List of superparticular intervals: Difference between revisions

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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.

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="vertical-align: super;">2</span>*3<span style="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.

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 || <span style="line-height: 15.6000003814697px;">(</span>3<span style="line-height: 1.5;">/</span><span style="line-height: 15.6000003814697px;">2)</span><span style="line-height: 1.5; vertical-align: super;">4</span><span style="line-height: 15.6000003814697px;">/</span><span style="line-height: 1.5;">5</span> || 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="line-height: 1.5;">/7)</span><span style="line-height: 1.5; 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, septimal semicomma ||
|| [[225_224|225/224]] || 7.7115 || (3*5)<span style="line-height: 1.5;">^2/(2^5*7)</span> || marvel comma, septimal kleisma ||
|| [[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="line-height: 15.6000003814697px;">/</span><span style="line-height: 1.5;">2)^</span><span style="line-height: 15.6000003814697px;">2*</span><span style="line-height: 1.5;">(</span><span style="line-height: 15.6000003814697px;">5/</span><span style="line-height: 1.5;">11)</span> || 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="line-height: 1.5;">/7)</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">*(11/2)</span> || small undecimal comma, mothwellsma ||
|| [[100_99|100/99]] || 17.399 || (2<span style="line-height: 1.5;">*5/3)</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">/11)</span> || Ptolemy's comma, ptolemisma ||
|| [[121_120|121/120]] || 14.376 || 11^2/(2^3*3*5) || undecimal seconds comma, biyatisma ||
|| [[176_175|176/175]] || 9.8646 || (2^4*11)/(5^2*7) || valinorsma ||
|| [[243_242|243/242]] || 7.1391 || 3^5/(2*11^2) || neutral third comma, rastma ||
|| [[385_384|385/384]] || 4.5026 || (5*7*11)/(2^7*3) || keenanisma ||
|| [[441_440|441/440]] || 3.9302 || (3*7)^2/(2^3*5*11) || Werckmeister's undecimal septenarian schisma, werckisma ||
|| [[540_539|540/539]] || 3.2090 || (2/7)^2*3^3*5/11 || Swets' comma, swetisma ||
|| [[3025_3024|3025/3024]] || 0.57240 || (5*11)^2/(2^4*3^3*7) || Lehmerisma ||
|| [[9801_9800|9801/9800]] || 0.17665 || <span style="line-height: 1.5;">[11/(5*7)]</span><span style="line-height: 15.6000003814697px;">^2*</span><span style="line-height: 1.5;">3^4/2^3</span> || Gauss comma, kalisma ||
||||||||~ 13-limit ||
|| [[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> || wilsorma, 13th-partial chroma ||
|| [[66_65|66/65]] || 26.432 || (2*3*11)/(5*13) || winmeanma ||
|| [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) || negustma ||
|| [[91_90|91/90]] || 19.130 || (7*13)/(2*3<span style="vertical-align: super;">2</span>*5) || [[The Biosphere|Biome]] comma, superleap comma ||
|| [[105_104|105/104]] || 16.567 || (3*5*7)/(2^3*13) || small tridecimal comma, animist comma ||
|| [[144_143|144/143]] || 12.064 || (<span style="line-height: 1.5;">2</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">*3)^2/(11*13)</span> || grossma ||
|| [[169_168|169/168]] || 10.274 || 13<span style="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3*7) || buzurgisma, dhanvantarisma ||
|| [[196_195|196/195]] || 8.8554 || (2*7)^2/(3*5*13) || marveltwin comma ||
|| [[351_350|351/350]] || 4.9393 || (3/5)^2*13/(2*7) || ratwolfsma ||
|| [[352_351|352/351]] || 4.9253 || (<span style="line-height: 1.5;">2</span><span style="line-height: 1.5; vertical-align: super;">5</span><span style="line-height: 1.5;">*11)/(</span><span style="line-height: 15.6000003814697px;">3^</span>2<span style="line-height: 15.6000003814697px;">*13)</span> || minthma ||
|| [[364_363|364/363]] || 4.7627 || (2/11)^2*7*13/3 || gentle comma ||
|| [[625_624|625/624]] || 2.7722 ||   || tunbarsma ||
|| [[676_675|676/675]] || 2.5629 ||   || island comma ||
|| [[729_728|729/728]] || 2.3764 ||   || squbema ||
|| [[1001_1000|1001/1000]] || 1.7304 ||   || sinbadma ||
|| [[1716_1715|1716/1715]] || 1.0092 ||   || lummic comma ||
|| [[2080_2079|2080/2079]] || 0.83252 ||   || ibnsinma ||
|| [[4096_4095|4096/4095]] || 0.42272 ||   || tridecimal schisma, Sagittal schismina ||
|| [[4225_4224|4225/4224]] || 0.40981 ||   || leprechaun comma ||
|| [[6656_6655|6656/6655]] || 0.26012 ||   || jacobin comma ||
|| [[10648_10647|10648/10647]] || 0.16260 ||   || harmonisma ||
|| [[123201_123200|123201/123200]] || 0.014052 ||   || chalmersia ||
||||||||~ 17-limit (complete!) ||
|| [[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*11) ||   ||
|| [[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) ||   ||
|| 120/119 || 14.487 || (2<span style="vertical-align: super;">3</span>*3*5)/(7*17) ||   ||
|| 136/135 || 12.777 || (2/<span style="line-height: 1.5;">3)</span><span style="line-height: 1.5; vertical-align: super;">3</span><span style="line-height: 1.5;">*17/5</span> ||   ||
|| 154/153 || 11.278 || (2*7*11)/(3<span style="vertical-align: super;">2</span>*17) ||   ||
|| 170/169 || 10.214 || (2*5*17)/13<span style="vertical-align: super;">2</span> ||   ||
|| 221/220 || 7.8514 || (13*17)/(2<span style="vertical-align: super;">2</span>*5*11) ||   ||
|| 256/255 || 6.7759 || (2^8)/(3*5*17) || 255th subharmonic ||
