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: 0.721649
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: 0.004906
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:
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: