Talk:Marvel
Subheadings for scales
I suggest this although I realize that an extensive table of contents has a certain repellent effect on some readers. What do you think? --Xenwolf (talk) 09:42, 1 June 2021 (UTC)
Challenge on optimality of 53edo for FloraC
53edo is consistent in the 7-limited 105-odd-limit except for two interval pairs (50/49 and 75/49 and their octave-complements). Can any other edo tuning of marvel even come close to this faithful of a representation of the 7-limit lattice? 72edo does better with only one inconsistent interval pair in the 125-odd-limit (128/125 and its octave-complement, unsurprisingly), but it's optimized for different things than just pure marvel. Similarly 41edo does even better in terms of consistency but it's clearly more overtempered than 72edo. I also don't believe that the inconsistency of 50/49 and 75/49 are particularly important, except for the damage on 7/5 and 10/7 which as far as I can tell is the only real flaw of 53edo's marvel.
Here is how every edo up to and including 240 which tempers out 225/224 with a consistent 9-odd-limit performs in the 105-odd-limit, which seems the largest 7-limited odd-limit that is reasonable to consider because 125 is obviously gonna cause inconsistencies in most tunings as 5 is the most tempered prime in marvel cuz of 32/25 = 9/7 and 7/6 = 75/64 among others.
>>> for edo in range(1,241): # using https://en.xen.wiki/w/User:Godtone#My_Python_3_code
... if inconsistent_ivs_by_val(odd_lim(9),val(lim(7),ed(edo)))==[] and pval(S(15),ed(edo))==0:
... print(edo,'EDO:',', '.join([ striv(x) for x in inconsistent_ivs_by_val( odd_lim(9,[],[15,21,25,27,35,45,49,63,75,81,105]), val(lim(7),ed(edo)) ) ])+'\n')
...
12 EDO: 49/48, 49/45, 54/49, 81/70, 98/81, 60/49, 35/27, 64/49, 49/36, 72/49, 49/32, 54/35, 49/30, 81/49, 140/81, 49/27, 90/49, 96/49
19 EDO: 64/63, 49/48, 128/105, 49/40, 64/49, 49/32, 80/49, 105/64, 96/49, 63/32
22 EDO: 81/80, 50/49, 27/25, 25/21, 49/40, 100/81, 63/50, 81/64, 80/63, 98/75, 75/49, 63/40, 128/81, 100/63, 81/50, 80/49, 42/25, 50/27, 49/25, 160/81
29 EDO: 49/48, 36/35, 28/27, 25/24, 27/25, 49/45, 35/32, 54/49, 81/70, 75/64, 98/81, 128/105, 60/49, 100/81, 32/25, 35/27, 64/49, 49/36, 48/35, 112/81, 25/18, 36/25, 81/56, 35/24, 72/49, 49/32, 54/35, 25/16, 81/50, 49/30, 105/64, 81/49, 128/75, 140/81, 49/27, 64/35, 90/49, 50/27, 48/25, 27/14, 35/18, 96/49
31 EDO: 81/80, 81/70, 100/81, 81/64, 112/81, 81/56, 128/81, 81/50, 140/81, 160/81
41 EDO:
50 EDO: 81/80, 64/63, 50/49, 21/20, 27/25, 81/70, 32/27, 128/105, 49/40, 100/81, 63/50, 81/64, 80/63, 64/49, 21/16, 27/20, 112/81, 45/32, 64/45, 81/56, 40/27, 32/21, 49/32, 63/40, 128/81, 100/63, 81/50, 80/49, 105/64, 27/16, 140/81, 50/27, 40/21, 49/25, 63/32, 160/81
53 EDO: 50/49, 98/75, 75/49, 49/25
60 EDO: 64/63, 49/48, 36/35, 25/24, 35/32, 54/49, 75/64, 128/105, 49/40, 32/25, 64/49, 21/16, 49/36, 48/35, 45/32, 64/45, 35/24, 72/49, 32/21, 49/32, 25/16, 80/49, 105/64, 128/75, 49/27, 64/35, 48/25, 35/18, 96/49, 63/32
72 EDO:
82 EDO: 81/80, 36/35, 25/24, 27/25, 35/32, 54/49, 28/25, 81/70, 75/64, 25/21, 98/81, 128/105, 100/81, 63/50, 32/25, 35/27, 75/56, 48/35, 25/18, 36/25, 35/24, 112/75, 54/35, 25/16, 100/63, 81/50, 105/64, 81/49, 42/25, 128/75, 140/81, 25/14, 49/27, 64/35, 50/27, 48/25, 35/18, 160/81
84 EDO: 81/80, 49/48, 28/27, 49/45, 54/49, 81/70, 98/81, 60/49, 81/64, 35/27, 98/75, 49/36, 112/81, 81/56, 72/49, 75/49, 54/35, 128/81, 49/30, 81/49, 140/81, 49/27, 90/49, 27/14, 96/49, 160/81
91 EDO: 81/80, 64/63, 49/48, 16/15, 35/32, 75/64, 32/27, 128/105, 49/40, 81/64, 80/63, 32/25, 64/49, 21/16, 48/35, 45/32, 64/45, 35/24, 32/21, 49/32, 25/16, 63/40, 128/81, 80/49, 105/64, 27/16, 128/75, 64/35, 15/8, 96/49, 63/32, 160/81
94 EDO: 50/49, 25/24, 27/25, 28/25, 75/64, 25/21, 100/81, 63/50, 32/25, 98/75, 75/56, 25/18, 36/25, 112/75, 75/49, 25/16, 100/63, 81/50, 42/25, 128/75, 25/14, 50/27, 48/25, 49/25
113 EDO: 25/24, 35/32, 28/25, 75/64, 128/105, 32/25, 75/56, 48/35, 25/18, 45/32, 64/45, 36/25, 35/24, 112/75, 25/16, 105/64, 128/75, 25/14, 64/35, 48/25
125 EDO: 50/49, 49/45, 54/49, 28/25, 75/64, 98/81, 60/49, 56/45, 98/75, 75/56, 112/81, 81/56, 112/75, 75/49, 45/28, 49/30, 81/49, 128/75, 25/14, 49/27, 90/49, 49/25
144 EDO: 81/80, 64/63, 16/15, 35/32, 75/64, 32/27, 128/105, 56/45, 81/64, 32/25, 64/49, 75/56, 112/81, 45/32, 64/45, 81/56, 112/75, 49/32, 25/16, 128/81, 45/28, 105/64, 27/16, 128/75, 64/35, 15/8, 63/32, 160/81
166 EDO: 50/49, 25/24, 16/15, 15/14, 27/25, 49/45, 28/25, 75/64, 25/21, 128/105, 60/49, 56/45, 63/50, 32/25, 98/75, 75/56, 25/18, 45/32, 64/45, 36/25, 112/75, 75/49, 25/16, 100/63, 45/28, 49/30, 105/64, 42/25, 128/75, 25/14, 90/49, 50/27, 28/15, 15/8, 48/25, 49/25
197 EDO: 81/80, 64/63, 50/49, 28/27, 25/24, 16/15, 15/14, 49/45, 54/49, 28/25, 75/64, 32/27, 25/21, 98/81, 128/105, 60/49, 56/45, 81/64, 32/25, 98/75, 75/56, 112/81, 45/32, 64/45, 81/56, 112/75, 75/49, 25/16, 128/81, 45/28, 49/30, 105/64, 81/49, 42/25, 27/16, 128/75, 25/14, 49/27, 90/49, 28/15, 15/8, 48/25, 27/14, 49/25, 63/32, 160/81