|| 273/272 || 6.3532 || (3*7*13)/(2<span style="vertical-align: super;">4</span>*17) ||   ||
|| 289/288 || 6.0008 || (17<span style="line-height: 1.5;">/3)^</span><span style="line-height: 15.6000003814697px;">2</span><span style="line-height: 1.5;">/2</span><span style="line-height: 1.5; vertical-align: super;">5</span> ||   ||
|| 375/374 || 4.6228 || (3*5<span style="vertical-align: super;">3</span>)/(2*11*17) ||   ||
|| 442/441 || 3.9213 || (2*13*17)/(3*7)<span style="vertical-align: super;">2</span> ||   ||
|| 561/560 || 3.0887 || (3*11*17)/(2<span style="vertical-align: super;">4</span>*5*7) ||   ||
|| 595/594 || 2.9121 || (5*7*17)/(2*3<span style="vertical-align: super;">3</span>*11) ||   ||
|| 715/714 || 2.4230 || (5*11*13)/(2*3*7*17) ||   ||
|| 833/832 || 2.0796 || (7<span style="vertical-align: super;">2</span>*17)/(2<span style="vertical-align: super;">6</span>*13) ||   ||
|| 936/935 || 1.8506 || (2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>*13)/(5*11*17) ||   ||
|| 1089/1088 || 1.5905 || (3<span style="vertical-align: super;">2</span>*11<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">6</span>*17) ||   ||
|| 1156/1155 || 1.4983 || (2<span style="vertical-align: super;">2</span>*17<span style="vertical-align: super;">2</span>)/(3*5*7*11) ||   ||
|| 1225/1224 || 1.4138 || (5<span style="vertical-align: super;">2</span>*7<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>*17) ||   ||
|| 1275/1274 || 1.3584 || (3*5<span style="vertical-align: super;">2</span>*17)/(2*7<span style="vertical-align: super;">2</span>*13) ||   ||
|| 1701/1700 || 1.0181 || (3<span style="vertical-align: super;">5</span>*7)/[(2*5)<span style="vertical-align: super;">2</span>*17] ||   ||
|| 2058/2057 || 0.8414 || (2*3*7<span style="vertical-align: super;">3</span>)/(11<span style="vertical-align: super;">2</span>*17) || xenisma ||
|| 2431/2430 || 0.7123 || (11*13*17)/(2*3<span style="vertical-align: super;">5</span>*5) ||   ||
|| 2500/2499 || 0.6926 || (2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">4</span>)/(3*7<span style="vertical-align: super;">2</span>*17) ||   ||
|| 2601/2600 || 0.6657 || (3<span style="vertical-align: super;">2</span>*17<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">3</span>*5<span style="vertical-align: super;">2</span>*13) ||   ||
|| 4914/4913 || 0.3523 || (2*3<span style="vertical-align: super;">3</span>*7*13)/(17<span style="vertical-align: super;">3</span>) ||   ||
|| 5832/5831 || 0.2969 || (2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">6</span>)/(7<span style="vertical-align: super;">3</span>*17) ||   ||
|| 12376/12375 || 0.1399 || (2<span style="vertical-align: super;">3</span>*7*13*17)/(3<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">3</span>*11) ||   ||
|| 14400/14399 || 0.1202 || (2<span style="vertical-align: super;">6</span>*3<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)/(7*11<span style="vertical-align: super;">2</span>*17) ||   ||
|| 28561/28560 || 0.0606 || (13<span style="vertical-align: super;">4</span>)/(2<span style="vertical-align: super;">4</span>*3*5*7*17) ||   ||
|| 31213/31212 || 0.0555 || (7<span style="vertical-align: super;">4</span>*13)/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>*17<span style="vertical-align: super;">2</span>) ||   ||
|| 37180/37179 || 0.0466 || (2<span style="vertical-align: super;">2</span>*5*11*13<span style="vertical-align: super;">2</span>)/(3<span style="vertical-align: super;">7</span>*17) ||   ||
|| 194481/194480 || 0.0089 || (3<span style="vertical-align: super;">4</span>*7<span style="vertical-align: super;">4</span>)/(2<span style="vertical-align: super;">4</span>*5*11*13*17) || scintillisma ||
|| 336141/336140 || 0.0052 || (3<span style="vertical-align: super;">2</span>*13<span style="vertical-align: super;">3</span>*17)/(2<span style="vertical-align: super;">2</span>*5*7<span style="vertical-align: super;">5</span>) ||   ||
||||||||~ 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) ||   ||
|| 133/132 || 13.066 || (19*7)/(2<span style="vertical-align: super;">2</span>*3*11) ||   ||
|| 153/152 || 11.352 || (3<span style="vertical-align: super;">2</span>*17)/(2<span style="vertical-align: super;">3</span>*19) ||   ||
|| 171/170 || 10.154 || (3<span style="vertical-align: super;">2</span>*19)/(2*5*17) ||   ||
|| 190/189 || 9.1358 || (2*5*19)/(3<span style="vertical-align: super;">3</span>*7) ||   ||
|| 209/208 || 8.3033 || (11*19)/(2<span style="vertical-align: super;">4</span>*13) ||   ||
|| 210/209 || 8.2637 || (2*3*5*7)/(11*19) ||   ||
|| 286/285 || 6.0639 || (2*11*13)/(3*5*19) ||   ||
|| 400/399 || 4.3335 || (2<span style="vertical-align: super;">4</span>*5<span style="vertical-align: super;">2</span>)/(3*7*19) ||   ||
|| 456/455 || 3.8007 || (2<span style="vertical-align: super;">3</span>*3*19)/(5*7*13) ||   ||
|| 476/475 || 3.6409 || (2<span style="vertical-align: super;">2</span>*7*17)/(5<span style="vertical-align: super;">2</span>*19) ||   ||
|| 495/494 || 3.501 || (3<span style="vertical-align: super;">2</span>*5*11)/(2*13*19) ||   ||
|| 513/512 || 3.378 || <span style="vertical-align: super;">(3^3*19)/2^9</span> || 513th harmonic ||
||||||||~ 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) ||   ||
|| 115/114 || 15.120 || (5*23)/(2*3*19) ||   ||
|| 161/160 || 10.7865 || (7*23)/(2^5*5) ||   ||
|| 162/161 || 10.720 || (2*3^4)/(7*23) ||   ||
|| 208/207 || 8.343 || (16*13)/(23*9) ||   ||
|| 576/575 || 3.008 || (64*9)/(23*25) ||   ||
||||||||~ 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 />
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="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 />
<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.<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><span style="line-height: 15.6000003814697px;">(</span>3<span style="line-height: 1.5;">/</span><span style="line-height: 15.6000003814697px;">2)</span><span style="line-height: 1.5; vertical-align: super;">4</span><span style="line-height: 15.6000003814697px;">/</span><span style="line-height: 1.5;">5</span><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="line-height: 1.5;">/7)</span><span style="line-height: 1.5; 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, 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="line-height: 1.5;">^2/(2^5*7)</span><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>7^4/(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="line-height: 15.6000003814697px;">/</span><span style="line-height: 1.5;">2)^</span><span style="line-height: 15.6000003814697px;">2*</span><span style="line-height: 1.5;">(</span><span style="line-height: 15.6000003814697px;">5/</span><span style="line-height: 1.5;">11)</span><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="line-height: 1.5;">/7)</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">*(11/2)</span><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<span style="line-height: 1.5;">*5/3)</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">/11)</span><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>11^2/(2^3*3*5)<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>(2^4*11)/(5^2*7)<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>3^5/(2*11^2)<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)/(2^7*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*7)^2/(2^3*5*11)<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)^2*3^3*5/11<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)^2/(2^4*3^3*7)<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><span style="line-height: 1.5;">[11/(5*7)]</span><span style="line-height: 15.6000003814697px;">^2*</span><span style="line-height: 1.5;">3^4/2^3</span><br />
</td>
        <td>Gauss comma, kalisma<br />
</td>
    </tr>
    <tr>
        <th colspan="4">13-limit<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>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>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>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="vertical-align: super;">2</span>*5)<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)/(2^3*13)<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>(<span style="line-height: 1.5;">2</span><span style="line-height: 1.5; vertical-align: super;">2</span><span style="line-height: 1.5;">*3)^2/(11*13)</span><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="vertical-align: super;">2</span>/(2<span style="vertical-align: super;">3</span>*3*7)<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)^2/(3*5*13)<br />
</td>
        <td>marveltwin comma<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)^2*13/(2*7)<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>(<span style="line-height: 1.5;">2</span><span style="line-height: 1.5; vertical-align: super;">5</span><span style="line-height: 1.5;">*11)/(</span><span style="line-height: 15.6000003814697px;">3^</span>2<span style="line-height: 15.6000003814697px;">*13)</span><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)^2*7*13/3<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>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>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>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>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>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>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>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>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>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>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>chalmersia<br />
</td>
    </tr>
    <tr>
        <th colspan="4">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="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*11)<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>
        <td>120/119<br />
</td>
        <td>14.487<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*3*5)/(7*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>136/135<br />
</td>
        <td>12.777<br />
</td>
        <td>(2/<span style="line-height: 1.5;">3)</span><span style="line-height: 1.5; vertical-align: super;">3</span><span style="line-height: 1.5;">*17/5</span><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>154/153<br />
</td>
        <td>11.278<br />
</td>
        <td>(2*7*11)/(3<span style="vertical-align: super;">2</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>170/169<br />
</td>
        <td>10.214<br />
</td>
        <td>(2*5*17)/13<span style="vertical-align: super;">2</span><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>221/220<br />
</td>
        <td>7.8514<br />
</td>
        <td>(13*17)/(2<span style="vertical-align: super;">2</span>*5*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>256/255<br />
</td>
        <td>6.7759<br />
</td>
        <td>(2^8)/(3*5*17)<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="vertical-align: super;">4</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>289/288<br />
</td>
        <td>6.0008<br />
</td>
        <td>(17<span style="line-height: 1.5;">/3)^</span><span style="line-height: 15.6000003814697px;">2</span><span style="line-height: 1.5;">/2</span><span style="line-height: 1.5; vertical-align: super;">5</span><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>375/374<br />
</td>
        <td>4.6228<br />
</td>
        <td>(3*5<span style="vertical-align: super;">3</span>)/(2*11*17)<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="vertical-align: super;">2</span><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>561/560<br />
</td>
        <td>3.0887<br />
</td>
        <td>(3*11*17)/(2<span style="vertical-align: super;">4</span>*5*7)<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="vertical-align: super;">3</span>*11)<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><br />
</td>
    </tr>
    <tr>
        <td>833/832<br />
</td>
        <td>2.0796<br />
</td>
        <td>(7<span style="vertical-align: super;">2</span>*17)/(2<span style="vertical-align: super;">6</span>*13)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>936/935<br />
</td>
        <td>1.8506<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>*13)/(5*11*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1089/1088<br />
</td>
        <td>1.5905<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*11<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">6</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1156/1155<br />
</td>
        <td>1.4983<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*17<span style="vertical-align: super;">2</span>)/(3*5*7*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1225/1224<br />
</td>
        <td>1.4138<br />
</td>
        <td>(5<span style="vertical-align: super;">2</span>*7<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">2</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1275/1274<br />
</td>
        <td>1.3584<br />
</td>
        <td>(3*5<span style="vertical-align: super;">2</span>*17)/(2*7<span style="vertical-align: super;">2</span>*13)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1701/1700<br />
</td>
        <td>1.0181<br />
</td>
        <td>(3<span style="vertical-align: super;">5</span>*7)/[(2*5)<span style="vertical-align: super;">2</span>*17]<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2058/2057<br />
</td>
        <td>0.8414<br />
</td>
        <td>(2*3*7<span style="vertical-align: super;">3</span>)/(11<span style="vertical-align: super;">2</span>*17)<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="vertical-align: super;">5</span>*5)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2500/2499<br />
</td>
        <td>0.6926<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">4</span>)/(3*7<span style="vertical-align: super;">2</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2601/2600<br />
</td>
        <td>0.6657<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*17<span style="vertical-align: super;">2</span>)/(2<span style="vertical-align: super;">3</span>*5<span style="vertical-align: super;">2</span>*13)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4914/4913<br />
</td>
        <td>0.3523<br />
</td>
        <td>(2*3<span style="vertical-align: super;">3</span>*7*13)/(17<span style="vertical-align: super;">3</span>)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5832/5831<br />
</td>
        <td>0.2969<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*3<span style="vertical-align: super;">6</span>)/(7<span style="vertical-align: super;">3</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>12376/12375<br />
</td>
        <td>0.1399<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*7*13*17)/(3<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">3</span>*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>14400/14399<br />
</td>
        <td>0.1202<br />
</td>
        <td>(2<span style="vertical-align: super;">6</span>*3<span style="vertical-align: super;">2</span>*5<span style="vertical-align: super;">2</span>)/(7*11<span style="vertical-align: super;">2</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>28561/28560<br />
</td>
        <td>0.0606<br />
</td>
        <td>(13<span style="vertical-align: super;">4</span>)/(2<span style="vertical-align: super;">4</span>*3*5*7*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>31213/31212<br />
</td>
        <td>0.0555<br />
</td>
        <td>(7<span style="vertical-align: super;">4</span>*13)/(2<span style="vertical-align: super;">2</span>*3<span style="vertical-align: super;">3</span>*17<span style="vertical-align: super;">2</span>)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37180/37179<br />
</td>
        <td>0.0466<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*5*11*13<span style="vertical-align: super;">2</span>)/(3<span style="vertical-align: super;">7</span>*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>194481/194480<br />
