User:Francium/Mirroring Numbers
Mirroring Numbers is an ongoing project started on 29th March, 2023 in which I tried to use rank-2 temperaments, using following rules:
- The numbers must mirror each other (e. g. 13&31)
- At least one number should be a prime.
The combinations I used resulted in following rank-2 temperaments:
13 & 31
Subgroup: 2.3.5/3
Comma list: [-7 11 -14⟩
Mapping: [⟨1 7 5], ⟨0 -14 -11]]
Mapping generators: 1202.1405, 465.8199
Optimal tuning (POTE): 1200.0000, 464.9905
Optimal ET sequence: 18*, 31, 49*, 80*
Badness: 49.143
14 & 41
Name: Quadbizo
Subgroup: 2.3.7
Comma list: [-5 -11 8⟩
Mapping: [⟨1 1 2], ⟨0 8 11]]
Mapping generators: 1200.1746, 87.8432
Optimal tuning (POTE): 1200.0000, 87.8304
Optimal ET sequence: 13d, 14, 27, 41
Badness: 2.622
2.3.7.11 subgroup
Comma list: 243/242, 2401/2376, 21609/21296, 26411/26244
Mapping: [⟨1 1 2 2], ⟨0 8 11 20]]
Optimal tuning (POTE): 1200.0000, 87.6512
Optimal ET sequence: 13dee, 14, 27e, 41, 96d, 137d, 178d
Badness: 0.815
2.3.7.11.17 subgroup
Comma list: 154/153, 189/187, 243/242, 294/289, 2401/2376, 5831/5808
Mapping: [⟨1 1 2 2 3], ⟨0 8 11 20 15]]
Optimal tuning (POTE): 1200.0000, 87.6541
Optimal ET sequence: 13deeg, 14, 27eg, 41
Badness: 0.811
16 & 61
Subgroup: 2.3.5.13
Comma list: [11 3 -2 -3⟩, [2 2 -7 3⟩, [13 5 -9 0⟩, [-9 -1 -5 6⟩
Mapping: [⟨1 10 7 9], ⟨0 -27 -15 -17]]
Mapping generators: 1199.4251, 373.8106
Optimal tuning (POTE): 1200.0000, 373.9898
Optimal ET sequence: 16, 61, 77, 93, 109b, 170, 247
Badness: 4.544
17 & 71
Subgroup: 2.25.11.13
Comma list: 2200/2197, 8192/8125
Mapping: [⟨1 5 1 3], ⟨0 -1 7 2]
Mapping generators: 1199.3097, 421.7111
Optimal tuning (POTE): 1200.0000, 421.9538
Optimal ET sequence: 17, 20, 23e, 37, 54, 57, 71, 91, 94
Badness: 0.526
19 & 91
Name: Catakleismic
Subgroup: 2.3.5.7
Comma list: 225/224, 4375/4374
Mapping: [⟨1 0 1 -3], ⟨0 6 5 23]
Mapping generators: 1200.5972, 316.8895
Optimal tuning (POTE): 1200.0000, 316.7318
Optimal ET sequence: 19, 23dd, 53, 72, 91, 110d, 125, 163d, 178, 197, 269c
Badness: 0.544