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List of superparticular intervals/41-limit

Revision as of 13:24, 18 September 2025 by FloraC (talk | contribs) (Created page with "== 41-limit (incomplete) == {| class="wikitable center-6" style="width:100%" ! width="10%" | Ratio ! width="10%" | Cents ! width="15%" | Factorization ! width="15%" | Monzo ! width="45%" | Name(s) ! width="5%" | Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See square superparticular for details.</ref> |- | 41/40 | 42.749 | 41/(2<sup>3</sup>×5) | 2.5.41 {{monzo| -3 -1 1 }} | Large qu...")
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41-limit (incomplete)

Ratio Cents Factorization Monzo Name(s) Meta[1]
41/40 42.749 41/(23×5) 2.5.41 [-3 -1 1⟩ Large quadracesimoprimal 1/5-tone
42/41 41.719 (2×3×7)/41 2.3.7.41 [1 1 1 -1⟩ Small quadracesimoprimal 1/5-tone
82/81 21.242 (2×41)/34 2.3.41 [1 -4 1⟩ 41st-partial chroma
124/123 14.018 (22×31)/(3×41) 2.3.31.41 [2 -1 1 -1⟩
165/164 10.524 (3×5×11)/(22×41) 2.3.5.11.41 [-2 1 1 1 -1⟩
205/204 8.4657 (5×41)/(22×3×17) 2.3.5.17.41 [-2 -1 1 -1 1⟩
246/245 7.0519 (2×3×41)/(5×72) 2.3.5.7.41 [1 1 -1 -2 1⟩
247/246 7.0233 (13×19)/(2×3×41) 2.3.13.19.41 [-1 -1 1 1 -1⟩
287/286 6.0427 (7×41)/(2×11×13) 2.7.11.13.41 [-1 1 -1 -1 1⟩
288/287 6.0217 (25×32)/(7×41) 2.3.7.41 [5 2 -1 -1⟩
369/368 4.6981 (32×41)/(24×23) 2.3.23.41 [-4 2 -1 1⟩
370/369 4.6853 (2×5×37)/(32×41) 2.3.5.37.41 [1 -2 1 1 -1⟩
451/450 3.8429 (11×41)/(2×(3×5)2) 2.3.5.11.41 [-1 -2 -2 1 1⟩
493/492 3.5152 (17×29)/(22×3×41) 2.3.17.29.41 [-2 -1 1 1 -1⟩
533/532 3.2511 (13×41)/(22×7×19) 2.7.13.19.41 [-2 -1 1 -1 1⟩
575/574 3.0135 (52×23)/(2×7×41) 2.5.7.23.41 [-1 2 -1 1 -1⟩ Renatisma
616/615 2.8127 (23×7×11)/(3×5×41) 2.3.5.7.11.41 [3 -1 -1 1 1 -1⟩ Ellisma
697/696 2.4856 (17×41)/(23×3×29) 2.3.17.29.41 [-3 -1 1 -1 1⟩
780/779 2.2210 (22×3×5×13)/(19×41) 2.3.5.13.19.41 [2 1 1 1 -1 -1⟩ Wiesentisma
820/819 2.1125 (22×5×41)/(32×7×13) 2.3.5.7.13.41 [2 -2 1 -1 -1 1⟩
1025/1024 1.6898 (52×41)/210 2.5.41 [-10 2 1⟩ Kilobytisma
1026/1025 1.6882 (2×33×19)/(52×41) 2.3.5.19.41 [1 3 -2 1 -1⟩ Ingridisma
1148/1147 1.5087 (22×7×41)/(31×37) 2.7.31.37.41 [2 1 -1 -1 1⟩
1189/1188 1.4567 (29×41)/(22×33×11) 2.3.11.29.41 [-2 -3 -1 1 1⟩
1190/1189 1.4554 (2×5×7×17)/(29×41) 2.5.7.17.29.41 [1 1 1 1 -1 -1⟩ Pelagisma
1312/1311 1.3200 (25×41)/(3×19×23) 2.3.19.23.41 [5 -1 -1 -1 1⟩
1353/1352 1.2800 (3×11×41)/(23×132) 2.3.11.13.41 [-3 1 1 -2 1⟩
1395/1394 1.2415 (32×5×31)/(2×17×41) 2.3.5.17.31.41 [-1 2 1 -1 1 -1⟩
1518/1517 1.1408 (2×3×11×23)/(37×41) 2.3.11.23.37.41 [1 1 1 1 -1 -1⟩ Rovaniemisma
1600/1599 1.0824 (23×5)2/(3×13×41) 2.3.5.13.41 [6 -1 2 -1 -1⟩ S40
1681/1680 1.0302 412/(24×3×5×7) 2.3.5.7.41 [-4 -1 -1 -1 2⟩ S41
1682/1681 1.0296 (2×292)/412 2.29.41 [1 2 -2⟩ Shaftesburisma
1805/1804 0.95940 (5×192)/(22×11×41) 2.5.11.19.41 [-2 1 -1 2 -1⟩
1886/1885 0.91818 (2×23×41)/(5×13×29) 2.5.13.23.29.41 [1 -1 -1 1 -1 1⟩
1887/1886 0.91770 (3×17×37)/(2×23×41) 2.3.17.23.37.41 [-1 1 1 -1 1 -1⟩
2091/2090 0.82814 (3×17×41)/(2×5×11×19) 2.3.5.11.17.19.41 [-1 1 -1 -1 1 -1 1⟩
2255/2254 0.76790 (5×11×41)/(2×72×23) 2.5.7.11.23.41 [-1 1 -2 1 -1 1⟩ Qinghaisma
2296/2295 0.75419 (23×7×41)/(33×5×17) 2.3.5.7.17.41 [3 -3 -1 1 -1 1⟩
2542/2541 0.68119 (2×31×41)/(3×7×112) 2.3.7.11.31.41 [1 -1 -1 -2 1 1⟩
2584/2583 0.67011 (23×17×19)/(32×7×41) 2.3.7.17.19.41 [3 -2 -1 1 1 -1⟩
2625/2624 0.65964 (3×53×7)/(26×41) 2.3.5.7.41 [-6 1 3 1 -1⟩
2665/2664 0.64974 (5×13×41)/(23×32×37) 2.3.5.13.37.41 [-3 -2 1 1 -1 1⟩
2871/2870 0.60311 (32×11×29)/(2×5×7×41) 2.3.5.7.11.29.41 [-1 2 -1 -1 1 1 -1⟩ Schoberisma
3690/3689 0.46923 (2×32×5×41)/(7×17×31) 2.3.5.7.17.31.41 [1 2 1 -1 -1 -1 1⟩
3773/3772 0.45891 (73×11)/(22×23×41) 2.7.11.23.41 [-2 3 1 -1 -1⟩ Smithsonianisma
4060/4059 0.42646 (22×5×7×29)/(32×11×41) 2.3.5.7.11.29.41 [2 -2 1 1 -1 1 -1⟩ Deipylosisma
4264/4263 0.40606 (23×13×41)/(3×72×29) 2.3.7.13.29.41 [3 -1 -2 1 -1 1⟩
4551/4550 0.38045 (3×37×41)/(2×52×7×13) 2.3.5.7.13.37.41 [-1 1 -2 -1 -1 1 1⟩
4675/4674 0.37036 (52×11×17)/(2×3×19×41) 2.3.5.11.17.19.41 [-1 -1 2 1 1 -1 -1⟩ Ohbokisma
4921/4920 0.35184 (7×19×37)/(23×3×5×41) 2.3.5.7.19.37.41 [-3 -1 -1 1 1 1 -1⟩ Volontisma
4961/4960 0.34900 (112×41)/(25×5×31) 2.5.11.31.41 [-5 -1 2 -1 1⟩
5084/5083 0.34056 (22×31×41)/(13×17×23) 2.13.17.23.31.41 [2 -1 -1 -1 1 1⟩
5577/5576 0.31045 (3×11×132)/(23×17×41) 2.3.11.13.17.41 [-3 1 1 2 -1 -1⟩ Priestlisma
6069/6068 0.28528 (3×7×172)/(22×37×41) 2.3.7.17.37.41 [-2 1 1 2 -1 -1⟩ Cevolanisma
6273/6272 0.27600 (32×17×41)/(27×72) 2.3.7.17.41 [-7 2 -2 1 1⟩
6561/6560 0.26389 38/(25×5×41) 2.3.5.41 [-5 8 -1 -1⟩ S81
6601/6600 0.26229 (7×23×41)/(23×3×52×11) 2.3.5.7.11.23.41 [-3 -1 -2 1 -1 1 1⟩
6930/6929 0.24984 (2×32×5×7×11)/(132×41) 2.3.5.7.11.13.41 [1 2 1 1 1 -2 -1⟩ Bedanisma
7176/7175 0.24127 (23×3×13×23)/(52×7×41) 2.3.5.7.13.23.41 [3 1 -2 -1 1 1 -1⟩ Kunijisma
7216/7215 0.23993 (24×11×41)/(3×5×13×37) 2.3.5.11.13.37.41 [4 -1 -1 1 -1 -1 1⟩
7750/7749 0.22340 (2×53×31)/(33×7×41) 2.3.5.7.31.41 [1 -3 3 -1 1 -1⟩
8569/8568 0.20205 (11×19×41)/(23×32×7×17) 2.3.7.11.17.19.41 [-3 -2 -1 1 -1 1 1⟩ Mamelisma
8856/8855 0.19550 ((2×3)3×41)/(5×7×11×23) 2.3.5.7.11.23.41 [3 3 -1 -1 -1 -1 1⟩
9472/9471 0.18278 (28×37)/(3×7×11×41) 2.3.7.11.37.41 [8 -1 -1 -1 1 -1⟩ Brugesisma
10045/10044 0.17236 (5×72×41)/(22×34×31) 2.3.5.7.31.41 [-2 -4 1 2 -1 1⟩
10374/10373 0.16689 (2×3×7×13×19)/(11×23×41) 2.3.7.11.13.19.23.41 [1 1 1 -1 1 1 -1 -1⟩ Etampesisma
10660/10659 0.16241 (22×5×13×41)/(3×11×17×19) 2.3.5.11.13.17.19.41 [2 -1 1 -1 1 -1 -1 1⟩
11440/11439 0.15134 (24×5×11×13)/(32×31×41) 2.3.5.11.13.31.41 [4 -2 1 1 1 -1 -1⟩ Massironisma
13776/13775 0.12567 (24×3×7×41)/(52×19×29) 2.3.5.7.19.29.41 [4 1 -2 1 -1 -1 1⟩
14145/14144 0.12240 (3×5×23×41)/(26×13×17) 2.3.5.13.17.23.41 [-6 1 1 -1 -1 1 1⟩
14801/14800 0.11697 (192×41)/(24×52×37) 2.5.19.37.41 [-4 -2 2 -1 1⟩
15376/15375 0.11260 (22×31)2/(3×53×41) 2.3.5.31.41 [4 -1 -3 2 -1⟩ Martakisma S124
15457/15456 0.11201 (13×29×41)/(25×3×7×23) 2.3.7.13.23.29.41 [-5 -1 -1 1 -1 1 1⟩
16400/16399 0.10557 (24×52×41)/(232×31) 2.5.23.31.41 [4 2 -2 -1 1⟩
16524/16523 0.10477 (22×35×17)/(13×31×41) 2.3.13.17.31.41 [2 5 -1 1 -1 -1⟩
16606/16605 0.10426 (2×192×23)/(34×5×41) 2.3.5.19.23.41 [1 -4 -1 2 1 -1⟩
17425/17424 0.099356 (52×17×41)/(22×3×11)2 2.3.5.11.17.41 [-4 -2 2 -2 1 1⟩
17836/17835 0.097067 (22×73×13)/(3×5×29×41) 2.3.5.7.13.29.41 [2 -1 -1 3 1 -1 -1⟩ Canupisma
17918/17917 0.096623 (2×172×31)/(19×23×41) 2.17.19.23.31.41 [1 2 -1 -1 1 -1⟩
19721/19720 0.087789 (13×37×41)/(23×5×17×29) 2.5.13.17.29.37.41 [-3 -1 1 -1 -1 1 1⟩
19845/19844 0.087240 (34×5×72)/((2×11)2×41) 2.3.5.7.11.41 [-2 4 1 2 -2 -1⟩
76384/76383 0.022665 (25×7×11×31)/(34×23×41) 2.3.7.11.23.31.41 [5 -4 1 1 -1 1 -1⟩ Vernonisma
1048576/1048575 0.0016510 220/(3×52×11×31×41) 2.3.5.11.31.41 [20 -1 -2 -1 -1 -1⟩ Mebisma S1024

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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