List of superparticular intervals/29-limit

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29-limit

Ratio Cents Factorization Monzo Name(s) Meta[1]
29/28 60.751 29/(22×7) 2.7.29 [-2 -1 1⟩ Vicesimononal thirdtone, vicesimononal subchroma, large vicesimononal quartertone, large vicesimononal 2/7-tone
30/29 58.692 (2×3×5)/29 2.3.5.29 [1 1 1 -1⟩ Small vicesimononal quartertone, small vicesimononal 2/7-tone
58/57 30.109 (2×29)/(3×19) 2.3.19.29 [1 -1 -1 1⟩ Vicesimononal 1/7-tone
88/87 19.786 (23×11)/(3×29) 2.3.11.29 [3 -1 1 -1⟩ Vicesimononal 1/10-tone, farewell comma
116/115 14.989 (22×29)/(5×23) 2.5.23.29 [2 -1 -1 1⟩ Sironisma
117/116 14.860 (32×13)/(22×29) 2.3.13.29 [-2 2 1 -1⟩ Lomisma
145/144 11.981 (5×29)/(22×3)2 2.3.5.29 [-4 -2 1 1⟩ Adeonisma, 29th-partial chroma
175/174 9.9211 (52×7)/(2×3×29) 2.3.5.7.29 [-1 -1 2 1 -1⟩ Major chthonovinema
204/203 8.5073 (22×3×17)/(7×29) 2.3.7.17.29 [2 1 -1 1 -1⟩ Kallistisma
232/231 7.4783 (23×29)/(3×7×11) 2.3.7.11.29 [3 -1 -1 -1 1⟩ Major paravinema
261/260 6.6458 (32×29)/(22×5×13) 2.3.5.13.29 [-2 2 -1 -1 1⟩ Major vinetonema
290/289 5.9801 (2×5×29)/172 2.5.17.29 [1 1 -2 1⟩ Brunisma
320/319 5.4186 (26×5)/(11×29) 2.5.11.29 [6 1 -1 -1⟩ Minor paravinema
378/377 4.5861 (2×33×7)/(13×29) 2.3.7.13.29 [1 3 1 -1 -1⟩ Major semivinema
406/405 4.2694 (2×7×29)/(34×5) 2.3.5.7.29 [1 -4 -1 1 1⟩ Minor semivinema
494/493 3.5081 (2×13×19)/(17×29) 2.13.17.19.29 [1 1 -1 1 -1⟩ Minor vinetonema
551/550 3.1448 (19×29)/(2×52×11) 2.5.11.19.29 [-1 -2 -1 1 1⟩ Minor chthonovinema
552/551 3.1391 (23×3×23)/(19×29) 2.3.19.23.29 [3 1 -1 1 -1⟩ Sigelindisma
609/608 2.8451 (3×7×29)/(25×19) 2.3.7.19.29 [-5 1 1 -1 1⟩ Vineyard comma
638/637 2.7157 (2×11×29)/(72×13) 2.7.11.13.29 [1 -2 1 -1 1⟩ Moirisma
726/725 2.3863 (2×3×112)/(52×29) 2.3.5.11.29 [1 1 -2 2 -1⟩ Joellisma
783/782 2.2124 (33×29)/(2×17×23) 2.3.17.23.29 [-1 3 -1 -1 1⟩ Norisma
784/783 2.2096 (22×7)2/(33×29) 2.3.7.29 [4 -3 2 -1⟩ Biminorisma, spoogalactic comma S28
841/840 2.0598 292/(23×3×5×7) 2.3.5.7.29 [-3 -1 -1 -1 2⟩ Arabellisma S29
1015/1014 1.7065 (5×7×29)/(2×3×132) 2.3.5.7.13.29 [-1 -1 1 1 -2 1⟩ Christisma
1045/1044 1.6575 (5×11×19)/((2×3)2×29) 2.3.5.11.19.29 [-2 -2 1 1 1 -1⟩ Michelisma
1276/1275 1.3573 (22×11×29)/(3×52×17) 2.3.5.11.17.29 [2 -1 -2 1 -1 1⟩ Ucclisma
1450/1449 1.1944 (2×52×29)/(32×7×23) 2.3.5.7.23.29 [1 -2 2 -1 -1 1⟩ Raimondisma
1596/1595 1.0851 (22×3×7×19)/(5×11×29) 2.3.5.7.11.19.29 [2 1 -1 1 -1 1 -1⟩ Itzigsohnisma
1625/1624 1.0657 (53×13)/(23×7×29) 2.5.7.13.29 [-3 3 -1 1 -1⟩ Norcma
1683/1682 1.0290 (32×11×17)/(2×292) 2.3.11.17.29 [-1 2 1 1 -2⟩ Castafiorisma
2001/2000 0.86540 (3×23×29)/(24×53) 2.3.5.23.29 [-4 1 -3 1 1⟩ Major discoverisma
2002/2001 0.86497 (2×7×11×13)/(3×23×29) 2.3.7.11.13.23.29 [1 -1 1 1 1 -1 -1⟩ Minor discoverisma
2176/2175 0.79579 (27×17)/(3×52×29) 2.3.5.17.29 [7 -1 -2 1 -1⟩ Donarisma
2205/2204 0.78532 ((3×7)/2)2×(5/(19×29)) 2.3.5.7.19.29 [-2 2 1 2 -1 -1⟩ Glinkisma
2262/2261 0.76552 (2×3×13×29)/(7×17×19) 2.3.7.13.17.19.29 [1 1 -1 1 -1 -1 1⟩ Mitidikisma
2465/2464 0.70247 (5×17×29)/(25×7×11) 2.5.7.11.17.29 [-5 1 -1 -1 1 1⟩ Laservine comma
2640/2639 0.65589 (24×3×5×11)/(7×13×29) 2.3.5.7.11.13.29 [4 1 1 -1 1 -1 -1⟩ Hällströmisma
2755/2754 0.62851 (5×19×29)/(2×34×17) 2.3.5.17.19.29 [-1 -4 1 -1 1 1⟩ Avicema
2784/2783 0.62196 (25×3×29)/(112×23) 2.3.11.23.29 [5 1 -2 -1 1⟩ Domeykisma
3249/3248 0.53293 (3×19)2/(24×7×29) 2.3.7.19.29 [-4 2 -1 2 -1⟩ Musashinisma, Musashino comma S57
3451/3450 0.50173 (7×17×29)/(2×3×52×23) 2.3.5.7.17.23.29 [-1 -1 -2 1 1 -1 1⟩ Mentorisma
3510/3509 0.49330 (2×33×5×13)/(112×29) 2.3.5.11.13.29 [1 3 1 -2 1 -1⟩ Veederisma
4641/4640 0.37307 (3×7×13×17)/(25×5×29) 2.3.5.7.13.17.29 [-5 1 -1 1 1 1 -1⟩ Vinecute comma
4785/4784 0.36184 (3×5×11×29)/(24×13×23) 2.3.5.11.13.23.29 [-4 1 1 1 -1 -1 1⟩ Petrovsma
4901/4900 0.35328 (13/(2×5×7))2×29 2.5.7.13.29 [-2 -2 -2 2 1⟩ Large grapevine comma
5104/5103 0.33922 (24×11×29)/(36×7) 2.3.7.11.29 [4 -6 -1 1 1⟩
5888/5887 0.29405 (28×23)/(7×292) 2.7.23.29 [8 -1 1 -2⟩ Vinocular comma
5916/5915 0.29266 (22×3×17×29)/(5×7×132) 2.3.5.7.13.17.29 [2 1 -1 -1 -2 1 1⟩ Woudisma
6670/6669 0.25957 (2×5×23×29)/(33×13×19) 2.3.5.13.19.23.29 [1 -3 1 -1 -1 1 1⟩
7106/7105 0.24365 (2×11×17×19)/(5×72×29) 2.5.7.11.17.19.29 [1 -1 -2 1 1 1 -1⟩
7425/7424 0.23318 (33×52×11)/(28×29) 2.3.5.11.29 [-8 3 2 1 -1⟩ Small grapevine comma
7889/7888 0.21946 (73×23)/(24×17×29) 2.7.17.23.29 [-4 3 -1 1 -1⟩
8671/8670 0.19967 (13×23×29)/(2×3×5×172) 2.3.5.13.17.23.29 [-1 -1 -1 1 -2 1 1⟩ Vinous comma, vinousma
9802/9801 0.17663 (2×132×29)/(32×11)2 2.3.11.13.29 [1 -4 -2 2 1⟩
10557/10556 0.16400 (33×17×23)/(22×7×13×29) 2.3.7.13.17.23.29 [-2 3 -1 -1 1 1 -1⟩ Rowlandisma
11340/11339 0.15267 (22×34×5×7)/(17×23×29) 2.3.5.7.17.23.29 [2 4 1 1 -1 -1 -1⟩
12006/12005 0.14420 (2×32×23×29)/(5×74) 2.3.5.7.23.29 [1 2 -1 -4 1 1⟩ Uma, umic comma
12673/12672 0.13661 (19×23×29)/(27×32×11) 2.3.11.19.23.29 [-7 -2 -1 1 1 1⟩
13225/13224 0.13091 (5×23)2/(23×3×19×29) 2.3.5.19.23.29 [-3 -1 2 -1 2 -1⟩ S115
13311/13310 0.13007 (33×17×29)/(2×5×113) 2.3.5.11.17.29 [-1 3 -1 -3 1 1⟩
13312/13311 0.13006 (210×13)/(33×17×29) 2.3.13.17.29 [10 -3 1 -1 -1⟩
13456/13455 0.12866 (22×29)2/(32×5×13×23) 2.3.5.13.23.29 [4 -2 -1 -1 -1 2⟩ S116
19228/19227 0.090039 (22×11×19×23)/(3×13×17×29) 2.3.11.13.17.19.23.29 [2 -1 1 -1 -1 1 1 -1⟩
20736/20735 0.083491 (22×3)4/(5×11×13×29) 2.3.5.11.13.29 [8 4 -1 -1 -1 -1⟩ S144
23751/23750 0.072893 (32×7×13×29)/(2×54×19) 2.3.5.7.13.19.29 [-1 2 -4 1 1 -1 1⟩
24795/24794 0.069823 (32×5×19×29)/(2×72×11×23) 2.3.5.7.11.19.23.29 [-1 2 1 -2 -1 1 -1 1⟩
25840/25839 0.067000 (24×5×17×19)/(34×11×29) 2.3.5.11.17.19.29 [4 -4 1 -1 1 1 -1⟩ Vuillafansisma
27000/26999 0.064121 (2×3×5)3/(72×19×29) 2.3.5.7.19.29 [3 3 3 -2 -1 -1⟩
30625/30624 0.056531 (52×7)2/(25×3×11×29) 2.3.5.7.11.29 [-5 -1 4 2 -1 -1⟩ S175
30856/30855 0.056108 (23×7×19×29)/(3×5×112×17) 2.3.5.7.11.17.19.29 [3 -1 -1 1 -2 -1 1 1⟩
35322/35321 0.049014 (2×3×7×292)/(11×132×19) 2.3.7.11.13.19.29 [1 1 1 -1 -2 -1 2⟩
47125/47124 0.036737 (53×13×29)/((2×3)2×7×11×17) 2.3.5.7.11.13.17.29 [-2 -2 3 -1 -1 1 -1 1⟩
53361/53360 0.032444 (3×7×11)2/(24×5×23×29) 2.3.5.7.11.23.29 [-4 2 -1 2 2 -1 -1⟩ S231
72501/72500 0.023879 (3×11×133)/((2×52)2×29) 2.3.5.11.13.29 [-2 1 -4 1 3 -1⟩
83521/83520 0.020728 174/((23×3)2×5×29) 2.3.5.17.29 [-6 -2 -1 4 -1⟩ S289
87465/87464 0.019794 (3×5×73×17)/(23×13×292) 2.3.5.7.13.17.29 [-3 1 1 3 -1 1 -2⟩
136851/136850 0.012651 (3×112×13×29)/(2×52×7×17×23) 2.3.5.7.11.13.17.23.29 [-1 1 -2 -1 2 1 -1 -1 1⟩
158950/158949 0.010892 (2×(5×17)2×11)/(33×7×292) 2.3.5.7.11.17.29 [1 -3 2 -1 1 2 -2⟩
166635/166634 0.010389 ((3×23)2×5×7)/(2×132×17×29) 2.3.5.7.13.17.23.29 [-1 2 1 1 -2 -1 2 -1⟩
168751/168750 0.010259 (11×232×29)/(2×33×55) 2.3.5.11.23.29 [-1 -3 -5 1 2 1⟩
176001/176000 0.0098365 (3×7×172×29)/(27×53×11) 2.3.5.7.11.17.29 [-7 1 -3 1 -1 2 1⟩
176176/176175 0.0098268 (24×7×112×13)/(35×52×29) 2.3.5.7.11.13.29 [4 -5 -2 1 2 1 -1⟩
184093/184092 0.0094042 ((7×17)2×13)/((2×23)2×3×29) 2.3.7.13.17.23.29 [-2 -1 2 1 2 -2 -1⟩
240787/240786 0.0071899 (192×23×29)/(2×(3×7)3×13) 2.3.7.13.19.23.29 [-1 -3 -3 -1 2 1 1⟩
244036/244035 0.0070942 (2×13×19)2/(32×5×11×17×29) 2.3.5.11.13.17.19.29 [2 -2 -1 -1 2 -1 2 -1⟩ S494
303601/303600 0.0057023 ((19×29)/(22×5))2/(3×11×23) 2.3.5.11.19.23.29 [-4 -1 -2 -1 2 -1 2⟩ S551
410670/410669 0.0042156 (2×35×5×132)/((7×17)2×29) 2.3.5.7.13.17.29 [1 5 1 -2 2 -2 -1⟩
418761/418760 0.0041342 ((3×17)2×7×23)/(23×5×192×29) 2.3.5.7.17.19.23.29 [-3 2 -1 1 2 -2 1 -1⟩
613089/613088 0.0028238 (33×29)2/(25×72×17×23) 2.3.7.17.23.29 [-5 6 -2 -1 -1 2⟩ S783
949026/949025 0.0018242 (2×3×13×233)/(52×7×11×17×29) 2.3.5.7.11.13.17.23.29 [1 1 -2 -1 -1 1 -1 3 -1⟩
1163800/1163799 0.0014876 (23×(5×23)2×11)/(32×73×13×29) 2.3.5.7.11.13.23.29 [3 -2 2 -3 1 -1 2 -1⟩
1235169/1235168 0.0014016 (35×13×17×23)/(25×113×29) 2.3.11.13.17.23.29 [-5 5 -3 1 1 1 -1⟩
1243840/1243839 0.0013918 ((23×13)2×5×23)/(3×17×293) 2.3.5.13.17.23.29 [6 -1 1 2 -1 1 -3⟩
1625625/1625624 0.0010650 (3×52×17)2/(23×72×11×13×29) 2.3.5.7.11.13.17.29 [-3 2 4 -2 -1 -1 2 -1⟩ S1275
1852201/1852200 0.00093469 (13×173×29)/((2×3×7)3×52) 2.3.5.7.13.17.29 [-3 -3 -2 -3 1 3 1⟩
2697696/2697695 0.00064175 (25×32×17×19×29)/(5×73×112×13) 2.3.5.7.11.13.17.19.29 [5 2 -1 -3 -2 -1 1 1 1⟩
4004001/4004000 0.00043238 (3×23×29)2/(25×53×7×11×13) 2.3.5.7.11.13.23.29 [-5 2 -3 -1 -1 -1 2 2⟩ Odyssey comma S2001
4090625/4090624 0.00042322 (55×7×11×17)/((24×29)2×19) 2.5.7.11.17.19.29 [-8 5 1 1 1 -1 -2⟩
8268800/8268799 0.00020937 ((25×5)2×17×19)/((7×23)2×11×29) 2.5.7.11.17.19.23.29 [10 2 -2 -1 1 1 -2 -1⟩
10556001/10556000 0.00016400 (3×19)4/(25×53×7×13×29) 2.3.5.7.13.19.29 [-5 4 -3 -1 -1 4 -1⟩ S3249
18085705/18085704 9.5724×10-5 (5×11×17×23×292)/((2×7×13)3×3) 2.3.5.7.11.13.17.23.29 [-3 -1 1 -3 1 -3 1 1 2⟩
96059601/96059600 1.8022×10-5 (32×11)4/((22×5×7×13)2×29) 2.3.5.7.11.13.29 [-4 8 -2 -2 4 -2 -1⟩ S9801
177182721/177182720 9.7709×10-6 (33×17×29)2/(211×5×113×13) 2.3.5.11.13.17.29 [-11 6 -1 -3 -1 2 2⟩ S13311

Notes

  1. ↑ Denoted by S-expressions, where sk is defined as (k/(k - 1))/((k + 1)/k). See square superparticular for details.
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