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:

1. The numbers must mirror each other (e. g. 13&31)
2. 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: