Xenharmonic Wiki

List of superparticular intervals

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[[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.

The list below is ordered by [[harmonic limit]], or the largest prime involved in the prime factorization. [[36_35|36/35]], for instance, is an interval of the [[7-limit]], as it factors to (2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-limit.

[[http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem|Størmer's theorem]] guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. [[https://oeis.org/A145604|OEIS A145604]] gives the number of superparticular ratios in each prime 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 ||~ Factorization ||~ [[Monzo]] ||~ Name(s) ||
||||||||||~ 2-limit (complete) ||
|| [[2_1|2/1]] || 1200.000 || 2/1 || | 1 > || (perfect) unison, unity, perfect prime, tonic, duple ||
||||||||||~ 3-limit (complete) ||
|| [[3_2|3/2]] || 701.995 || 3/2 || | -1 1 > || [[perfect fifth]], 3rd harmonic (octave reduced), diapente ||
|| [[4_3|4/3]] || 498.045 || 2<span style="font-size: 70%; vertical-align: super;">2</span>/3 || | 2 -1 > || perfect fourth, 3rd subharmonic (octave reduced), diatessaron ||
|| [[9_8|9/8]] || 203.910 || 3<span style="font-size: 70%; vertical-align: super;">2</span>/2<span style="font-size: 70%; vertical-align: super;">3</span> || | -3 2 > || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) ||
||||||||||~ 5-limit (complete) ||
|| [[5_4|5/4]] || 386.314 || 5/2<span style="font-size: 70%; vertical-align: super;">2</span> || | -2 0 1 > || (classic) (5-limit) major third, 5th harmonic (octave reduced) ||
|| [[6_5|6/5]] || 315.641 || (2*3)/5 || | 1 1 -1 > || (classic) (5-limit) minor third ||
|| [[10_9|10/9]] || 182.404 || (2*5)/3<span style="font-size: 70%; vertical-align: super;">2</span> || | 1 -2 1 > || classic (whole) tone, classic major second, minor whole tone ||
|| [[16_15|16/15]] || 111.713 || 2<span style="font-size: 70%; vertical-align: super;">4</span>/(3*5) || | 4 -1 -1 > || minor diatonic semitone, 15th subharmonic ||
|| [[25_24|25/24]] || 70.672 || 5<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3) || | -3 -1 2 > || chroma, (classic) chromatic semitone, Zarlinian semitone ||
|| [[81_80|81/80]] || 21.506 || (3/2)<span style="font-size: 70%; vertical-align: super;">4</span>/5 || | -4 4 -1 > || syntonic comma, Didymus comma ||
||||||||||~ 7-limit (complete) ||
|| [[7_6|7/6]] || 266.871 || 7/(2*3) || | -1 -1 0 1 > || (septimal) subminor third, septimal minor third, augmented second ||
|| [[8_7|8/7]] || 231.174 || 2<span style="font-size: 70%; vertical-align: super;">3</span>/7 || | 3 0 0 -1 > || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic ||
|| [[15_14|15/14]] || 119.443 || (3*5)/(2*7) || | -1 1 1 -1 > || septimal diatonic semitone ||
|| [[21_20|21/20]] || 84.467 || (3*7)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5) || | -2 1 -1 1 > || minor semitone, large septimal chromatic semitone ||
|| [[28_27|28/27]] || 62.961 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*7)/3<span style="font-size: 70%; vertical-align: super;">3</span> || | 2 -3 0 1 > || septimal chroma, small septimal chromatic semitone, Archytas' 1/3-tone ||
|| [[36_35|36/35]] || 48.770 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>)/(5*7) || | 2 2 -1 -1 > || septimal quarter tone, septimal diesis ||
|| [[49_48|49/48]] || 35.697 || 7<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3) || | -4 -1 0 2 > || large septimal diesis, slendro diesis, septimal 1/6-tone ||
|| [[50_49|50/49]] || 34.976 || 2*(5/7)<span style="font-size: 70%; vertical-align: super;">2</span> || | 1 0 2 -2 > || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
|| [[64_63|64/63]] || 27.264 || 2<span style="font-size: 70%; vertical-align: super;">6</span>/(3<span style="font-size: 70%; vertical-align: super;">2</span>*7) || | 6 -2 0 -1 > || septimal comma, Archytas' comma ||
|| [[126_125|126/125]] || 13.795 || (2*3<span style="font-size: 70%; vertical-align: super;">2</span>*7)/5<span style="font-size: 70%; vertical-align: super;">3</span> || | 1 2 -3 1 > || starling comma, septimal semicomma ||
|| [[225_224|225/224]] || 7.7115 || (3*5)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">5</span>*7) || | -5 2 2 -1 > || marvel comma, septimal kleisma ||
|| [[2401_2400|2401/2400]] || 0.72120 || 7<span style="font-size: 70%; vertical-align: super;">4</span>/(2<span style="font-size: 70%; vertical-align: super;">5</span>*3*5<span style="font-size: 70%; vertical-align: super;">2</span>) || | -5 -1 -2 4 > || breedsma ||
|| [[4375_4374|4375/4374]] || 0.39576 || (5<span style="font-size: 70%; vertical-align: super;">4</span>*7)/(2*3<span style="font-size: 70%; vertical-align: super;">7</span>) || | -1 -7 4 1 > || ragisma ||
||||||||||~ 11-limit (complete) ||
|| [[11_10|11/10]] || 165.004 || 11/(2*5) || | -1 0 -1 0 1 > || (large) (undecimal) neutral second, 4/5-tone, Ptolemy's second ||
|| [[12_11|12/11]] || 150.637 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*3)/11 || | 2 1 0 0 -1 > || (small) (undecimal) neutral second, 3/4-tone ||
|| [[22_21|22/21]] || 80.537 || (2*11)/(3*7) || | 1 -1 0 -1 1 > || undecimal minor semitone ||
|| [[33_32|33/32]] || 53.273 || (3*11)/2<span style="font-size: 70%; vertical-align: super;">5</span> || | -5 1 0 0 1 > || undecimal quarter tone, undecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
|| [[45_44|45/44]] || 38.906 || (3/2)<span style="font-size: 70%; vertical-align: super;">2</span>*(5/11) || | -2 2 1 0 -1 > || 1/5-tone ||
|| [[55_54|55/54]] || 31.767 || (5*11)/(2*3<span style="font-size: 70%; vertical-align: super;">3</span>) || | -1 -3 1 0 1 > || undecimal diasecundal comma, eleventyfive comma ||
|| [[56_55|56/55]] || 31.194 || (2<span style="font-size: 70%; vertical-align: super;">3</span>*7)/(5*11) || | 3 0 -1 1 -1 > || undecimal tritonic comma, konbini comma ||
|| [[99_98|99/98]] || 17.576 || (3/7)<span style="font-size: 70%; vertical-align: super;">2</span>*(11/2) || | -1 2 0 -2 1 > || small undecimal comma, mothwellsma ||
|| [[100_99|100/99]] || 17.399 || (2*5/3)<span style="font-size: 70%; vertical-align: super;">2</span>/11) || | 2 -2 2 0 -1 > || Ptolemy's comma, ptolemisma ||
|| [[121_120|121/120]] || 14.376 || 11<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3*5) || | -3 -1 -1 0 2 > || undecimal seconds comma, biyatisma ||
|| [[176_175|176/175]] || 9.8646 || (2<span style="font-size: 70%; vertical-align: super;">4</span>*11)/(5<span style="font-size: 70%; vertical-align: super;">2</span>*7) || | 4 0 -2 -1 1 > || valinorsma ||
|| [[243_242|243/242]] || 7.1391 || 3<span style="font-size: 70%; vertical-align: super;">5</span>/(2*11<span style="font-size: 70%; vertical-align: super;">2</span>) || | -1 5 0 0 -2 > || neutral third comma, rastma ||
|| [[385_384|385/384]] || 4.5026 || (5*7*11)/(2<span style="font-size: 70%; vertical-align: super;">7</span>*3) || | -7 -1 1 1 1 > || keenanisma ||
|| [[441_440|441/440]] || 3.9302 || (3*7)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*5*11) || | -3 2 -1 2 -1 > || Werckmeister's undecimal septenarian schisma, werckisma ||
|| [[540_539|540/539]] || 3.2090 || (2/7)<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>*5/11 || | 2 3 1 -2 -1 > || Swets' comma, swetisma ||
|| [[3025_3024|3025/3024]] || 0.57240 || (5*11)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*7) || | -4 -3 2 -1 2 > || Lehmerisma ||
|| [[9801_9800|9801/9800]] || 0.17665 || [11/(5*7)]<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>/2<span style="font-size: 70%; vertical-align: super;">3</span> || | -3 4 -2 -2 2 > || Gauss comma, kalisma ||
||||||||||~ 13-limit (complete) ||
|| [[13_12|13/12]] || 138.573 || 13/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3) || | -2 -1 0 0 0 1 > || tridecimal 2/3-tone ||
|| [[14_13|14/13]] || 128.298 || (2*7)/13 || | 1 0 0 1 0 -1 > || 2/3-tone, trienthird ||
|| [[26_25|26/25]] || 67.900 || (2*13)/5<span style="font-size: 70%; vertical-align: super;">2</span> || | 1 0 -2 0 0 1 > || tridecimal 1/3-tone ||
|| [[27_26|27/26]] || 65.337 || 3<span style="font-size: 70%; vertical-align: super;">3</span>/(2*13) || | -1 3 0 0 0 -1 > || tridecimal comma ||
|| [[40_39|40/39]] || 43.831 || (2<span style="font-size: 70%; vertical-align: super;">3</span>*5)/(3*13) || | 3 -1 1 0 0 -1 > || tridecimal minor diesis ||
|| [[65_64|65/64]] || 26.841 || (5*13)/2<span style="font-size: 70%; vertical-align: super;">6</span> || | -6 0 1 0 0 1 > || wilsorma, 13th-partial chroma ||
|| [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) || | 1 1 -1 0 1 -1 > || winmeanma ||
|| [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) || | 1 1 0 -1 -1 1 > || negustma ||
|| [[91_90|91/90]] || 19.130 || (7*13)/(2*3<span style="font-size: 70%; vertical-align: super;">2</span>*5) || | -1 -2 -1 1 0 1 > || [[The Biosphere|Biome]] comma, superleap comma ||
|| [[105_104|105/104]] || 16.567 || (3*5*7)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*13) || | -3 1 1 1 0 -1 > || small tridecimal comma, animist comma ||
|| [[144_143|144/143]] || 12.064 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*3)<span style="font-size: 70%; vertical-align: super;">2</span>/(11*13) || | 4 2 0 0 -1 -1 > || grossma ||
|| [[169_168|169/168]] || 10.274 || 13<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3*7) || | -3 -1 0 -1 0 2 > || buzurgisma, dhanvantarisma ||
|| [[196_195|196/195]] || 8.8554 || (2*7)<span style="font-size: 70%; vertical-align: super;">2</span>/(3*5*13) || | 2 -1 -1 2 0 -1 > || marveltwin comma ||
|| [[325_324|325/324]] || 5.3351 || (5<span style="font-size: 70%; vertical-align: super;">2</span>*13)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>) || | -2 -4 2 0 0 1 > ||   ||
|| [[351_350|351/350]] || 4.9393 || (3/5)<span style="font-size: 70%; vertical-align: super;">2</span>*13/(2*7) || | -1 3 -2 -1 0 1 > || ratwolfsma ||
|| [[352_351|352/351]] || 4.9253 || (2<span style="font-size: 70%; vertical-align: super;">5</span>*11)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*13) || | 5 -3 0 0 1 -1 > || minthma ||
|| [[364_363|364/363]] || 4.7627 || (2/11)<span style="font-size: 70%; vertical-align: super;">2</span>*7*13/3 || | 2 -1 0 1 -2 1 > || gentle comma ||
|| [[625_624|625/624]] || 2.7722 ||   || | -4 -1 4 0 0 -1 > || tunbarsma ||
|| [[676_675|676/675]] || 2.5629 ||   || | 2 -3 -2 0 0 2 > || island comma ||
|| [[729_728|729/728]] || 2.3764 ||   || | -3 6 0 -1 0 -1 > || squbema ||
|| [[1001_1000|1001/1000]] || 1.7304 ||   || | -3 0 -3 1 1 1 > || sinbadma ||
|| [[1716_1715|1716/1715]] || 1.0092 ||   || | 2 1 -1 -3 1 1 > || lummic comma ||
|| [[2080_2079|2080/2079]] || 0.83252 ||   || | 5 -3 1 -1 -1 1 > || ibnsinma ||
|| [[4096_4095|4096/4095]] || 0.42272 ||   || | 12 -2 -1 -1 0 -1 > || tridecimal schisma, Sagittal schismina ||
|| [[4225_4224|4225/4224]] || 0.40981 ||   || | -7 -1 2 0 -1 2 > || leprechaun comma ||
|| [[6656_6655|6656/6655]] || 0.26012 ||   || | 9 0 -1 0 -3 1 > || jacobin comma ||
|| [[10648_10647|10648/10647]] || 0.16260 ||   || | 3 -2 0 -1 3 -2 > || harmonisma ||
|| [[123201_123200|123201/123200]] || 0.014052 ||   || | -6 6 -2 -1 -1 2 > || chalmersia ||
||||||||||~ 17-limit (complete) ||
|| [[17_16|17/16]] || 104.955 || 17/2<span style="font-size: 70%; vertical-align: super;">4</span> || | -4 0 0 0 0 0 1 > || 17th harmonic (octave reduced) ||
|| [[18_17|18/17]] || 98.955 || (2*3<span style="font-size: 70%; vertical-align: super;">2</span>)/17 || | 1 2 0 0 0 0 -1 > || Arabic lute index finger ||
|| [[34_33|34/33]] || 51.682 || (2*17)/(3*11) || | 1 -1 0 0 -1 0 1 > ||   ||
|| [[35_34|35/34]] || 50.184 || (5*7)/(2*17) || | -1 0 1 1 0 0 -1 > || septendecimal 1/4-tone ||
|| [[51_50|51/50]] || 34.283 || (3*17)/(2*5<span style="font-size: 70%; vertical-align: super;">2</span>) || | -1 1 -2 0 0 0 1 > || 17th-partial chroma ||
|| [[52_51|52/51]] || 33.617 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*13)/(3*17) || | 2 -1 0 0 0 1 -1 > ||   ||
|| [[85_84|85/84]] || 20.488 || (5*17)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3*7) || | -2 -1 1 -1 0 0 1 > ||   ||
|| 120/119 || 14.487 || (2<span style="font-size: 70%; vertical-align: super;">3</span>*3*5)/(7*17) || | 3 1 1 -1 0 0 -1 > ||   ||
|| 136/135 || 12.777 || (2/3)<span style="font-size: 70%; vertical-align: super;">3</span>*17/5 || | 3 -3 -1 0 0 0 1 > ||   ||
|| 154/153 || 11.278 || (2*7*11)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*17) || | 1 -2 0 1 1 0 -1 > ||   ||
|| 170/169 || 10.214 || (2*5*17)/13<span style="font-size: 70%; vertical-align: super;">2</span> || | 1 0 1 0 0 -2 1 > ||   ||
|| 221/220 || 7.8514 || (13*17)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5*11) || | -2 0 -1 0 -1 1 1 > ||   ||
|| 256/255 || 6.7759 || (2<span style="font-size: 70%; vertical-align: super;">8</span>)/(3*5*17) || | 8 -1 -1 0 0 0 -1 > || 255th subharmonic ||
|| 273/272 || 6.3532 || (3*7*13)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*17) || | -4 1 0 1 0 1 -1 > ||   ||
|| 289/288 || 6.0008 || (17/3)<span style="font-size: 70%; vertical-align: super;">2</span>/2<span style="font-size: 70%; vertical-align: super;">5</span> || | -5 -2 0 0 0 0 2 > ||   ||
|| 375/374 || 4.6228 || (3*5<span style="font-size: 70%; vertical-align: super;">3</span>)/(2*11*17) || | -1 1 3 0 -1 0 -1 > ||   ||
|| 442/441 || 3.9213 || (2*13*17)/(3*7)<span style="font-size: 70%; vertical-align: super;">2</span> || | 1 -2 0 -2 0 1 1 > ||   ||
|| 561/560 || 3.0887 || (3*11*17)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*5*7) || | -4 1 -1 -1 1 0 1 > ||   ||
|| 595/594 || 2.9121 || (5*7*17)/(2*3<span style="font-size: 70%; vertical-align: super;">3</span>*11) || | -1 -3 1 1 -1 0 1 > ||   ||
|| 715/714 || 2.4230 || (5*11*13)/(2*3*7*17) || | -1 -1 1 -1 1 1 -1 > ||   ||
|| 833/832 || 2.0796 || (7<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">6</span>*13) || | -6 0 0 2 0 -1 1 > ||   ||
|| 936/935 || 1.8506 || (2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*13)/(5*11*17) || | 3 2 -1 0 -1 1 -1 > ||   ||
|| 1089/1088 || 1.5905 || (3<span style="font-size: 70%; vertical-align: super;">2</span>*11<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">6</span>*17) || | -6 2 0 0 2 0 -1 > ||   ||
|| 1156/1155 || 1.4983 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>)/(3*5*7*11) || | 2 -1 -1 -1 -1 0 2 > ||   ||
|| 1225/1224 || 1.4138 || (5<span style="font-size: 70%; vertical-align: super;">2</span>*7<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*17) || | -3 -2 2 2 0 0 -1 > ||   ||
|| 1275/1274 || 1.3584 || (3*5<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2*7<span style="font-size: 70%; vertical-align: super;">2</span>*13) || | -1 1 2 -2 0 -1 1 > ||   ||
|| 1701/1700 || 1.0181 || (3<span style="font-size: 70%; vertical-align: super;">5</span>*7)/[(2*5)<span style="font-size: 70%; vertical-align: super;">2</span>*17] || | -2 5 -2 1 0 0 -1 > ||   ||
|| 2058/2057 || 0.8414 || (2*3*7<span style="font-size: 70%; vertical-align: super;">3</span>)/(11<span style="font-size: 70%; vertical-align: super;">2</span>*17) || | 1 1 0 3 -2 0 -1 > || xenisma ||
|| 2431/2430 || 0.7123 || (11*13*17)/(2*3<span style="font-size: 70%; vertical-align: super;">5</span>*5) || | -1 -5 -1 0 1 1 1 > ||   ||
|| 2500/2499 || 0.6926 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">4</span>)/(3*7<span style="font-size: 70%; vertical-align: super;">2</span>*17) || | 2 -1 4 -2 0 0 -1 > ||   ||
|| 2601/2600 || 0.6657 || (3<span style="font-size: 70%; vertical-align: super;">2</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>*13) || | -3 2 -2 0 0 -1 2 > ||   ||
|| 4914/4913 || 0.3523 || (2*3<span style="font-size: 70%; vertical-align: super;">3</span>*7*13)/(17<span style="font-size: 70%; vertical-align: super;">3</span>) || | 1 3 0 1 0 1 -3 > ||   ||
|| 5832/5831 || 0.2969 || (2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">6</span>)/(7<span style="font-size: 70%; vertical-align: super;">3</span>*17) || | 3 6 0 -3 0 0 -1 > ||   ||
|| 12376/12375 || 0.1399 || (2<span style="font-size: 70%; vertical-align: super;">3</span>*7*13*17)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">3</span>*11) || | 3 -2 -3 1 -1 1 1 > ||   ||
|| 14400/14399 || 0.1202 || (2<span style="font-size: 70%; vertical-align: super;">6</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>)/(7*11<span style="font-size: 70%; vertical-align: super;">2</span>*17) || | 6 2 2 -1 -2 0 -1 > ||   ||
|| 28561/28560 || 0.0606 || (13<span style="font-size: 70%; vertical-align: super;">4</span>)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3*5*7*17) || | -4 -1 -1 -1 0 4 -1 > ||   ||
|| 31213/31212 || 0.0555 || (7<span style="font-size: 70%; vertical-align: super;">4</span>*13)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>) || | -2 -3 0 4 0 1 -2 > ||   ||
|| 37180/37179 || 0.0466 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*5*11*13<span style="font-size: 70%; vertical-align: super;">2</span>)/(3<span style="font-size: 70%; vertical-align: super;">7</span>*17) || | 2 -7 1 0 1 2 -1 > ||   ||
|| 194481/194480 || 0.0089 || (3<span style="font-size: 70%; vertical-align: super;">4</span>*7<span style="font-size: 70%; vertical-align: super;">4</span>)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*5*11*13*17) || | -4 4 -1 4 -1 -1 -1> || scintillisma ||
|| 336141/336140 || 0.0052 || (3<span style="font-size: 70%; vertical-align: super;">2</span>*13<span style="font-size: 70%; vertical-align: super;">3</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5*7<span style="font-size: 70%; vertical-align: super;">5</span>) || | -2 2 -1 -5 0 3 1 > ||   ||
||||||||||~ 19-limit (incomplete) ||
|| [[19_18|19/18]] || 93.603 || 19/(2*3<span style="font-size: 70%; vertical-align: super;">2</span>) || | -1 -2 0 0 0 0 0 1 > || undevicesimal semitone ||
|| [[20_19|20/19]] || 88.801 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*5)/19 || | 2 0 1 0 0 0 0 -1 > || small undevicesimal semitone ||
|| [[39_38|39/38]] || 44.970 || (3*13)/(2*19) || | -1 1 0 0 0 1 0 -1 > ||   ||
|| [[57_56|57/56]] || 30.642 || (3*19)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*7) || | -3 1 0 -1 0 0 0 1 > ||   ||
|| [[76_75|76/75]] || 22.931 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*19)/(3*5<span style="font-size: 70%; vertical-align: super;">2</span>) || | 2 -1 -2 0 0 0 0 1 > ||   ||
|| [[77_76|77/76]] || 22.631 || (7*11)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*19) || | -2 0 0 1 1 0 0 -1 > ||   ||
|| [[96_95|96/95]] || 18.128 || (2<span style="font-size: 70%; vertical-align: super;">5</span>*3)/(5*19) || | 5 1 -1 0 0 0 0 -1 > ||   ||
|| 133/132 || 13.066 || (19*7)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3*11) || | -2 -1 0 1 -1 0 0 1 > ||   ||
|| 153/152 || 11.352 || (3<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*19) || | -3 2 0 0 0 0 1 -1 > ||   ||
|| 171/170 || 10.154 || (3<span style="font-size: 70%; vertical-align: super;">2</span>*19)/(2*5*17) || | -1 2 -1 0 0 0 -1 1 > ||   ||
|| 190/189 || 9.1358 || (2*5*19)/(3<span style="font-size: 70%; vertical-align: super;">3</span>*7) || | 1 -3 1 -1 0 0 0 1 > ||   ||
|| 209/208 || 8.3033 || (11*19)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*13) || | -4 0 0 0 1 -1 0 1 > ||   ||
|| 210/209 || 8.2637 || (2*3*5*7)/(11*19) || | 1 1 1 1 -1 0 0 -1 > ||   ||
|| 286/285 || 6.0639 || (2*11*13)/(3*5*19) || | 1 -1 -1 0 1 1 0 -1 > ||   ||
|| 324/323 || 5.3516 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>)/(17*19) || | 2 4 0 0 0 0 -1 -1 > ||   ||
|| 343/342 || 5.0547 || 7<span style="font-size: 70%; vertical-align: super;">4</span>/(2*3<span style="font-size: 70%; vertical-align: super;">3</span>*19) || | -1 -2 0 3 0 0 0 -1 > ||   ||
|| 361/360 || 4.8023 || 19<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*5) || | -3 -2 -1 0 0 0 0 2 > ||   ||
|| 400/399 || 4.3335 || (2<span style="font-size: 70%; vertical-align: super;">4</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>)/(3*7*19) || | 4 -1 2 -1 0 0 0 -1 > ||   ||
|| 456/455 || 3.8007 || (2<span style="font-size: 70%; vertical-align: super;">3</span>*3*19)/(5*7*13) || | 3 1 -1 -1 0 -1 0 1 > ||   ||
|| 476/475 || 3.6409 || (2<span style="font-size: 70%; vertical-align: super;">2</span>*7*17)/(5<span style="font-size: 70%; vertical-align: super;">2</span>*19) || | 2 0 -2 1 0 0 1 -1 > ||   ||
|| 495/494 || 3.501 || (3<span style="font-size: 70%; vertical-align: super;">2</span>*5*11)/(2*13*19) || | -1 2 1 0 1 -1 0 -1 > ||   ||
|| 513/512 || 3.378 || (3<span style="font-size: 70%; vertical-align: super;">3</span>*19)/2<span style="font-size: 70%; vertical-align: super;">9</span> || | -9 3 0 0 0 0 0 1 > || 513th harmonic ||
||||||||||~ 23-limit (incomplete) ||
|| [[23_22|23/22]] || 76.956 || 23/(2*11) ||   ||   ||
|| [[24_23|24/23]] || 73.681 || (2<span style="font-size: 70%; vertical-align: super;">3</span>*3)/23 ||   ||   ||
|| [[46_45|46/45]] || 38.051 || (2*23)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*5) ||   ||   ||
|| [[69_68|69/68]] || 25.274 || (3*23)/(2<span style="font-size: 70%; 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="font-size: 70%; vertical-align: super;">2</span>*23)/(7*13) ||   ||   ||
|| 115/114 || 15.120 || (5*23)/(2*3*19) ||   ||   ||
|| 161/160 || 10.7865 || (7*23)/(2<span style="font-size: 70%; vertical-align: super;">5</span>*5) ||   ||   ||
|| 162/161 || 10.720 || (2*3<span style="font-size: 70%; vertical-align: super;">4</span>)/(7*23) ||   ||   ||
|| 208/207 || 8.343 || (2<span style="font-size: 70%; vertical-align: super;">4</span>*13)/(23*9) ||   ||   ||
|| 576/575 || 3.008 || (2<span style="font-size: 70%; vertical-align: super;">6</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/(23*25) ||   ||   ||
||||||||||~ 29-limit (incomplete) ||
|| [[29_28|29/28]] || 60.751 || 29/(2<span style="font-size: 70%; 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="font-size: 70%; 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="font-size: 70%; vertical-align: super;">5</span>/31 ||   || 31st subharmonic ||
