2</span>)/(2*37)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">41-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/41_40">41/40</a><br />
</td>
        <td>42.749<br />
</td>
        <td>41/(2<span style="vertical-align: super;">3</span>*5)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/42_41">42/41</a><br />
</td>
        <td>41.719<br />
</td>
        <td>(2*3*7)/41<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/82_81">82/81</a><br />
</td>
        <td>21.242<br />
</td>
        <td>(2*41)/3<span style="vertical-align: super;">4</span><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">43-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/43_42">43/42</a><br />
</td>
        <td>40.737<br />
</td>
        <td>43/(2*3*7)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/44_43">44/43</a><br />
</td>
        <td>39.800<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*11)/43<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/86_85">86/85</a><br />
</td>
        <td>20.249<br />
</td>
        <td>(2*43)/(5*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/87_86">87/86</a><br />
</td>
        <td>20.014<br />
</td>
        <td>(3*29)/(2*43)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">47-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/47_46">47/46</a><br />
</td>
        <td>37.232<br />
</td>
        <td>47/(2*23)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/48_47">48/47</a><br />
</td>
        <td>36.448<br />
</td>
        <td>(2<span style="vertical-align: super;">4</span>*3)/47<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/94_93">94/93</a><br />
</td>
        <td>18.516<br />
</td>
        <td>(2*47)/(3*31)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/95_94">95/94</a><br />
</td>
        <td>18.320<br />
</td>
        <td>(5*19)/(2*47)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">53-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/53_52">53/52</a><br />
</td>
        <td>32.977<br />
</td>
        <td>53/(2<span style="vertical-align: super;">2</span>*13)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/54_53">54/53</a><br />
</td>
        <td>32.360<br />
</td>
        <td>(2*3<span style="vertical-align: super;">3</span>)/53<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">59-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/59_58">59/58</a><br />
</td>
        <td>29.594<br />
</td>
        <td>59/(2*29)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/60_59">60/59</a><br />
</td>
        <td>29.097<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*3*5)/59<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">61-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/61_60">61/60</a><br />
</td>
        <td>28.616<br />
</td>
        <td>61/(2<span style="vertical-align: super;">2</span>*3*5)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/62_61">62/61</a><br />
</td>
        <td>28.151<br />
</td>
        <td>(2*31)/61<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">67-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/67_66">67/66</a><br />
</td>
        <td>26.034<br />
</td>
        <td>67/(2*3*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/68_67">68/67</a><br />
</td>
        <td>25.648<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*17)/67<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">71-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/71_70">71/70</a><br />
</td>
        <td>24.557<br />
</td>
        <td>71/(2*5*7)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/72_71">72/71</a><br />
</td>
        <td>24.213<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>)/71<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">73-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/73_72">73/72</a><br />
</td>
        <td>23.879<br />
</td>
        <td>73/(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/74_73">74/73</a><br />
</td>
        <td>23.555<br />
</td>
        <td>(2*37)/73<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">79-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/79_78">79/78</a><br />
</td>
        <td>22.054<br />
</td>
        <td>79/(2*3*13)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/80_79">80/79</a><br />
</td>
        <td>21.777<br />
</td>
        <td>(2<span style="vertical-align: super;">4</span>*5)/79<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">83-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/83_82">83/82</a><br />
</td>
        <td>20.985<br />
</td>
        <td>83/(2*41)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/84_83">84/83</a><br />
</td>
        <td>20.734<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*3*7)/83<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">89-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/89_88">89/88</a><br />
</td>
        <td>19.562<br />
</td>
        <td>89/(2<span style="vertical-align: super;">3</span>*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/90_89">90/89</a><br />
</td>
        <td>19.344<br />
</td>
        <td>(2*3<span style="vertical-align: super;">2</span>*5)/89<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">97-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/97_96">97/96</a><br />
</td>
        <td>17.940<br />
</td>
        <td>97/(2<span style="vertical-align: super;">5</span>*3)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/98_97">98/97</a><br />
</td>
        <td>17.756<br />
</td>
        <td>(2*7<span style="vertical-align: super;">2</span>)/97<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="4">101-limit (incomplete)<br />
</th>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/101_100">101/100</a><br />
</td>
        <td>17.226<br />
</td>
        <td>101/(2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)<br />
</td>
        <td><br />
</td>
    </tr>
</table>

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