User:Godtone/optimal edo sequences

In the below I detail the optimal_edo_sequences for a large range of odd-limits (19 thru 123). However, the formatting requires some explanation. I was originally specifically interested in how fifth-chroma temperaments 77, 80, 84(, 87, 94) fare relative to each-other, to get a sense of what their relative strengths and weaknesses are. Therefore I list which of those five edos appear in the sequence separately, followed by what edos appear after them (to get a sense of what the smallest edos that are improvements are). However, this excludes edos smaller than 94 (other than 77, 80, 84 and 87 ofc), so I later did a sequence for smaller edos (in the 1 to 94 range) for completeness. A notable edo appearing frequently in these sequences (which is excluded in the first lists for being < 94) is 89edo, which interestingly splits 25/24 either into 4 or 6 depending on if you use the flat or sharp mapping of 5/4 (respectively), so that it's almost like it's approximately fifth-chroma in resolution. This is also notable because other than 82edo, it's the only edo to appear relatively frequently which is in the 77 to 94 range other than 77, 80, 84, 87, 94. I also only calculate with pure-octave and patent vals, but since I know the correct high-limit val for 80edo (as it's one of my favourite tuning systems), I use that val for it instead.

patent_vals[80] = val(lim(255),ed(80),'koprsuvBC')

for ol in range(19,52,2):
  result = optimal_edo_sequence(odd_lim(ol,complements=False))
  print(str(ol)+'-odd-limit:',[ x for x in result if x in [77,80,84,87,94] ],'\n  & additionally:',[ x for x in result if x > 94 ])

19-odd-limit: [80, 94] 
  & additionally: [111, 121, 137, 149, 159, 161, 181, 193, 217, 270, 311]
21-odd-limit: [94] 
  & additionally: [111, 130, 137, 145, 159, 161, 181, 193, 217, 270, 311]
23-odd-limit: [77, 80, 84, 94] 
  & additionally: [111, 113, 130, 145, 159, 161, 181, 193, 217, 243, 261, 270, 279, 282, 311]
25-odd-limit: [80, 84, 94] 
  & additionally: [109, 111, 118, 130, 137, 140, 149, 159, 183, 193, 214, 217, 270, 282, 311]
27-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [111, 118, 130, 149, 159, 183, 217, 270, 282, 311]
29-odd-limit: [77, 80, 84, 87] 
  & additionally: [99, 111, 118, 140, 159, 183, 217, 270, 282, 311]
31-odd-limit: [77, 80, 84, 87] 
  & additionally: [106, 111, 118, 125, 128, 130, 140, 149, 159, 171, 183, 217, 270, 282, 311]
33-odd-limit: [77, 80, 84, 87] 
  & additionally: [111, 118, 128, 130, 140, 159, 183, 217, 270, 282, 311]
35-odd-limit: [77, 80, 84] 
  & additionally: [111, 118, 130, 140, 149, 159, 171, 183, 193, 217, 270, 282, 311]
37-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [106, 118, 125, 130, 140, 149, 159, 171, 183, 202, 205, 217, 224, 270, 282, 296, 311]
39-odd-limit: [77, 80, 84, 87] 
  & additionally: [106, 109, 118, 125, 130, 140, 149, 159, 171, 183, 205, 217, 224, 270, 282, 296, 311]
41-odd-limit: [77, 80, 84] 
  & additionally: [106, 109, 118, 130, 133, 137, 140, 149, 159, 171, 193, 217, 224, 270, 277, 282, 311]
43-odd-limit: [77, 80, 84] 
  & additionally: [106, 118, 130, 133, 140, 159, 171, 193, 202, 224, 246, 248, 270, 277, 296, 311]
45-odd-limit: [77, 80, 84, 87] 
  & additionally: [106, 118, 130, 133, 140, 159, 171, 183, 193, 224, 246, 248, 270, 277, 311]
47-odd-limit: [77, 80, 84, 87] 
  & additionally: [106, 118, 130, 133, 140, 159, 171, 193, 224, 248, 270, 296, 301, 311]
49-odd-limit: [77, 80, 84, 94] 
  & additionally: [118, 125, 130, 140, 161, 171, 193, 202, 224, 270, 301, 311]
51-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [118, 125, 130, 140, 171, 202, 224, 248, 260, 265, 270, 296, 311]

# I separated it into two calculations because beyond the 51-odd-limit the usefulness is more dubious beyond just general sources of opportunistic concordance.
for ol in range(53,124,2): # (Also because these calculations took significantly longer.)
  result = optimal_edo_sequence(odd_lim(ol,complements=False))
  print(str(ol)+'-odd-limit:',[ x for x in result if x in [77,80,84,87,94] ],'\n  & additionally:',[ x for x in result if x > 94 ])

53-odd-limit: [77, 84, 94] 
  & additionally: [111, 113, 118, 125, 130, 140, 171, 193, 202, 224, 253, 265, 270, 296, 301]
55-odd-limit: [77, 84, 87, 94] 
  & additionally: [99, 111, 113, 118, 130, 140, 161, 171, 193, 202, 224, 265, 270, 296, 301, 311]
57-odd-limit: [77, 84, 94] 
  & additionally: [111, 113, 118, 130, 140, 161, 171, 183, 190, 193, 202, 224, 239, 265, 270, 296, 301, 311]
59-odd-limit: [77, 84, 94] 
  & additionally: [111, 118, 130, 137, 140, 159, 161, 171, 193, 202, 224, 239, 265, 270, 296]
61-odd-limit: [77, 80, 84, 94] 
  & additionally: [111, 113, 118, 130, 140, 159, 161, 171, 193, 202, 229, 265, 270, 296]
63-odd-limit: [77, 84, 94] 
  & additionally: [111, 113, 118, 125, 130, 140, 159, 161, 171, 202, 229, 260, 265, 270, 296]
65-odd-limit: [77, 80, 84, 94] 
  & additionally: [111, 113, 118, 125, 130, 140, 159, 161, 171, 202, 224, 229, 265, 270, 296, 301]
67-odd-limit: [77, 84, 87, 94] 
  & additionally: [113, 118, 125, 130, 137, 140, 161, 171, 202, 224, 229, 260, 265, 270, 301]
69-odd-limit: [77, 80, 84, 94] 
  & additionally: [113, 118, 125, 130, 137, 140, 161, 171, 183, 193, 202, 224, 229, 260, 265, 270, 301]
71-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [113, 118, 125, 128, 130, 137, 140, 161, 171, 181, 183, 193, 202, 229, 258, 260, 265, 270, 289, 296, 301]
73-odd-limit: [77, 80, 84, 94] 
  & additionally: [113, 118, 125, 128, 130, 137, 140, 161, 171, 181, 183, 193, 202, 243, 258, 260, 265, 270, 289, 296, 301]
75-odd-limit: [77, 80, 84, 94] 
  & additionally: [113, 118, 128, 130, 137, 140, 161, 171, 181, 183, 193, 202, 258, 270, 289, 296, 301]
77-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [113, 118, 125, 128, 130, 137, 140, 161, 171, 181, 183, 193, 202, 239, 255, 258, 270, 289, 301]
79-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [111, 113, 118, 125, 128, 137, 140, 159, 161, 171, 181, 193, 202, 255, 258, 270, 289, 301]
81-odd-limit: [77, 80, 87, 94] 
  & additionally: [111, 113, 118, 128, 130, 140, 159, 171, 183, 193, 202, 224, 248, 258, 270, 289, 301]
83-odd-limit: [77, 80, 87, 94] 
  & additionally: [111, 113, 118, 128, 140, 152, 159, 161, 171, 193, 202, 224, 248, 258, 270, 289, 301]
85-odd-limit: [77, 80, 87, 94] 
  & additionally: [111, 113, 118, 128, 130, 140, 152, 159, 171, 193, 202, 224, 258, 270, 289, 301]
87-odd-limit: [77, 80, 87, 94] 
  & additionally: [111, 113, 118, 130, 140, 152, 159, 171, 183, 202, 224, 258, 270, 289, 301]
89-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 111, 113, 118, 130, 140, 152, 159, 161, 171, 181, 183, 202, 224, 248, 258, 270, 289, 301]
91-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 111, 113, 118, 130, 140, 152, 161, 171, 181, 183, 202, 214, 217, 224, 248, 258, 270, 289, 296, 301]
93-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 111, 113, 118, 128, 130, 140, 152, 161, 171, 181, 183, 193, 202, 217, 224, 248, 258, 289, 296, 301]
95-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 106, 111, 113, 118, 128, 130, 140, 152, 161, 171, 181, 183, 193, 202, 224, 248, 258, 296, 301]
97-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 106, 111, 113, 118, 128, 130, 140, 152, 161, 171, 181, 183, 193, 202, 224, 246, 248, 258, 301]
99-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [106, 111, 113, 118, 128, 130, 140, 152, 161, 171, 181, 183, 202, 224, 246, 248, 258, 270, 301]
101-odd-limit: [77, 80, 87, 94] 
  & additionally: [106, 111, 113, 118, 128, 130, 140, 152, 161, 171, 181, 183, 193, 202, 224, 246, 248, 258, 270, 301]
103-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 106, 111, 113, 118, 128, 130, 140, 161, 171, 181, 202, 217, 224, 246, 248, 258, 270, 289, 301]
105-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [99, 106, 111, 113, 118, 128, 130, 140, 161, 171, 181, 202, 217, 224, 246, 248, 258, 270, 289, 301]
107-odd-limit: [77, 80, 84, 87, 94] 
  & additionally: [99, 106, 111, 113, 118, 128, 130, 140, 161, 171, 181, 202, 217, 224, 246, 248, 258, 270, 289, 301]
109-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 106, 108, 111, 113, 118, 128, 130, 140, 161, 171, 181, 202, 217, 224, 246, 248, 258, 270, 289, 301]
111-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 106, 108, 111, 113, 118, 128, 130, 140, 161, 171, 181, 202, 217, 224, 248, 258, 289, 296, 301]
113-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 106, 111, 113, 118, 128, 130, 140, 161, 171, 181, 202, 217, 224, 248, 258, 277, 289, 301]
115-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 111, 113, 118, 128, 130, 140, 161, 171, 181, 202, 217, 224, 246, 248, 258, 277, 289, 301, 311]
117-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 111, 113, 118, 128, 130, 140, 161, 171, 181, 193, 202, 214, 217, 224, 246, 248, 258, 277, 289, 301, 311]
119-odd-limit: [77, 80, 87, 94] 
  & additionally: [99, 111, 113, 118, 128, 130, 140, 152, 159, 161, 171, 181, 193, 202, 207, 217, 224, 229, 239, 248, 258, 277, 289, 301, 311]
121-odd-limit: [77, 80, 87, 94] 
  & additionally: [109, 111, 113, 118, 128, 130, 137, 140, 152, 159, 161, 181, 207, 217, 224, 239, 248, 270, 277, 296, 301, 311]
123-odd-limit: [77, 80, 87, 94] 
  & additionally: [106, 109, 111, 113, 118, 128, 130, 137, 140, 152, 159, 161, 181, 202, 207, 217, 224, 239, 248, 270, 277, 296, 301, 311]

