Ragismic family: Difference between revisions
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Temperaments not discussed here include [[Breed family #Ennealimmic|ennealimmic]]. | Temperaments not discussed here include [[Breed family #Ennealimmic|ennealimmic]]. | ||
= Ragismic = | == Ragismic == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Scales: [[Ragismic19]] | Scales: [[Ragismic19]] | ||
= Thor = | == Thor == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 46: | Line 46: | ||
Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11 | Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11 | ||
== Donar == | === Donar === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 71: | Line 71: | ||
Scales: [[Donar46]] | Scales: [[Donar46]] | ||
== Thunor == | === Thunor === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.341 × 10<sup>-3</sup> | Badness: 0.341 × 10<sup>-3</sup> | ||
== Rym == | === Rym === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.549 × 10<sup>-3</sup> | Badness: 0.549 × 10<sup>-3</sup> | ||
= Vidar = | == Vidar == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 117: | Line 117: | ||
{{Val list|legend=1| 46, 224, 270, 494, 764, 1395, 1889 }} | {{Val list|legend=1| 46, 224, 270, 494, 764, 1395, 1889 }} | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 128: | Line 128: | ||
Vals: {{Val list| 46, 224, 270, 494, 764, 1395, 1889 }} | Vals: {{Val list| 46, 224, 270, 494, 764, 1395, 1889 }} | ||
= Bragi = | == Bragi == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 139: | Line 139: | ||
{{Val list|legend=1| 46, 224, 270, 494, 764, 1053, 1547 }} | {{Val list|legend=1| 46, 224, 270, 494, 764, 1053, 1547 }} | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 150: | Line 150: | ||
Vals: {{Val list| 19, 46, 224, 270, 494, 764 }} | Vals: {{Val list| 19, 46, 224, 270, 494, 764 }} | ||
= Beyla = | == Beyla == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 163: | Line 163: | ||
[[Badness]]: 0.000721 | [[Badness]]: 0.000721 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 176: | Line 176: | ||
Badness: 0.840 × 10<sup>-3</sup> | Badness: 0.840 × 10<sup>-3</sup> | ||
= Heimdall = | == Heimdall == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Revision as of 15:04, 31 May 2021
The ragismic family of temperaments are rank-3 microtemperaments which temper out 4375/4374.
Temperaments not discussed here include ennealimmic.
Ragismic
Subgroup: 2.3.5.7
Comma list: 4375/4374
Mapping: [⟨1 0 0 1], ⟨0 1 0 7], ⟨0 0 1 -4]]
Mapping generators: ~2, ~3, ~5
Map to lattice: [⟨0 -1 -1 -3], ⟨0 -1 -2 1]]
Lattice basis:
- 10/9 length = 0.789, 6/5 length = 0.921
- Angle (10/9, 6/5) = 105.299°
- 7-odd-limit eigenmonzos: 2, 8/7, 5/4
- 9-odd-limit eigenmonzos: 2, 4/3, 7/5
Projection pair: ~7 = ~4374/625
Scales: Ragismic19
Thor
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374
Mapping: [⟨2 0 0 2 5], ⟨0 1 0 7 5], ⟨0 0 1 -4 -3]]
Mapping generators: ~99/70, ~3, ~5
- 11-odd-limit eigenmonzos: 2, 11/10, 8/7
Badness: 0.0888 × 10-3
Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11
Donar
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 4225/4224, 4375/4374
Mapping: [⟨2 0 1 -2 2 7], ⟨0 1 0 7 5 3], ⟨0 0 2 -8 -6 -5]]
Mapping generators: ~99/70, ~3, ~220/117
Map to lattice: [⟨0 2 2 6 4 1], ