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Mike Battaglia (talk | contribs)
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==Superparticular Ratios==
==Superparticular Ratios==


Below is a list of superparticular ratios from 2/1 to 100/99, ranked by this "Wilson height," as well as a note about the smallest prime limit each fits into. Below I will refer to the "prime limit" of a ratio to mean the smallest prime limit that it fits into.
Below is a list of superparticular ratios from 2/1 to 100/99, ranked by this "Wilson height," as well as a note about the smallest prime limit each ratio fits into.


You can see that as the Wilson height increases, you get ratios that are generally get higher in Tenney height, but where these "simple-prime-limit" ratios are given an increase in the ranking. For instance, note how 100/99 (11-limit) is ahead of 24/23 (23-limit), for instance.
You can see that as the Wilson height increases, you get ratios that are generally get higher in Tenney height, but where these "simple-prime-limit" ratios are given an increase in the ranking. For instance, note how 100/99 (11-limit) is ahead of 24/23 (23-limit), for instance.


 
2/1: 2 (2-limit)<br>
2/1: 2 (2-limit)
3/2: 5 (3-limit)<br>
3/2: 5 (3-limit)
4/3: 7 (3-limit)<br>
4/3: 7 (3-limit)
5/4: 9 (5-limit)<br>
5/4: 9 (5-limit)
6/5: 10 (5-limit)<br>
6/5: 10 (5-limit)
7/6: 12 (7-limit)<br>
7/6: 12 (7-limit)
9/8: 12 (3-limit)<br>
9/8: 12 (3-limit)
8/7: 13 (7-limit)<br>
8/7: 13 (7-limit)
10/9: 13 (5-limit)<br>
10/9: 13 (5-limit)
16/15: 16 (5-limit)<br>
16/15: 16 (5-limit)
15/14: 17 (7-limit)<br>
15/14: 17 (7-limit)
11/10: 18 (11-limit)<br>
11/10: 18 (11-limit)
12/11: 18 (11-limit)<br>
12/11: 18 (11-limit)
21/20: 19 (7-limit)<br>
21/20: 19 (7-limit)
25/24: 19 (5-limit)<br>
25/24: 19 (5-limit)
13/12: 20 (13-limit)<br>
13/12: 20 (13-limit)
28/27: 20 (7-limit)<br>
28/27: 20 (7-limit)
14/13: 22 (13-limit)<br>
14/13: 22 (13-limit)
36/35: 22 (7-limit)<br>
36/35: 22 (7-limit)
22/21: 23 (11-limit)<br>
22/21: 23 (11-limit)
27/26: 24 (13-limit)<br>
27/26: 24 (13-limit)
33/32: 24 (11-limit)<br>
33/32: 24 (11-limit)
17/16: 25 (17-limit)<br>
17/16: 25 (17-limit)
18/17: 25 (17-limit)<br>
18/17: 25 (17-limit)
26/25: 25 (13-limit)<br>
26/25: 25 (13-limit)
49/48: 25 (7-limit)<br>
49/48: 25 (7-limit)
64/63: 25 (7-limit)<br>
64/63: 25 (7-limit)
81/80: 25 (5-limit)<br>
81/80: 25 (5-limit)
45/44: 26 (11-limit)<br>
45/44: 26 (11-limit)
50/49: 26 (7-limit)<br>
50/49: 26 (7-limit)
19/18: 27 (19-limit)<br>
19/18: 27 (19-limit)
40/39: 27 (13-limit)<br>
40/39: 27 (13-limit)
55/54: 27 (11-limit)<br>
55/54: 27 (11-limit)
20/19: 28 (19-limit)<br>
20/19: 28 (19-limit)
56/55: 29 (11-limit)<br>
56/55: 29 (11-limit)
65/64: 30 (13-limit)<br>
65/64: 30 (13-limit)
35/34: 31 (17-limit)<br>
35/34: 31 (17-limit)
100/99: 31 (11-limit)<br>
100/99: 31 (11-limit)
24/23: 32 (23-limit)<br>
24/23: 32 (23-limit)
51/50: 32 (17-limit)<br>
51/50: 32 (17-limit)
34/33: 33 (17-limit)<br>
34/33: 33 (17-limit)
91/90: 33 (13-limit)<br>
91/90: 33 (13-limit)
99/98: 33 (11-limit)<br>
99/98: 33 (11-limit)
66/65: 34 (13-limit)<br>
66/65: 34 (13-limit)
57/56: 35 (19-limit)<br>
57/56: 35 (19-limit)
23/22: 36 (23-limit)<br>
23/22: 36 (23-limit)
46/45: 36 (23-limit)<br>
46/45: 36 (23-limit)
76/75: 36 (19-limit)<br>
76/75: 36 (19-limit)
78/77: 36 (13-limit)<br>
78/77: 36 (13-limit)
85/84: 36 (17-limit)<br>
85/84: 36 (17-limit)
39/38: 37 (19-limit)<br>
39/38: 37 (19-limit)
52/51: 37 (17-limit)<br>
52/51: 37 (17-limit)
96/95: 37 (19-limit)<br>
96/95: 37 (19-limit)
30/29: 39 (29-limit)<br>
30/29: 39 (29-limit)
29/28: 40 (29-limit)<br>
29/28: 40 (29-limit)
70/69: 40 (23-limit)<br>
70/69: 40 (23-limit)
31/30: 41 (31-limit)<br>
31/30: 41 (31-limit)
32/31: 41 (31-limit)<br>
32/31: 41 (31-limit)
77/76: 41 (19-limit)<br>
77/76: 41 (19-limit)
63/62: 46 (31-limit)<br>
63/62: 46 (31-limit)
37/36: 47 (37-limit)<br>
37/36: 47 (37-limit)
69/68: 47 (23-limit)<br>
69/68: 47 (23-limit)
92/91: 47 (23-limit)<br>
92/91: 47 (23-limit)
88/87: 49 (29-limit)<br>
88/87: 49 (29-limit)
41/40: 52 (41-limit)<br>
41/40: 52 (41-limit)
75/74: 52 (37-limit)<br>
75/74: 52 (37-limit)
42/41: 53 (41-limit)<br>
42/41: 53 (41-limit)
58/57: 53 (29-limit)<br>
58/57: 53 (29-limit)
43/42: 55 (43-limit)<br>
43/42: 55 (43-limit)
82/81: 55 (41-limit)<br>
82/81: 55 (41-limit)
38/37: 58 (37-limit)<br>
38/37: 58 (37-limit)
44/43: 58 (43-limit)<br>
44/43: 58 (43-limit)
48/47: 58 (47-limit)<br>
48/47: 58 (47-limit)
93/92: 61 (31-limit)<br>
93/92: 61 (31-limit)
54/53: 64 (53-limit)<br>
54/53: 64 (53-limit)
86/85: 67 (43-limit)<br>
86/85: 67 (43-limit)
53/52: 70 (53-limit)<br>
53/52: 70 (53-limit)
60/59: 71 (59-limit)<br>
60/59: 71 (59-limit)
47/46: 72 (47-limit)<br>
47/46: 72 (47-limit)
61/60: 73 (61-limit)<br>
61/60: 73 (61-limit)
95/94: 73 (47-limit)<br>
95/94: 73 (47-limit)
87/86: 77 (43-limit)<br>
87/86: 77 (43-limit)
67/66: 83 (67-limit)<br>
67/66: 83 (67-limit)
72/71: 83 (71-limit)<br>
72/71: 83 (71-limit)
94/93: 83 (47-limit)<br>
94/93: 83 (47-limit)
71/70: 85 (71-limit)<br>
71/70: 85 (71-limit)
73/72: 85 (73-limit)<br>
73/72: 85 (73-limit)
68/67: 88 (67-limit)<br>
68/67: 88 (67-limit)
59/58: 90 (59-limit)<br>
59/58: 90 (59-limit)
80/79: 92 (79-limit)<br>
80/79: 92 (79-limit)
62/61: 94 (61-limit)<br>
62/61: 94 (61-limit)
79/78: 97 (79-limit)<br>
79/78: 97 (79-limit)
84/83: 97 (83-limit)<br>
84/83: 97 (83-limit)
90/89: 102 (89-limit)<br>
90/89: 102 (89-limit)
89/88: 106 (89-limit)<br>
89/88: 106 (89-limit)
97/96: 110 (97-limit)<br>
97/96: 110 (97-limit)
74/73: 112 (73-limit)<br>
74/73: 112 (73-limit)
98/97: 113 (97-limit)<br>
98/97: 113 (97-limit)
83/82: 126 (83-limit)
83/82: 126 (83-limit)


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