31-limit

In 31-limit Just Intonation, all ratios in the system will contain no primes higher than 31.

Intervals

2^{32/^{⋅3^{-26/^{⋅31^{2/^{4127463571456/2541865828329 dd7^31,31 839.241122428}}}}}}	2^{30/^{⋅3^{-25/^{⋅31^{2/^{1031865892864/847288609443 dd4^31,31 341.196123294}}}}}}	2^{29/^{⋅3^{-24/^{⋅31^{2/^{515932946432/282429536481 dd8^31,31 1043.151124159}}}}}}	2^{27/^{⋅3^{-23/^{⋅31^{2/^{128983236608/94143178827 dd5^31,31 545.106125025}}}}}}	2^{25/^{⋅3^{-22/^{⋅31^{2/^{32245809152/31381059609 d2^31,31 47.061125890}}}}}}	2^{24/^{⋅3^{-21/^{⋅31^{2/^{16122904576/10460353203 d6^31,31 749.016126755}}}}}}	2^{22/^{⋅3^{-20/^{⋅31^{2/^{4030726144/3486784401 d3^31,31 250.971127621}}}}}}	2^{21/^{⋅3^{-19/^{⋅31^{2/^{2015363072/1162261467 d7^31,31 952.926128486}}}}}}	2^{19/^{⋅3^{-18/^{⋅31^{2/^{503840768/387420489 d4^31,31 454.881129352}}}}}}	2^{18/^{⋅3^{-17/^{⋅31^{2/^{251920384/129140163 d8^31,31 1156.836130217}}}}}}	2^{16/^{⋅3^{-16/^{⋅31^{2/^{62980096/43046721 d5^31,31 658.791131082}}}}}}	2^{14/^{⋅3^{-15/^{⋅31^{2/^{15745024/14348907 m2^31,31 160.746131948}}}}}}	2^{13/^{⋅3^{-14/^{⋅31^{2/^{7872512/4782969 m6^31,31 862.701132813}}}}}}	2^{11/^{⋅3^{-13/^{⋅31^{2/^{1968128/1594323 m3^31,31 364.656133678}}}}}}	2^{10/^{⋅3^{-12/^{⋅31^{2/^{984064/531441 m7^31,31 1066.611134544}}}}}}	2^{8/^{⋅3^{-11/^{⋅31^{2/^{246016/177147 P4^31,31 568.566135409}}}}}}	2^{6/^{⋅3^{-10/^{⋅31^{2/^{61504/59049 P1^31,31 70.521136275}}}}}}	2^{5/^{⋅3^{-9/^{⋅31^{2/^{30752/19683 P5^31,31 772.476137140}}}}}}	2^{3/^{⋅3^{-8/^{⋅31^{2/^{7688/6561 M2^31,31 274.431138005}}}}}}	2^{2/^{⋅3^{-7/^{⋅31^{2/^{3844/2187 M6^31,31 976.386138871}}}}}}	3^{-6/^{⋅31^{2/^{961/729 M3^31,31 478.341139736}}}}	2^{-1/^{⋅3^{-5/^{⋅31^{2/^{961/486 M7^31,31 1180.296140602}}}}}}	2^{-3/^{⋅3^{-4/^{⋅31^{2/^{961/648 A4^31,31 682.251141467}}}}}}	2^{-5/^{⋅3^{-3/^{⋅31^{2/^{961/864 A1^31,31 184.206142332}}}}}}	2^{-6/^{⋅3^{-2/^{⋅31^{2/^{961/576 A5^31,31 886.161143198}}}}}}	2^{-8/^{⋅3^{-1/^{⋅31^{2/^{961/768 A2^31,31 388.116144063}}}}}}	2^{-9/^{⋅31^{2/^{961/512 A6^31,31 1090.071144929}}}}	2^{-11/^{⋅3^{1/^{⋅31^{2/^{2883/2048 A3^31,31 592.026145794}}}}}}	2^{-13/^{⋅3^{2/^{⋅31^{2/^{8649/8192 -cA7^31,31 93.981146659}}}}}}	2^{-14/^{⋅3^{3/^{⋅31^{2/^{25947/16384 