Limmic temperaments
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
Limmic temperaments are temperaments that temper out the Pythagorean limma, 256/243. As a consequence, 3/2 is always represented by 3\5, 720 cents assuming pure octaves. While quite sharp, this is close enough to a just fifth to serve as a fifth, and some people are fond of it.
Blacksmith
5-limit (blackwood)
Subgroup: 2.3.5
Comma list: 256/243
Mapping: [⟨5 8 0], ⟨0 0 1]]
- mapping generators: ~9/8, ~5
Optimal tuning (POTE): ~9/8 = 1\5, ~5/4 = 399.594
Optimal ET sequence: 5, 10, 15
Badness: 0.063760
Blackwood major scale in 15edo
7-limit
Subgroup: 2.3.5.7
Comma list: 28/27, 49/48
Mapping: [⟨5 8 0 14], ⟨0 0 1 0]]
Wedgie: ⟨⟨ 0 5 0 8 0 -14 ]]
Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 392.767
Optimal ET sequence: 5, 10, 15, 40b, 55b
Badness: 0.025640
11-limit
Subgroup: 2.3.5.7.11
Comma list: 28/27, 49/48, 55/54
Mapping: [⟨5 8 0 14 29], ⟨0 0 1 0 -1]]
Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 394.948
Optimal ET sequence: 5, 10, 15, 40be, 55be, 70bde, 85bcde
Badness: 0.024641
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 49/48, 55/54
Mapping: [⟨5 8 0 14 29 7], ⟨0 0 1 0 -1 1]]
Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 391.037
Optimal ET sequence: 5, 10, 15, 25e, 40bef
Badness: 0.020498
Farrier
Subgroup: 2.3.5.7.11
Comma list: 28/27, 49/48, 77/75
Mapping: [⟨5 8 0 14 -6], ⟨0 0 1 0 2]]
Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 398.070
Optimal ET sequence: 5e, 10e, 15
Badness: 0.029200
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 28/27, 40/39, 49/48, 66/65
Mapping: [⟨5 8 0 14 -6 7], ⟨0 0 1 0 2 1]]
Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 396.812
Optimal ET sequence: 5e, 10e, 15
Badness: 0.022325
Ferrum
Subgroup: 2.3.5.7.11
Comma list: 28/27, 35/33, 49/48
Mapping: [⟨5 8 0 14 6], ⟨0 0 1 0 1]]
Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 374.763
Badness: 0.030883
Blackweed
Blackweed is a variant of blackwood as it tempers out 256/243 alike but in the 2.3.11/7 subgroup. 20edo is close to the optimum, which has 4\20 as the period and 420¢ as the generator.
Subgroup: 2.3.11/7
Comma list: [8 -5⟩ = 256/243
Sval mapping: [⟨5 8 0], ⟨0 0 1]]
- sval mapping generators: ~9/8, ~11/7
Optimal tuning (subgroup POTE): ~11/7 = 786.2215