</td>
        <td>0.0089<br />
</td>
        <td>(3<span style="vertical-align: super;">4</span>*7<span style="vertical-align: super;">4</span>)/(2<span style="vertical-align: super;">4</span>*5*11*13*17)<br />
</td>
        <td>scintillisma<br />
</td>
    </tr>
    <tr>
        <td>336141/336140<br />
</td>
        <td>0.0052<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*13<span style="vertical-align: super;">3</span>*17)/(2<span style="vertical-align: super;">2</span>*5*7<span style="vertical-align: super;">5</span>)<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>
        <td>133/132<br />
</td>
        <td>13.066<br />
</td>
        <td>(19*7)/(2<span style="vertical-align: super;">2</span>*3*11)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>153/152<br />
</td>
        <td>11.352<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*17)/(2<span style="vertical-align: super;">3</span>*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>171/170<br />
</td>
        <td>10.154<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*19)/(2*5*17)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>190/189<br />
</td>
        <td>9.1358<br />
</td>
        <td>(2*5*19)/(3<span style="vertical-align: super;">3</span>*7)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>209/208<br />
</td>
        <td>8.3033<br />
</td>
        <td>(11*19)/(2<span style="vertical-align: super;">4</span>*13)<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><br />
</td>
    </tr>
    <tr>
        <td>286/285<br />
</td>
        <td>6.0639<br />
</td>
        <td>(2*11*13)/(3*5*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>400/399<br />
</td>
        <td>4.3335<br />
</td>
        <td>(2<span style="vertical-align: super;">4</span>*5<span style="vertical-align: super;">2</span>)/(3*7*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>456/455<br />
</td>
        <td>3.8007<br />
</td>
        <td>(2<span style="vertical-align: super;">3</span>*3*19)/(5*7*13)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>476/475<br />
</td>
        <td>3.6409<br />
</td>
        <td>(2<span style="vertical-align: super;">2</span>*7*17)/(5<span style="vertical-align: super;">2</span>*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>495/494<br />
</td>
        <td>3.501<br />
</td>
        <td>(3<span style="vertical-align: super;">2</span>*5*11)/(2*13*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>513/512<br />
</td>
        <td>3.378<br />
</td>
        <td><span style="vertical-align: super;">(3^3*19)/2^9</span><br />
</td>
        <td>513th harmonic<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>
        <td>115/114<br />
</td>
        <td>15.120<br />
</td>
        <td>(5*23)/(2*3*19)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>161/160<br />
</td>
        <td>10.7865<br />
</td>
        <td>(7*23)/(2^5*5)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>162/161<br />
</td>
        <td>10.720<br />
</td>
        <td>(2*3^4)/(7*23)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>208/207<br />
</td>
        <td>8.343<br />
</td>
        <td>(16*13)/(23*9)<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>576/575<br />
</td>
        <td>3.008<br />
</td>
        <td>(64*9)/(23*25)<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>

</body></html>

List of superparticular intervals: Difference between revisions

Wikispaces>JosephRuhf

Revision as of 16:19, 28 January 2015

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2014-06-14 14:45:38 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-01-28 16:19:01 UTC</tt>.<br>
-: The original revision id was <tt>513947714</tt>.<br>
+: The original revision id was <tt>538882498</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>
@@ Line 29: / Line 29: @@
 || [[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 ||
 || [[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 ||
-|| [[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 ||
+|| [[81_80|81/80]] || 21.506 || &lt;span style="line-height: 15.6000003814697px;"&gt;(&lt;/span&gt;3&lt;span style="line-height: 1.5;"&gt;/&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;4&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;5&lt;/span&gt; || syntonic comma, Didymus comma ||
 ||||||||~ 7-limit ||
 || [[7_6|7/6]] || 266.871 || 7/(2*3) || (septimal) subminor third, septimal minor third, augmented second ||
@@ Line 38: / Line 38: @@
 || [[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 ||
 || [[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 ||
-|| [[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 ||
+|| [[50_49|50/49]] || 34.976 || 2*(5&lt;span style="line-height: 1.5;"&gt;/7)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt; || septimal sixth-tone, jubilisma, small septimal diesis, tritonic diesis, Erlich's decatonic comma ||
 || [[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 ||
 || [[126_125|126/125]] || 13.795 || (2*3^2*7)/5^3 || starling comma, septimal semicomma ||
-|| [[225_224|225/224]] || 7.7115 || (3^2*5^2)/(2^5*7) || marvel comma, septimal kleisma ||
+|| [[225_224|225/224]] || 7.7115 || (3*5)&lt;span style="line-height: 1.5;"&gt;^2/(2^5*7)&lt;/span&gt; || marvel comma, septimal kleisma ||