AA4^31,31 795.936147525}}}}}}	2^{-16/^{⋅3^{4/^{⋅31^{2/^{77841/65536 AA1^31,31 297.891148390}}}}}}	2^{-17/^{⋅3^{5/^{⋅31^{2/^{233523/131072 AA5^31,31 999.846149255}}}}}}	2^{-19/^{⋅3^{6/^{⋅31^{2/^{700569/524288 AA2^31,31 501.801150121}}}}}}	2^{-21/^{⋅3^{7/^{⋅31^{2/^{2101707/2097152 -cAA6^31,31 3.756150986}}}}}}	2^{-22/^{⋅3^{8/^{⋅31^{2/^{6305121/4194304 AA3^31,31 705.711151852}}}}}}	2^{-24/^{⋅3^{9/^{⋅31^{2/^{18915363/16777216 -cAA7^31,31 207.666152717}}}}}}	2^{-25/^{⋅3^{10/^{⋅31^{2/^{56746089/33554432 AAA4^31,31 909.621153582}}}}}}	2^{-27/^{⋅3^{11/^{⋅31^{2/^{170238267/134217728 AAA1^31,31 411.576154448}}}}}}	2^{-28/^{⋅3^{12/^{⋅31^{2/^{510714801/268435456 AAA5^31,31 1113.531155313}}}}}}	2^{-30/^{⋅3^{13/^{⋅31^{2/^{1532144403/1073741824 AAA2^31,31 615.486156179}}}}}}	2^{-32/^{⋅3^{14/^{⋅31^{2/^{4596433209/4294967296 -cAAA6^31,31 117.441157044}}}}}}	2^{-33/^{⋅3^{15/^{⋅31^{2/^{13789299627/8589934592 AAA3^31,31 819.396157909}}}}}}	2^{-35/^{⋅3^{16/^{⋅31^{2/^{41367898881/34359738368 -cAAA7^31,31 321.351158775}}}}}}	2^{-36/^{⋅3^{17/^{⋅31^{2/^{124103696643/68719476736 AAAA4^31,31 1023.306159640}}}}}}	2^{-38/^{⋅3^{18/^{⋅31^{2/^{372311089929/274877906944 AAAA1^31,31 525.261160505}}}}}}	2^{-40/^{⋅3^{19/^{⋅31^{2/^{1116933269787/1099511627776 -cAAAA5^31,31 27.216161371}}}}}}	2^{-41/^{⋅3^{20/^{⋅31^{2/^{3350799809361/2199023255552 AAAA2^31,31 729.171162236}}}}}}	2^{-43/^{⋅3^{21/^{⋅31^{2/^{10052399428083/8796093022208 -cAAAA6^31,31 231.126163102}}}}}}	2^{-44/^{⋅3^{22/^{⋅31^{2/^{30157198284249/17592186044416 AAAA3^31,31 933.081163967}}}}}}	2^{-46/^{⋅3^{23/^{⋅31^{2/^{90471594852747/70368744177664 -cAAAA7^31,31 435.036164832}}}}}}	2^{-47/^{⋅3^{24/^{⋅31^{2/^{271414784558241/140737488355328 AAAAA4^31,31 1136.991165698}}}}}}	2^{-49/^{⋅3^{25/^{⋅31^{2/^{814244353674723/562949953421312 AAAAA1^31,31 638.946166563}}}}}}	2^{-51/^{⋅3^{26/^{⋅31^{2/^{2442733061024169/2251799813685248 -cAAAAA5^31,31 140.901167429}}}}}}