|| [[63_62|63/62]] || 27.700 || (3<span style="font-size: 70%; vertical-align: super;">2</span>*7)/(2*31) ||   ||   ||
|| [[93_92|93/92]] || 18.716 || (3*31)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*23) ||   ||   ||
||||||||||~ 37-limit (incomplete) ||
|| [[37_36|37/36]] || 47.434 || 37/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>) ||   ||   ||
|| [[38_37|38/37]] || 46.169 || (2*19)/37 ||   ||   ||
|| [[75_74|75/74]] || 23.238 || (3*5<span style="font-size: 70%; vertical-align: super;">2</span>)/(2*37) ||   ||   ||
||||||||||~ 41-limit (incomplete) ||
|| [[41_40|41/40]] || 42.749 || 41/(2<span style="font-size: 70%; 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="font-size: 70%; 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="font-size: 70%; 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="font-size: 70%; 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="font-size: 70%; vertical-align: super;">2</span>*13) ||   ||   ||
|| [[54_53|54/53]] || 32.360 || (2*3<span style="font-size: 70%; 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="font-size: 70%; vertical-align: super;">2</span>*3*5)/59 ||   ||   ||
||||||||||~ 61-limit (incomplete) ||
|| [[61_60|61/60]] || 28.616 || 61/(2<span style="font-size: 70%; 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="font-size: 70%; 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="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/71 ||   ||   ||
||||||||||~ 73-limit (incomplete) ||
|| [[73_72|73/72]] || 23.879 || 73/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; 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="font-size: 70%; 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="font-size: 70%; vertical-align: super;">2</span>*3*7)/83 ||   ||   ||
||||||||||~ 89-limit (incomplete) ||
|| [[89_88|89/88]] || 19.562 || 89/(2<span style="font-size: 70%; vertical-align: super;">3</span>*11) ||   ||   ||
|| [[90_89|90/89]] || 19.344 || (2*3<span style="font-size: 70%; vertical-align: super;">2</span>*5)/89 ||   ||   ||
||||||||||~ 97-limit (incomplete) ||
|| [[97_96|97/96]] || 17.940 || 97/(2<span style="font-size: 70%; vertical-align: super;">5</span>*3) ||   ||   ||
|| [[98_97|98/97]] || 17.756 || (2*7<span style="font-size: 70%; vertical-align: super;">2</span>)/97 ||   ||   ||
||||||||||~ 101-limit (incomplete) ||
|| [[101_100|101/100]] || 17.226 || 101/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>) ||   ||   ||
|| [[102_101|102/101]] || 17.057 || (2*3*17)/101 ||   ||   ||

Original HTML content:

<html><head><title>List of Superparticular Intervals</title></head><body><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 />
The list below is ordered by <a class="wiki_link" href="/harmonic%20limit">harmonic limit</a>, or the largest prime involved in the prime factorization. <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="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/(5*7), while 37/36 would belong to the 37-limit.<br />
<br />
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem" rel="nofollow">Størmer's theorem</a> guarantees that, in each limit, there are only a finite number of superparticular ratios. Many of the sections below are complete. For example, there is no 3-limit superparticular ratio other than 2/1, 3/2, 4/3, and 9/8. <a class="wiki_link_ext" href="https://oeis.org/A145604" rel="nofollow">OEIS A145604</a> gives the number of superparticular ratios in each prime 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<br />
</th>
        <th>Factorization<br />
</th>
        <th><a class="wiki_link" href="/Monzo">Monzo</a><br />
</th>
        <th>Name(s)<br />
</th>
    </tr>
    <tr>
        <th colspan="5">2-limit (complete)<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>| 1 &gt;<br />
</td>
        <td>(perfect) unison, unity, perfect prime, tonic, duple<br />
</td>
    </tr>
    <tr>
        <th colspan="5">3-limit (complete)<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>| -1 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>/3<br />
</td>
        <td>| 2 -1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>/2<span style="font-size: 70%; vertical-align: super;">3</span><br />
</td>
        <td>| -3 2 &gt;<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="5">5-limit (complete)<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="font-size: 70%; vertical-align: super;">2</span><br />
</td>
        <td>| -2 0 1 &gt;<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>| 1 1 -1 &gt;<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="font-size: 70%; vertical-align: super;">2</span><br />
</td>
        <td>| 1 -2 1 &gt;<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="font-size: 70%; vertical-align: super;">4</span>/(3*5)<br />
</td>
        <td>| 4 -1 -1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3)<br />
</td>
        <td>| -3 -1 2 &gt;<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>(3/2)<span style="font-size: 70%; vertical-align: super;">4</span>/5<br />
</td>
        <td>| -4 4 -1 &gt;<br />
</td>
        <td>syntonic comma, Didymus comma<br />
</td>
    </tr>
    <tr>
        <th colspan="5">7-limit (complete)<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>| -1 -1 0 1 &gt;<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="font-size: 70%; vertical-align: super;">3</span>/7<br />
</td>
        <td>| 3 0 0 -1 &gt;<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>| -1 1 1 -1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*5)<br />
</td>
        <td>| -2 1 -1 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*7)/3<span style="font-size: 70%; vertical-align: super;">3</span><br />
</td>
        <td>| 2 -3 0 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>)/(5*7)<br />
</td>
        <td>| 2 2 -1 -1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3)<br />
</td>
        <td>| -4 -1 0 2 &gt;<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*(5/7)<span style="font-size: 70%; vertical-align: super;">2</span><br />
</td>
        <td>| 1 0 2 -2 &gt;<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="font-size: 70%; vertical-align: super;">6</span>/(3<span style="font-size: 70%; vertical-align: super;">2</span>*7)<br />
</td>
        <td>| 6 -2 0 -1 &gt;<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<span style="font-size: 70%; vertical-align: super;">2</span>*7)/5<span style="font-size: 70%; vertical-align: super;">3</span><br />
</td>
        <td>| 1 2 -3 1 &gt;<br />
</td>
        <td>starling comma, septimal semicomma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/225_224">225/224</a><br />
</td>
        <td>7.7115<br />
</td>
        <td>(3*5)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">5</span>*7)<br />
</td>
        <td>| -5 2 2 -1 &gt;<br />
</td>
        <td>marvel comma, septimal kleisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/2401_2400">2401/2400</a><br />
</td>
        <td>0.72120<br />
</td>
        <td>7<span style="font-size: 70%; vertical-align: super;">4</span>/(2<span style="font-size: 70%; vertical-align: super;">5</span>*3*5<span style="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td>| -5 -1 -2 4 &gt;<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<span style="font-size: 70%; vertical-align: super;">4</span>*7)/(2*3<span style="font-size: 70%; vertical-align: super;">7</span>)<br />