# SMALLER EDOS (up to 94):
19-odd-limit: [1, 2, 3, 4, 5, 7, 9, 12, 15, 16, 19, 20, 22, 24, 36, 41, 43, 44, 50, 56, 62, 68, 72, 80, 94]
21-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 16, 20, 24, 26, 31, 33, 36, 41, 43, 50, 53, 56, 62, 68, 72, 89, 94]
23-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 16, 21, 24, 29, 31, 36, 43, 46, 50, 53, 62, 68, 77, 80, 84, 89, 94]
25-odd-limit: [1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 16, 24, 27, 28, 29, 31, 41, 43, 46, 50, 53, 62, 68, 80, 84, 94]
27-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 29, 31, 41, 46, 50, 53, 68, 72, 77, 80, 84, 87, 94]
29-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 29, 31, 34, 41, 46, 50, 53, 62, 65, 72, 77, 80, 84, 87]
31-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 29, 31, 34, 41, 46, 53, 60, 62, 65, 77, 84, 87]
33-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 29, 31, 34, 36, 41, 43, 46, 53, 60, 62, 65, 77, 84, 87]
35-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 31, 36, 41, 46, 53, 62, 65, 68, 72, 77, 84]
37-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 31, 34, 36, 41, 43, 46, 53, 62, 63, 65, 68, 72, 77, 84, 87, 94]
39-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 16, 19, 22, 24, 31, 34, 36, 38, 41, 43, 46, 53, 62, 63, 68, 72, 77, 84, 87]
41-odd-limit: [1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 14, 15, 16, 17, 19, 22, 24, 31, 34, 36, 41, 43, 46, 50, 53, 62, 65, 72, 77, 80, 84]
43-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 16, 17, 19, 22, 24, 26, 31, 40, 41, 43, 44, 46, 50, 53, 62, 63, 65, 72, 77, 80, 84]
45-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 16, 17, 19, 22, 24, 29, 31, 36, 40, 41, 43, 44, 46, 50, 53, 62, 63, 65, 72, 77, 82, 84, 87]
47-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 16, 17, 19, 22, 24, 29, 31, 36, 40, 41, 43, 50, 53, 62, 63, 65, 72, 77, 82, 84, 87]
49-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 16, 17, 19, 21, 22, 26, 31, 36, 40, 41, 43, 46, 50, 53, 58, 62, 63, 72, 77, 82, 84, 94]
51-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 21, 22, 26, 31, 41, 43, 46, 53, 58, 62, 68, 72, 77, 82, 84, 87, 94]
53-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 21, 22, 26, 27, 31, 36, 41, 43, 46, 50, 53, 56, 58, 62, 72, 77, 84, 89, 94]
55-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 21, 22, 26, 31, 40, 41, 46, 50, 53, 56, 62, 72, 77, 84, 87, 94]
57-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 26, 27, 31, 37, 40, 41, 46, 50, 53, 56, 62, 72, 77, 84, 94]
59-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 26, 27, 31, 37, 40, 41, 43, 50, 53, 62, 63, 68, 72, 77, 84, 94]
61-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 24, 26, 27, 31, 40, 41, 43, 53, 56, 62, 63, 72, 77, 84, 94]
63-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 24, 26, 31, 41, 43, 53, 56, 62, 63, 72, 77, 82, 84, 94]
65-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 31, 41, 43, 53, 56, 62, 63, 68, 72, 77, 84, 94]
67-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 43, 53, 56, 62, 63, 72, 77, 84, 87, 89, 94]
69-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 43, 53, 56, 62, 63, 72, 77, 84, 89, 94]
71-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 43, 46, 53, 56, 62, 72, 77, 82, 84, 87, 89, 94]
73-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 43, 46, 53, 62, 63, 72, 77, 84, 89, 94]
75-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 43, 46, 53, 62, 63, 72, 77, 84, 89, 94]
77-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 46, 53, 62, 63, 72, 77, 84, 87, 89, 94]
79-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 43, 46, 53, 63, 72, 77, 82, 84, 87, 89, 94]
81-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 46, 53, 63, 72, 77, 84, 87, 89, 94]
83-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 41, 46, 53, 63, 72, 77, 84, 87, 89, 94]
85-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 36, 41, 46, 53, 63, 72, 77, 84, 87, 89, 94]
87-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 36, 41, 46, 53, 63, 72, 77, 84, 87, 94]
89-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 46, 53, 63, 72, 77, 82, 84, 87, 89, 94]
91-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 46, 53, 63, 72, 77, 84, 87, 89, 94]
93-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 41, 46, 53, 62, 63, 72, 77, 82, 84, 87, 89, 94]
95-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 41, 46, 53, 62, 63, 72, 77, 84, 87, 89, 94]
97-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 27, 31, 34, 41, 46, 53, 62, 63, 72, 77, 84, 87, 94]
99-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 27, 31, 34, 36, 41, 46, 53, 63, 72, 77, 84, 87, 94]
101-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 27, 31, 34, 36, 41, 46, 53, 63, 72, 77, 84, 87, 94]
103-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 46, 53, 63, 72, 77, 84, 87, 94]
105-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 46, 53, 63, 72, 77, 84, 87, 94]
107-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 46, 53, 63, 72, 77, 84, 87, 89, 94]
109-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 43, 46, 53, 63, 65, 72, 77, 84, 87, 94]
111-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 43, 46, 53, 63, 72, 77, 84, 87, 94]
113-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 43, 46, 53, 58, 63, 72, 77, 84, 87, 89, 94]
115-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 22, 24, 26, 27, 31, 34, 36, 41, 43, 46, 53, 58, 63, 65, 72, 77, 84, 87, 94]
117-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 34, 36, 41, 43, 46, 53, 58, 63, 72, 77, 84, 87, 94]
119-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 24, 26, 27, 31, 34, 36, 41, 43, 46, 53, 58, 63, 65, 72, 77, 84, 87, 94]
121-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 24, 26, 27, 29, 31, 36, 41, 43, 46, 53, 58, 63, 65, 72, 77, 84, 87, 94]
123-odd-limit: [1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 22, 24, 26, 27, 29, 31, 36, 41, 46, 53, 58, 63, 65, 72, 77, 84, 87, 94]