 || [[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 ||
@@ Line 49: / Line 49: @@
 || [[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; || unidecimal quarter tone, unidecimal diesis, al-Farabi's 1/4-tone, 33rd harmonic (octave reduced) ||
-|| [[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 ||
+|| [[45_44|45/44]] || 38.906 || (3&lt;span style="line-height: 15.6000003814697px;"&gt;/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;2)^&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2*&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;(&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;5/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;11)&lt;/span&gt; || 1/5-tone ||
 || [[55_54|55/54]] || 31.767 || (5*11)/(2*3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;) ||   ||
 || [[56_55|56/55]] || 31.194 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*7)/(5*11) ||   ||
-|| [[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;) || small undecimal comma, mothwellsma ||
+|| [[99_98|99/98]] || 17.576 || (3&lt;span style="line-height: 1.5;"&gt;/7)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*(11/2)&lt;/span&gt; || small undecimal comma, mothwellsma ||
-|| [[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, ptolemisma ||
+|| [[100_99|100/99]] || 17.399 || (2&lt;span style="line-height: 1.5;"&gt;*5/3)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;/11)&lt;/span&gt; || Ptolemy's comma, ptolemisma ||
 || [[121_120|121/120]] || 14.376 || 11^2/(2^3*3*5) || undecimal seconds comma, biyatisma ||
 || [[176_175|176/175]] || 9.8646 || (2^4*11)/(5^2*7) || valinorsma ||
 || [[243_242|243/242]] || 7.1391 || 3^5/(2*11^2) || neutral third comma, rastma ||
 || [[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) || Werckmeister's undecimal septenarian schisma, werckisma ||
+|| [[441_440|441/440]] || 3.9302 || (3*7)^2/(2^3*5*11) || Werckmeister's undecimal septenarian schisma, werckisma ||
-|| [[540_539|540/539]] || 3.2090 || (2^2*3^3*5)/(7^2*11) || Swets' comma, swetisma ||
+|| [[540_539|540/539]] || 3.2090 || (2/7)^2*3^3*5/11 || Swets' comma, swetisma ||
-|| [[3025_3024|3025/3024]] || 0.57240 || (5^2*11^2)/(2^4*3^3*7) || Lehmerisma ||
+|| [[3025_3024|3025/3024]] || 0.57240 || (5*11)^2/(2^4*3^3*7) || Lehmerisma ||
-|| [[9801_9800|9801/9800]] || 0.17665 || (3^4*11^2)/(2^3*5^2*7^2) || Gauss comma, kalisma ||
+|| [[9801_9800|9801/9800]] || 0.17665 || &lt;span style="line-height: 1.5;"&gt;[11/(5*7)]&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;^2*&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;3^4/2^3&lt;/span&gt; || Gauss comma, kalisma ||
 ||||||||~ 13-limit ||
 || [[13_12|13/12]] || 138.573 || 13/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3) || tridecimal 2/3-tone ||
@@ Line 72: / Line 72: @@
 || [[78_77|78/77]] || 22.339 || (2*3*13)/(7*11) || negustma ||
 || [[91_90|91/90]] || 19.130 || (7*13)/(2*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5) || [[The Biosphere|Biome]] comma, superleap comma ||
-|| [[105_104|105/104]] || 16.567 ||   || small tridecimal comma, animist comma ||
+|| [[105_104|105/104]] || 16.567 || (3*5*7)/(2^3*13) || small tridecimal comma, animist comma ||
-|| [[144_143|144/143]] || 12.064 ||   || grossma ||
+|| [[144_143|144/143]] || 12.064 || (&lt;span style="line-height: 1.5;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*3)^2/(11*13)&lt;/span&gt; || grossma ||
-|| [[169_168|169/168]] || 10.274 ||   || buzurgisma, dhanvantarisma ||
+|| [[169_168|169/168]] || 10.274 || 13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*7) || buzurgisma, dhanvantarisma ||
-|| [[196_195|196/195]] || 8.8554 ||   || mynucuma ||
+|| [[196_195|196/195]] || 8.8554 || (2*7)^2/(3*5*13) || marveltwin comma ||
-|| [[325_324|325/324]] || 5.3351 ||   || marveltwin comma ||
+|| [[351_350|351/350]] || 4.9393 || (3/5)^2*13/(2*7) || ratwolfsma ||
-|| [[351_350|351/350]] || 4.9393 ||   || ratwolfsma ||
+|| [[352_351|352/351]] || 4.9253 || (&lt;span style="line-height: 1.5;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;5&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*11)/(&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;3^&lt;/span&gt;2&lt;span style="line-height: 15.6000003814697px;"&gt;*13)&lt;/span&gt; || minthma ||
-|| [[352_351|352/351]] || 4.9253 ||   || minthma ||
+|| [[364_363|364/363]] || 4.7627 || (2/11)^2*7*13/3 || gentle comma ||
-|| [[364_363|364/363]] || 4.7627 ||   || gentle comma ||
 || [[625_624|625/624]] || 2.7722 ||   || tunbarsma ||
 || [[676_675|676/675]] || 2.5629 ||   || island comma ||
@@ Line 100: / Line 99: @@
 || [[85_84|85/84]] || 20.488 || (5*17)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*3*7) ||   ||
 || 120/119 || 14.487 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*5)/(7*17) ||   ||
-|| 136/135 || 12.777 || (2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*17)/(3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5) ||   ||
+|| 136/135 || 12.777 || (2/&lt;span style="line-height: 1.5;"&gt;3)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;3&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*17/5&lt;/span&gt; ||   ||
 || 154/153 || 11.278 || (2*7*11)/(3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||   ||
 || 170/169 || 10.214 || (2*5*17)/13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; ||   ||
@@ Line 106: / Line 105: @@
 || 256/255 || 6.7759 || (2^8)/(3*5*17) || 255th subharmonic ||
 || 273/272 || 6.3532 || (3*7*13)/(2&lt;span style="vertical-align: super;"&gt;4&lt;/span&gt;*17) ||   ||
-|| 289/288 || 6.0008 || 17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;) ||   ||
+|| 289/288 || 6.0008 || (17&lt;span style="line-height: 1.5;"&gt;/3)^&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;/2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;5&lt;/span&gt; ||   ||
 || 375/374 || 4.6228 || (3*5&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(2*11*17) ||   ||
 || 442/441 || 3.9213 || (2*13*17)/(3*7)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt; ||   ||
@@ Line 118: / Line 117: @@
 || 1225/1224 || 1.4138 || (5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7&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;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||   ||
 || 1275/1274 || 1.3584 || (3*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)/(2*7&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*13) ||   ||
-|| 1701/1700 || 1.0181 || (3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) ||   ||
+|| 1701/1700 || 1.0181 || (3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*7)/[(2*5)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17] ||   ||
 || 2058/2057 || 0.8414 || (2*3*7&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;)/(11&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17) || xenisma ||
 || 2431/2430 || 0.7123 || (11*13*17)/(2*3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*5) ||   ||
@@ Line 159: / Line 158: @@
 || [[70_69|70/69]] || 24.910 || (2*5*7)/(3*23) ||   ||
 || [[92_91|92/91]] || 18.921 || (2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*23)/(7*13) ||   ||
-|| 208/207 ||   || 16*13/23*9 ||   ||
+|| 115/114 || 15.120 || (5*23)/(2*3*19) ||   ||
-|| 576/575 ||   || 64*9/23*25 ||   ||
+|| 161/160 || 10.7865 || (7*23)/(2^5*5) ||   ||
+|| 162/161 || 10.720 || (2*3^4)/(7*23) ||   ||
+|| 208/207 || 8.343 || (16*13)/(23*9) ||   ||
+|| 576/575 || 3.008 || (64*9)/(23*25) ||   ||
 ||||||||~ 29-limit (incomplete) ||
 || [[29_28|29/28]] || 60.751 || 29/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*7) ||   ||
@@ Line 352: / Line 354: @@
          &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;span style="line-height: 15.6000003814697px;"&gt;(&lt;/span&gt;3&lt;span style="line-height: 1.5;"&gt;/&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;4&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;5&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;syntonic comma, Didymus comma&lt;br /&gt;
@@ Line 436: / Line 438: @@
          &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;2*(5&lt;span style="line-height: 1.5;"&gt;/7)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&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;
@@ Line 466: / Line 468: @@
          &lt;td&gt;7.7115&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(3^2*5^2)/(2^5*7)&lt;br /&gt;
+         &lt;td&gt;(3*5)&lt;span style="line-height: 1.5;"&gt;^2/(2^5*7)&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;marvel comma, septimal kleisma&lt;br /&gt;
@@ Line 540: / Line 542: @@
          &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;(3&lt;span style="line-height: 15.6000003814697px;"&gt;/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;2)^&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2*&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;(&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;5/&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;11)&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1/5-tone&lt;br /&gt;
@@ Line 570: / Line 572: @@
          &lt;td&gt;17.576&lt;br /&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;(3&lt;span style="line-height: 1.5;"&gt;/7)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*(11/2)&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;small undecimal comma, mothwellsma&lt;br /&gt;
@@ Line 580: / Line 582: @@
          &lt;td&gt;17.399&lt;br /&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&lt;span style="line-height: 1.5;"&gt;*5/3)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;/11)&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Ptolemy's comma, ptolemisma&lt;br /&gt;
@@ Line 630: / Line 632: @@
          &lt;td&gt;3.9302&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(3^2*7^2)/(2^3*5*11)&lt;br /&gt;
+         &lt;td&gt;(3*7)^2/(2^3*5*11)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Werckmeister's undecimal septenarian schisma, werckisma&lt;br /&gt;
@@ Line 640: / Line 642: @@
          &lt;td&gt;3.2090&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(2^2*3^3*5)/(7^2*11)&lt;br /&gt;
+         &lt;td&gt;(2/7)^2*3^3*5/11&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Swets' comma, swetisma&lt;br /&gt;
@@ Line 650: / Line 652: @@
          &lt;td&gt;0.57240&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(5^2*11^2)/(2^4*3^3*7)&lt;br /&gt;
+         &lt;td&gt;(5*11)^2/(2^4*3^3*7)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Lehmerisma&lt;br /&gt;
@@ Line 660: / Line 662: @@
          &lt;td&gt;0.17665&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(3^4*11^2)/(2^3*5^2*7^2)&lt;br /&gt;