2^{42/^{⋅3^{-26/^{⋅29^{-1/^{⋅31^{1/^{136339441844224/73714109021541 cdd2³¹₂₉ 1064.628355811}}}}}}}}	2^{40/^{⋅3^{-25/^{⋅29^{-1/^{⋅31^{1/^{34084860461056/24571369673847 dd6³¹₂₉ 566.583356676}}}}}}}}	2^{38/^{⋅3^{-24/^{⋅29^{-1/^{⋅31^{1/^{8521215115264/8190456557949 dd3³¹₂₉ 68.538357542}}}}}}}}	2^{37/^{⋅3^{-23/^{⋅29^{-1/^{⋅31^{1/^{4260607557632/2730152185983 dd7³¹₂₉ 770.493358407}}}}}}}}	2^{35/^{⋅3^{-22/^{⋅29^{-1/^{⋅31^{1/^{1065151889408/910050728661 dd4³¹₂₉ 272.448359273}}}}}}}}	2^{34/^{⋅3^{-21/^{⋅29^{-1/^{⋅31^{1/^{532575944704/303350242887 dd8³¹₂₉ 974.403360138}}}}}}}}	2^{32/^{⋅3^{-20/^{⋅29^{-1/^{⋅31^{1/^{133143986176/101116747629 dd5³¹₂₉ 476.358361003}}}}}}}}	2^{31/^{⋅3^{-19/^{⋅29^{-1/^{⋅31^{1/^{66571993088/33705582543 cd2³¹₂₉ 1178.313361869}}}}}}}}	2^{29/^{⋅3^{-18/^{⋅29^{-1/^{⋅31^{1/^{16642998272/11235194181 d6³¹₂₉ 680.268362734}}}}}}}}	2^{27/^{⋅3^{-17/^{⋅29^{-1/^{⋅31^{1/^{4160749568/3745064727 d3³¹₂₉ 182.223363600}}}}}}}}	2^{26/^{⋅3^{-16/^{⋅29^{-1/^{⋅31^{1/^{2080374784/1248354909 d7³¹₂₉ 884.178364465}}}}}}}}	2^{24/^{⋅3^{-15/^{⋅29^{-1/^{⋅31^{1/^{520093696/416118303 d4³¹₂₉ 386.133365330}}}}}}}}	2^{23/^{⋅3^{-14/^{⋅29^{-1/^{⋅31^{1/^{260046848/138706101 d8³¹₂₉ 1088.088366196}}}}}}}}	2^{21/^{⋅3^{-13/^{⋅29^{-1/^{⋅31^{1/^{65011712/46235367 d5³¹₂₉ 590.043367061}}}}}}}}	2^{19/^{⋅3^{-12/^{⋅29^{-1/^{⋅31^{1/^{16252928/15411789 m2³¹₂₉ 91.998367927}}}}}}}}	2^{18/^{⋅3^{-11/^{⋅29^{-1/^{⋅31^{1/^{8126464/5137263 m6³¹₂₉ 793.953368792}}}}}}}}	2^{16/^{⋅3^{-10/^{⋅29^{-1/^{⋅31^{1/^{2031616/1712421 m3³¹₂₉ 295.908369657}}}}}}}}	2^{15/^{⋅3^{-9/^{⋅29^{-1/^{⋅31^{1/^{1015808/570807 m7³¹₂₉ 997.863370523}}}}}}}}	2^{13/^{⋅3^{-8/^{⋅29^{-1/^{⋅31^{1/^{253952/190269 P4³¹₂₉ 499.818371388}}}}}}}}	2^{11/^{⋅3^{-7/^{⋅29^{-1/^{⋅31^{1/^{63488/63423 P1³¹₂₉ 1.773372253}}}}}}}}	2^{10/^{⋅3^{-6/^{⋅29^{-1/^{⋅31^{1/^{31744/21141 P5³¹₂₉ 703.728373119}}}}}}}}	2^{8/^{⋅3^{-5/^{⋅29^{-1/^{⋅31^{1/^{7936/7047 M2³¹₂₉ 205.683373984}}}}}}}}	2^{7/^{⋅3^{-4/^{⋅29^{-1/^{⋅31^{1/^{3968/2349 M6³¹₂₉ 907.638374850}}}}}}}}	2^{5/^{⋅3^{-3/^{⋅29^{-1/^{⋅31^{1/^{992/783 M3³¹₂₉ 409.593375715}}}}}}}}	2^{4/^{⋅3^{-2/^{⋅29^{-1/^{⋅31^{1/^{496/261 M7³¹₂₉ 1111.548376580}}}}}}}}	2^{2/^{⋅3^{-1/^{⋅29^{-1/^{⋅31^{1/^{124/87 A4³¹₂₉ 613.503377446}}}}}}}}	29^{-1/^{⋅31^{1/^{31/29 A1³¹₂₉ 115.458378311}}}}	2^{-1/^{⋅3^{1/^{⋅29^{-1/^{⋅31^{1/^{93/58 A5³¹₂₉ 817.413379177}}}}}}}}	2^{-3/^{⋅3^{2/^{⋅29^{-1/^{⋅31^{1/^{279/232 A2³¹₂₉ 319.368380042}}}}}}}}	2^{-4/^{⋅3^{3/^{⋅29^{-1/^{⋅31^{1/^{837/464 A6³¹₂₉ 1021.323380907}}}}}}}}	2^{-6/^{⋅3^{4/^{⋅29^{-1/^{⋅31^{1/^{2511/1856 A3³¹₂₉ 523.278381773}}}}}}}}	2^{-8/^{⋅3^{5/^{⋅29^{-1/^{⋅31^{1/^{7533/7424 -cA7³¹₂₉ 25.233382638}}}}}}}}	2^{-9/^{⋅3^{6/^{⋅29^{-1/^{⋅31^{1/^{22599/14848 AA4³¹₂₉ 727.188383503}}}}}}}}	2^{-11/^{⋅3^{7/^{⋅29^{-1/^{⋅31^{1/^{67797/59392 AA1³¹₂₉ 229.143384369}}}}}}}}	2^{-12/^{⋅3^{8/^{⋅29^{-1/^{⋅31^{1/^{203391/118784 AA5³¹₂₉ 931.098385234}}}}}}}}	2^{-14/^{⋅3^{9/^{⋅29^{-1/^{⋅31^{1/^{610173/475136 AA2³¹₂₉ 433.053386100}}}}}}}}	2^{-15/^{⋅3^{10/^{⋅29^{-1/^{⋅31^{1/^{1830519/950272 AA6³¹₂₉ 1135.008386965}}}}}}}}	2^{-17/^{⋅3^{11/^{⋅29^{-1/^{⋅31^{1/^{5491557/3801088 AA3³¹₂₉ 636.963387830}}}}}}}}	2^{-19/^{⋅3^{12/^{⋅29^{-1/^{⋅31^{1/^{16474671/15204352 -cAA7³¹₂₉ 138.918388696}}}}}}}}	2^{-20/^{⋅3^{13/^{⋅29^{-1/^{⋅31^{1/^{49424013/30408704 AAA4³¹₂₉ 840.873389561}}}}}}}}	2^{-22/^{⋅3^{14/^{⋅29^{-1/^{⋅31^{1/^{148272039/121634816 AAA1³¹₂₉ 342.828390427}}}}}}}}	2^{-23/^{⋅3^{15/^{⋅29^{-1/^{⋅31^{1/^{444816117/243269632 AAA5³¹₂₉ 1044.783391292}}}}}}}}	2^{-25/^{⋅3^{16/^{⋅29^{-1/^{⋅31^{1/^{1334448351/973078528 AAA2³¹₂₉ 546.738392157}}}}}}}}	2^{-27/^{⋅3^{17/^{⋅29^{-1/^{⋅31^{1/^{4003345053/3892314112 -cAAA6³¹₂₉ 48.693393023}}}}}}}}	2^{-28/^{⋅3^{18/^{⋅29^{-1/^{⋅31^{1/^{12010035159/7784628224 AAA3³¹₂₉ 750.648393888}}}}}}}}	2^{-30/^{⋅3^{19/^{⋅29^{-1/^{⋅31^{1/^{36030105477/31138512896 -cAAA7³¹₂₉ 252.603394754}}}}}}}}	2^{-31/^{⋅3^{20/^{⋅29^{-1/^{⋅31^{1/^{108090316431/62277025792 AAAA4³¹₂₉ 954.558395619}}}}}}}}	2^{-33/^{⋅3^{21/^{⋅29^{-1/^{⋅31^{1/^{324270949293/249108103168 AAAA1³¹₂₉ 456.513396484}}}}}}}}	2^{-34/^{⋅3^{22/^{⋅29^{-1/^{⋅31^{1/^{972812847879/498216206336 AAAA5³¹₂₉ 1158.468397350}}}}}}}}	2^{-36/^{⋅3^{23/^{⋅29^{-1/^{⋅31^{1/^{2918438543637/1992864825344 AAAA2³¹₂₉ 660.423398215}}}}}}}}	2^{-38/^{⋅3^{24/^{⋅29^{-1/^{⋅31^{1/^{8755315630911/7971459301376 -cAAAA6³¹₂₉ 162.378399080}}}}}}}}	2^{-39/^{⋅3^{25/^{⋅29^{-1/^{⋅31^{1/^{26265946892733/15942918602752 AAAA3³¹₂₉ 864.333399946}}}}}}}}	2^{-41/^{⋅3^{26/^{⋅29^{-1/^{⋅31^{1/^{78797840678199/63771674411008 -cAAAA7³¹₂₉ 366.288400811}}}}}}}}
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31-limit

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31-limit

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