</td>
        <td>| -1 -7 4 1 &gt;<br />
</td>
        <td>ragisma<br />
</td>
    </tr>
    <tr>
        <th colspan="5">11-limit (complete)<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>| -1 0 -1 0 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*3)/11<br />
</td>
        <td>| 2 1 0 0 -1 &gt;<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>| 1 -1 0 -1 1 &gt;<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="font-size: 70%; vertical-align: super;">5</span><br />
</td>
        <td>| -5 1 0 0 1 &gt;<br />
</td>
        <td>undecimal quarter tone, undecimal 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>(3/2)<span style="font-size: 70%; vertical-align: super;">2</span>*(5/11)<br />
</td>
        <td>| -2 2 1 0 -1 &gt;<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="font-size: 70%; vertical-align: super;">3</span>)<br />
</td>
        <td>| -1 -3 1 0 1 &gt;<br />
</td>
        <td>undecimal diasecundal comma, eleventyfive comma<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="font-size: 70%; vertical-align: super;">3</span>*7)/(5*11)<br />
</td>
        <td>| 3 0 -1 1 -1 &gt;<br />
</td>
        <td>undecimal tritonic comma, konbini comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/99_98">99/98</a><br />
</td>
        <td>17.576<br />
</td>
        <td>(3/7)<span style="font-size: 70%; vertical-align: super;">2</span>*(11/2)<br />
</td>
        <td>| -1 2 0 -2 1 &gt;<br />
</td>
        <td>small undecimal comma, mothwellsma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/100_99">100/99</a><br />
</td>
        <td>17.399<br />
</td>
        <td>(2*5/3)<span style="font-size: 70%; vertical-align: super;">2</span>/11)<br />
</td>
        <td>| 2 -2 2 0 -1 &gt;<br />
</td>
        <td>Ptolemy's comma, ptolemisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/121_120">121/120</a><br />
</td>
        <td>14.376<br />
</td>
        <td>11<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3*5)<br />
</td>
        <td>| -3 -1 -1 0 2 &gt;<br />
</td>
        <td>undecimal seconds comma, biyatisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/176_175">176/175</a><br />
</td>
        <td>9.8646<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">4</span>*11)/(5<span style="font-size: 70%; vertical-align: super;">2</span>*7)<br />
</td>
        <td>| 4 0 -2 -1 1 &gt;<br />
</td>
        <td>valinorsma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/243_242">243/242</a><br />
</td>
        <td>7.1391<br />
</td>
        <td>3<span style="font-size: 70%; vertical-align: super;">5</span>/(2*11<span style="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td>| -1 5 0 0 -2 &gt;<br />
</td>
        <td>neutral third comma, rastma<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<span style="font-size: 70%; vertical-align: super;">7</span>*3)<br />
</td>
        <td>| -7 -1 1 1 1 &gt;<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*7)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*5*11)<br />
</td>
        <td>| -3 2 -1 2 -1 &gt;<br />
</td>
        <td>Werckmeister's undecimal septenarian schisma, werckisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/540_539">540/539</a><br />
</td>
        <td>3.2090<br />
</td>
        <td>(2/7)<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>*5/11<br />
</td>
        <td>| 2 3 1 -2 -1 &gt;<br />
</td>
        <td>Swets' comma, swetisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/3025_3024">3025/3024</a><br />
</td>
        <td>0.57240<br />
</td>
        <td>(5*11)<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*7)<br />
</td>
        <td>| -4 -3 2 -1 2 &gt;<br />
</td>
        <td>Lehmerisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/9801_9800">9801/9800</a><br />
</td>
        <td>0.17665<br />
</td>
        <td>[11/(5*7)]<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>/2<span style="font-size: 70%; vertical-align: super;">3</span><br />
</td>
        <td>| -3 4 -2 -2 2 &gt;<br />
</td>
        <td>Gauss comma, kalisma<br />
</td>
    </tr>
    <tr>
        <th colspan="5">13-limit (complete)<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="font-size: 70%; vertical-align: super;">2</span>*3)<br />
</td>
        <td>| -2 -1 0 0 0 1 &gt;<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>| 1 0 0 1 0 -1 &gt;<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="font-size: 70%; vertical-align: super;">2</span><br />
</td>
        <td>| 1 0 -2 0 0 1 &gt;<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="font-size: 70%; vertical-align: super;">3</span>/(2*13)<br />
</td>
        <td>| -1 3 0 0 0 -1 &gt;<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="font-size: 70%; vertical-align: super;">3</span>*5)/(3*13)<br />
</td>
        <td>| 3 -1 1 0 0 -1 &gt;<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="font-size: 70%; vertical-align: super;">6</span><br />
</td>
        <td>| -6 0 1 0 0 1 &gt;<br />
</td>
        <td>wilsorma, 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>| 1 1 -1 0 1 -1 &gt;<br />
</td>
        <td>winmeanma<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>| 1 1 0 -1 -1 1 &gt;<br />
</td>
        <td>negustma<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="font-size: 70%; vertical-align: super;">2</span>*5)<br />
</td>
        <td>| -1 -2 -1 1 0 1 &gt;<br />
</td>
        <td><a class="wiki_link" href="/The%20Biosphere">Biome</a> comma, superleap comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/105_104">105/104</a><br />
</td>
        <td>16.567<br />
</td>
        <td>(3*5*7)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*13)<br />
</td>
        <td>| -3 1 1 1 0 -1 &gt;<br />
</td>
        <td>small tridecimal comma, animist comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/144_143">144/143</a><br />
</td>
        <td>12.064<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">2</span>*3)<span style="font-size: 70%; vertical-align: super;">2</span>/(11*13)<br />
</td>
        <td>| 4 2 0 0 -1 -1 &gt;<br />
</td>
        <td>grossma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/169_168">169/168</a><br />
</td>
        <td>10.274<br />
</td>
        <td>13<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3*7)<br />
</td>
        <td>| -3 -1 0 -1 0 2 &gt;<br />
</td>
        <td>buzurgisma, dhanvantarisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/196_195">196/195</a><br />
</td>
        <td>8.8554<br />
</td>
        <td>(2*7)<span style="font-size: 70%; vertical-align: super;">2</span>/(3*5*13)<br />
</td>
        <td>| 2 -1 -1 2 0 -1 &gt;<br />
</td>
        <td>marveltwin comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/325_324">325/324</a><br />
</td>
        <td>5.3351<br />
</td>
        <td>(5<span style="font-size: 70%; vertical-align: super;">2</span>*13)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>)<br />
</td>
        <td>| -2 -4 2 0 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/351_350">351/350</a><br />
</td>
        <td>4.9393<br />
</td>
        <td>(3/5)<span style="font-size: 70%; vertical-align: super;">2</span>*13/(2*7)<br />
</td>
        <td>| -1 3 -2 -1 0 1 &gt;<br />
</td>
