Limmic temperaments: Difference between revisions
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[[Badness]]: 0.063760 | [[Badness]]: 0.063760 | ||
== Blacksmith == | === Blacksmith === | ||
[[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of blacksmith]] | [[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of blacksmith]] | ||
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[[Badness]]: 0.025640 | [[Badness]]: 0.025640 | ||
=== 11-limit === | ==== 11-limit ==== | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 48: | Line 48: | ||
Badness: 0.024641 | Badness: 0.024641 | ||
==== 13-limit ==== | ===== 13-limit ===== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 61: | Line 61: | ||
Badness: 0.020498 | Badness: 0.020498 | ||
=== Farrier === | ==== Farrier ==== | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 74: | Line 74: | ||
Badness: 0.029200 | Badness: 0.029200 | ||
==== 13-limit ==== | ===== 13-limit ===== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 87: | Line 87: | ||
Badness: 0.022325 | Badness: 0.022325 | ||
=== Ferrum === | ==== Ferrum ==== | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Revision as of 14:42, 26 September 2021
The limma family tempers out the Pythagorean limma, 256/243. As a consequence, the 3/2 is always represented by 3\5, 720 cents. While quite sharp, this is close enough to a just fifth to serve as one, and some people are fond of it.
Blackwood
Subgroup: 2.3.5
Comma list: 256/243
Mapping: [⟨5 8 0], ⟨0 0 1]]
Mapping generators: ~9/8, ~5
POTE generator: ~5/4 = 399.594
Badness: 0.063760
Blacksmith
Subgroup: 2.3.5.7
Comma list: 28/27, 49/48
Mapping: [⟨5 8 0 14], ⟨0 0 1 0]]
Mapping generators: ~7/6, ~5
Wedgie: ⟨⟨ 0 5 0 8 0 -14 ]]
POTE generator: ~5/4 = 392.767
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]]
POTE generator: ~5/4 = 394.948
Vals: Template:Val list
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]]
POTE generator: ~5/4 = 391.037
Vals: Template:Val list
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]]
POTE generator: ~5/4 = 398.070
Vals: Template:Val list
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]]
POTE generator: ~5/4 = 396.812
Vals: Template:Val list
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]]
POTE generator: ~5/4 = 374.763
Vals: Template:Val list
Badness: 0.030883