+         &lt;td&gt;&lt;span style="line-height: 1.5;"&gt;[11/(5*7)]&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;^2*&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;3^4/2^3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Gauss comma, kalisma&lt;br /&gt;
@@ Line 764: / Line 766: @@
          &lt;td&gt;16.567&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;(3*5*7)/(2^3*13)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;small tridecimal comma, animist comma&lt;br /&gt;
@@ Line 774: / Line 776: @@
          &lt;td&gt;12.064&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;(&lt;span style="line-height: 1.5;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*3)^2/(11*13)&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;grossma&lt;br /&gt;
@@ Line 784: / Line 786: @@
          &lt;td&gt;10.274&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;13&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*3*7)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;buzurgisma, dhanvantarisma&lt;br /&gt;
@@ Line 794: / Line 796: @@
          &lt;td&gt;8.8554&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;(2*7)^2/(3*5*13)&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;mynucuma&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td&gt;&lt;a class="wiki_link" href="/325_324"&gt;325/324&lt;/a&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;5.3351&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;marveltwin comma&lt;br /&gt;
@@ Line 814: / Line 806: @@
          &lt;td&gt;4.9393&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;(3/5)^2*13/(2*7)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;ratwolfsma&lt;br /&gt;
@@ Line 824: / Line 816: @@
          &lt;td&gt;4.9253&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;(&lt;span style="line-height: 1.5;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;5&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*11)/(&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;3^&lt;/span&gt;2&lt;span style="line-height: 15.6000003814697px;"&gt;*13)&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;minthma&lt;br /&gt;
@@ Line 834: / Line 826: @@
          &lt;td&gt;4.7627&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;(2/11)^2*7*13/3&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;gentle comma&lt;br /&gt;
@@ Line 1,038: / Line 1,030: @@
          &lt;td&gt;12.777&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(2&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*17)/(3&lt;span style="vertical-align: super;"&gt;3&lt;/span&gt;*5)&lt;br /&gt;
+         &lt;td&gt;(2/&lt;span style="line-height: 1.5;"&gt;3)&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;3&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;*17/5&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,098: / Line 1,090: @@
          &lt;td&gt;6.0008&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;17&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;/(2&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*3&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;)&lt;br /&gt;
+         &lt;td&gt;(17&lt;span style="line-height: 1.5;"&gt;/3)^&lt;/span&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;2&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;/2&lt;/span&gt;&lt;span style="line-height: 1.5; vertical-align: super;"&gt;5&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,218: / Line 1,210: @@
          &lt;td&gt;1.0181&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*7)/(2&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*5&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17)&lt;br /&gt;
+         &lt;td&gt;(3&lt;span style="vertical-align: super;"&gt;5&lt;/span&gt;*7)/[(2*5)&lt;span style="vertical-align: super;"&gt;2&lt;/span&gt;*17]&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,607: / Line 1,599: @@
 &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;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;115/114&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15.120&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;(5*23)/(2*3*19)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;161/160&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10.7865&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;(7*23)/(2^5*5)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;162/161&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10.720&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;(2*3^4)/(7*23)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,614: / Line 1,636: @@
          &lt;td&gt;208/207&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;8.343&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;16*13/23*9&lt;br /&gt;
+         &lt;td&gt;(16*13)/(23*9)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,624: / Line 1,646: @@
          &lt;td&gt;576/575&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;3.008&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;64*9/23*25&lt;br /&gt;
+         &lt;td&gt;(64*9)/(23*25)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;

List of superparticular intervals: Difference between revisions

Wikispaces>JosephRuhf

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