        <td>ratwolfsma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/352_351">352/351</a><br />
</td>
        <td>4.9253<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">5</span>*11)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*13)<br />
</td>
        <td>| 5 -3 0 0 1 -1 &gt;<br />
</td>
        <td>minthma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/364_363">364/363</a><br />
</td>
        <td>4.7627<br />
</td>
        <td>(2/11)<span style="font-size: 70%; vertical-align: super;">2</span>*7*13/3<br />
</td>
        <td>| 2 -1 0 1 -2 1 &gt;<br />
</td>
        <td>gentle comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/625_624">625/624</a><br />
</td>
        <td>2.7722<br />
</td>
        <td><br />
</td>
        <td>| -4 -1 4 0 0 -1 &gt;<br />
</td>
        <td>tunbarsma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/676_675">676/675</a><br />
</td>
        <td>2.5629<br />
</td>
        <td><br />
</td>
        <td>| 2 -3 -2 0 0 2 &gt;<br />
</td>
        <td>island comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/729_728">729/728</a><br />
</td>
        <td>2.3764<br />
</td>
        <td><br />
</td>
        <td>| -3 6 0 -1 0 -1 &gt;<br />
</td>
        <td>squbema<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/1001_1000">1001/1000</a><br />
</td>
        <td>1.7304<br />
</td>
        <td><br />
</td>
        <td>| -3 0 -3 1 1 1 &gt;<br />
</td>
        <td>sinbadma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/1716_1715">1716/1715</a><br />
</td>
        <td>1.0092<br />
</td>
        <td><br />
</td>
        <td>| 2 1 -1 -3 1 1 &gt;<br />
</td>
        <td>lummic comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/2080_2079">2080/2079</a><br />
</td>
        <td>0.83252<br />
</td>
        <td><br />
</td>
        <td>| 5 -3 1 -1 -1 1 &gt;<br />
</td>
        <td>ibnsinma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/4096_4095">4096/4095</a><br />
</td>
        <td>0.42272<br />
</td>
        <td><br />
</td>
        <td>| 12 -2 -1 -1 0 -1 &gt;<br />
</td>
        <td>tridecimal schisma, Sagittal schismina<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/4225_4224">4225/4224</a><br />
</td>
        <td>0.40981<br />
</td>
        <td><br />
</td>
        <td>| -7 -1 2 0 -1 2 &gt;<br />
</td>
        <td>leprechaun comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/6656_6655">6656/6655</a><br />
</td>
        <td>0.26012<br />
</td>
        <td><br />
</td>
        <td>| 9 0 -1 0 -3 1 &gt;<br />
</td>
        <td>jacobin comma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/10648_10647">10648/10647</a><br />
</td>
        <td>0.16260<br />
</td>
        <td><br />
</td>
        <td>| 3 -2 0 -1 3 -2 &gt;<br />
</td>
        <td>harmonisma<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/123201_123200">123201/123200</a><br />
</td>
        <td>0.014052<br />
</td>
        <td><br />
</td>
        <td>| -6 6 -2 -1 -1 2 &gt;<br />
</td>
        <td>chalmersia<br />
</td>
    </tr>
    <tr>
        <th colspan="5">17-limit (complete)<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="font-size: 70%; vertical-align: super;">4</span><br />
</td>
        <td>| -4 0 0 0 0 0 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>)/17<br />
</td>
        <td>| 1 2 0 0 0 0 -1 &gt;<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*11)<br />
</td>
        <td>| 1 -1 0 0 -1 0 1 &gt;<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>| -1 0 1 1 0 0 -1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td>| -1 1 -2 0 0 0 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*13)/(3*17)<br />
</td>
        <td>| 2 -1 0 0 0 1 -1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*3*7)<br />
</td>
        <td>| -2 -1 1 -1 0 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>120/119<br />
</td>
        <td>14.487<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">3</span>*3*5)/(7*17)<br />
</td>
        <td>| 3 1 1 -1 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>136/135<br />
</td>
        <td>12.777<br />
</td>
        <td>(2/3)<span style="font-size: 70%; vertical-align: super;">3</span>*17/5<br />
</td>
        <td>| 3 -3 -1 0 0 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>154/153<br />
</td>
        <td>11.278<br />
</td>
        <td>(2*7*11)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*17)<br />
</td>
        <td>| 1 -2 0 1 1 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>170/169<br />
</td>
        <td>10.214<br />
</td>
        <td>(2*5*17)/13<span style="font-size: 70%; vertical-align: super;">2</span><br />
</td>
        <td>| 1 0 1 0 0 -2 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>221/220<br />
</td>
        <td>7.8514<br />
</td>
        <td>(13*17)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5*11)<br />
</td>
        <td>| -2 0 -1 0 -1 1 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>256/255<br />
</td>
        <td>6.7759<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">8</span>)/(3*5*17)<br />
</td>
        <td>| 8 -1 -1 0 0 0 -1 &gt;<br />
</td>
        <td>255th subharmonic<br />
</td>
    </tr>
    <tr>
        <td>273/272<br />
</td>
        <td>6.3532<br />
</td>
        <td>(3*7*13)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*17)<br />
</td>
        <td>| -4 1 0 1 0 1 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>289/288<br />
</td>
        <td>6.0008<br />
</td>
        <td>(17/3)<span style="font-size: 70%; vertical-align: super;">2</span>/2<span style="font-size: 70%; vertical-align: super;">5</span><br />
</td>
        <td>| -5 -2 0 0 0 0 2 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>375/374<br />
</td>
        <td>4.6228<br />
</td>
        <td>(3*5<span style="font-size: 70%; vertical-align: super;">3</span>)/(2*11*17)<br />
</td>
        <td>| -1 1 3 0 -1 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>442/441<br />
</td>
        <td>3.9213<br />
</td>
        <td>(2*13*17)/(3*7)<span style="font-size: 70%; vertical-align: super;">2</span><br />
</td>
        <td>| 1 -2 0 -2 0 1 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>561/560<br />
</td>
        <td>3.0887<br />
</td>
        <td>(3*11*17)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*5*7)<br />
</td>
        <td>| -4 1 -1 -1 1 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>595/594<br />
</td>
        <td>2.9121<br />
</td>
        <td>(5*7*17)/(2*3<span style="font-size: 70%; vertical-align: super;">3</span>*11)<br />
</td>
        <td>| -1 -3 1 1 -1 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>715/714<br />
</td>
        <td>2.4230<br />
</td>
        <td>(5*11*13)/(2*3*7*17)<br />
</td>
        <td>| -1 -1 1 -1 1 1 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>833/832<br />
</td>
        <td>2.0796<br />
</td>
        <td>(7<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">6</span>*13)<br />
</td>
        <td>| -6 0 0 2 0 -1 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>936/935<br />
</td>
        <td>1.8506<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*13)/(5*11*17)<br />
</td>
        <td>| 3 2 -1 0 -1 1 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1089/1088<br />
</td>
        <td>1.5905<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">2</span>*11<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">6</span>*17)<br />
</td>
        <td>| -6 2 0 0 2 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1156/1155<br />
</td>
        <td>1.4983<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">2</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>)/(3*5*7*11)<br />
</td>
        <td>| 2 -1 -1 -1 -1 0 2 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1225/1224<br />
</td>
        <td>1.4138<br />
</td>
        <td>(5<span style="font-size: 70%; vertical-align: super;">2</span>*7<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*17)<br />
</td>
        <td>| -3 -2 2 2 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1275/1274<br />
</td>
        <td>1.3584<br />
</td>
        <td>(3*5<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2*7<span style="font-size: 70%; vertical-align: super;">2</span>*13)<br />
</td>
        <td>| -1 1 2 -2 0 -1 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1701/1700<br />
</td>
        <td>1.0181<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">5</span>*7)/[(2*5)<span style="font-size: 70%; vertical-align: super;">2</span>*17]<br />
</td>
        <td>| -2 5 -2 1 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2058/2057<br />
</td>
        <td>0.8414<br />
</td>
        <td>(2*3*7<span style="font-size: 70%; vertical-align: super;">3</span>)/(11<span style="font-size: 70%; vertical-align: super;">2</span>*17)<br />
</td>
        <td>| 1 1 0 3 -2 0 -1 &gt;<br />
</td>
        <td>xenisma<br />
</td>
    </tr>
    <tr>
        <td>2431/2430<br />
</td>
        <td>0.7123<br />
</td>
        <td>(11*13*17)/(2*3<span style="font-size: 70%; vertical-align: super;">5</span>*5)<br />
</td>
        <td>| -1 -5 -1 0 1 1 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2500/2499<br />
</td>
        <td>0.6926<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">4</span>)/(3*7<span style="font-size: 70%; vertical-align: super;">2</span>*17)<br />
</td>
        <td>| 2 -1 4 -2 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2601/2600<br />
</td>
        <td>0.6657<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">2</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>*13)<br />
</td>
        <td>| -3 2 -2 0 0 -1 2 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4914/4913<br />
</td>
        <td>0.3523<br />
</td>
        <td>(2*3<span style="font-size: 70%; vertical-align: super;">3</span>*7*13)/(17<span style="font-size: 70%; vertical-align: super;">3</span>)<br />
</td>
        <td>| 1 3 0 1 0 1 -3 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5832/5831<br />
</td>
        <td>0.2969<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">6</span>)/(7<span style="font-size: 70%; vertical-align: super;">3</span>*17)<br />
</td>
        <td>| 3 6 0 -3 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12376/12375<br />
</td>
        <td>0.1399<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">3</span>*7*13*17)/(3<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">3</span>*11)<br />
</td>
        <td>| 3 -2 -3 1 -1 1 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14400/14399<br />
</td>
        <td>0.1202<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">6</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>)/(7*11<span style="font-size: 70%; vertical-align: super;">2</span>*17)<br />
</td>
        <td>| 6 2 2 -1 -2 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28561/28560<br />
</td>
        <td>0.0606<br />
</td>
        <td>(13<span style="font-size: 70%; vertical-align: super;">4</span>)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*3*5*7*17)<br />
</td>
        <td>| -4 -1 -1 -1 0 4 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>31213/31212<br />
</td>
        <td>0.0555<br />
</td>
        <td>(7<span style="font-size: 70%; vertical-align: super;">4</span>*13)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">3</span>*17<span style="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td>| -2 -3 0 4 0 1 -2 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37180/37179<br />
</td>
        <td>0.0466<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">2</span>*5*11*13<span style="font-size: 70%; vertical-align: super;">2</span>)/(3<span style="font-size: 70%; vertical-align: super;">7</span>*17)<br />
</td>
        <td>| 2 -7 1 0 1 2 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>194481/194480<br />
</td>
        <td>0.0089<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">4</span>*7<span style="font-size: 70%; vertical-align: super;">4</span>)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*5*11*13*17)<br />
</td>
        <td>| -4 4 -1 4 -1 -1 -1&gt;<br />
</td>
        <td>scintillisma<br />
</td>
    </tr>
    <tr>
        <td>336141/336140<br />
</td>
        <td>0.0052<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">2</span>*13<span style="font-size: 70%; vertical-align: super;">3</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*5*7<span style="font-size: 70%; vertical-align: super;">5</span>)<br />
</td>
        <td>| -2 2 -1 -5 0 3 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td>| -1 -2 0 0 0 0 0 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*5)/19<br />
</td>
        <td>| 2 0 1 0 0 0 0 -1 &gt;<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>| -1 1 0 0 0 1 0 -1 &gt;<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="font-size: 70%; vertical-align: super;">3</span>*7)<br />
</td>
        <td>| -3 1 0 -1 0 0 0 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*19)/(3*5<span style="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td>| 2 -1 -2 0 0 0 0 1 &gt;<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="font-size: 70%; vertical-align: super;">2</span>*19)<br />
</td>
        <td>| -2 0 0 1 1 0 0 -1 &gt;<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="font-size: 70%; vertical-align: super;">5</span>*3)/(5*19)<br />
</td>
        <td>| 5 1 -1 0 0 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>133/132<br />
</td>
        <td>13.066<br />
</td>
        <td>(19*7)/(2<span style="font-size: 70%; vertical-align: super;">2</span>*3*11)<br />
</td>
        <td>| -2 -1 0 1 -1 0 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>153/152<br />
</td>
        <td>11.352<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">2</span>*17)/(2<span style="font-size: 70%; vertical-align: super;">3</span>*19)<br />
</td>
        <td>| -3 2 0 0 0 0 1 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>171/170<br />
</td>
        <td>10.154<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">2</span>*19)/(2*5*17)<br />
</td>
        <td>| -1 2 -1 0 0 0 -1 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>190/189<br />
</td>
        <td>9.1358<br />
</td>
        <td>(2*5*19)/(3<span style="font-size: 70%; vertical-align: super;">3</span>*7)<br />
</td>
        <td>| 1 -3 1 -1 0 0 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>209/208<br />
</td>
        <td>8.3033<br />
</td>
        <td>(11*19)/(2<span style="font-size: 70%; vertical-align: super;">4</span>*13)<br />
</td>
        <td>| -4 0 0 0 1 -1 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>210/209<br />
</td>
        <td>8.2637<br />
</td>
        <td>(2*3*5*7)/(11*19)<br />
</td>
        <td>| 1 1 1 1 -1 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>286/285<br />
</td>
        <td>6.0639<br />
</td>
        <td>(2*11*13)/(3*5*19)<br />
</td>
        <td>| 1 -1 -1 0 1 1 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>324/323<br />
</td>
        <td>5.3516<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">4</span>)/(17*19)<br />
</td>
        <td>| 2 4 0 0 0 0 -1 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>343/342<br />
</td>
        <td>5.0547<br />
</td>
        <td>7<span style="font-size: 70%; vertical-align: super;">4</span>/(2*3<span style="font-size: 70%; vertical-align: super;">3</span>*19)<br />
</td>
        <td>| -1 -2 0 3 0 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>361/360<br />
</td>
        <td>4.8023<br />
</td>
        <td>19<span style="font-size: 70%; vertical-align: super;">2</span>/(2<span style="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>*5)<br />
</td>
        <td>| -3 -2 -1 0 0 0 0 2 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>400/399<br />
</td>
        <td>4.3335<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">4</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>)/(3*7*19)<br />
</td>
        <td>| 4 -1 2 -1 0 0 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>456/455<br />
</td>
        <td>3.8007<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">3</span>*3*19)/(5*7*13)<br />
</td>
        <td>| 3 1 -1 -1 0 -1 0 1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>476/475<br />
</td>
        <td>3.6409<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">2</span>*7*17)/(5<span style="font-size: 70%; vertical-align: super;">2</span>*19)<br />
</td>
        <td>| 2 0 -2 1 0 0 1 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>495/494<br />
</td>
        <td>3.501<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">2</span>*5*11)/(2*13*19)<br />
</td>
        <td>| -1 2 1 0 1 -1 0 -1 &gt;<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>513/512<br />
</td>
        <td>3.378<br />
</td>
        <td>(3<span style="font-size: 70%; vertical-align: super;">3</span>*19)/2<span style="font-size: 70%; vertical-align: super;">9</span><br />
</td>
        <td>| -9 3 0 0 0 0 0 1 &gt;<br />
</td>
        <td>513th harmonic<br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">3</span>*3)/23<br />
</td>
        <td><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="font-size: 70%; vertical-align: super;">2</span>*5)<br />
</td>
        <td><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="font-size: 70%; vertical-align: super;">2</span>*17)<br />
</td>
        <td><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>
        <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="font-size: 70%; vertical-align: super;">2</span>*23)/(7*13)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>115/114<br />
</td>
        <td>15.120<br />
</td>
        <td>(5*23)/(2*3*19)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>161/160<br />
</td>
        <td>10.7865<br />
</td>
        <td>(7*23)/(2<span style="font-size: 70%; vertical-align: super;">5</span>*5)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>162/161<br />
</td>
        <td>10.720<br />
</td>
        <td>(2*3<span style="font-size: 70%; vertical-align: super;">4</span>)/(7*23)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>208/207<br />
</td>
        <td>8.343<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">4</span>*13)/(23*9)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>576/575<br />
</td>
        <td>3.008<br />
</td>
        <td>(2<span style="font-size: 70%; vertical-align: super;">6</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/(23*25)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">2</span>*7)<br />
</td>
        <td><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>
        <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>
        <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="font-size: 70%; vertical-align: super;">3</span>*11)/(3*29)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">5</span>/31<br />
</td>
        <td><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="font-size: 70%; vertical-align: super;">2</span>*7)/(2*31)<br />
</td>
        <td><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="font-size: 70%; vertical-align: super;">2</span>*23)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">2</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td><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>
        <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="font-size: 70%; vertical-align: super;">2</span>)/(2*37)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">3</span>*5)<br />
</td>
        <td><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>
        <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="font-size: 70%; vertical-align: super;">4</span><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">2</span>*11)/43<br />
</td>
        <td><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>
        <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>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">4</span>*3)/47<br />
</td>
        <td><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>
        <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>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">2</span>*13)<br />
</td>
        <td><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="font-size: 70%; vertical-align: super;">3</span>)/53<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">2</span>*3*5)/59<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">2</span>*3*5)<br />
</td>
        <td><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>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">2</span>*17)/67<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)/71<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">3</span>*3<span style="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td><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>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">4</span>*5)/79<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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>
        <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="font-size: 70%; vertical-align: super;">2</span>*3*7)/83<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">3</span>*11)<br />
</td>
        <td><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="font-size: 70%; vertical-align: super;">2</span>*5)/89<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">5</span>*3)<br />
</td>
        <td><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="font-size: 70%; vertical-align: super;">2</span>)/97<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <th colspan="5">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="font-size: 70%; vertical-align: super;">2</span>*5<span style="font-size: 70%; vertical-align: super;">2</span>)<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/102_101">102/101</a><br />
</td>
        <td>17.057<br />
</td>
        <td>(2*3*17)/101<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

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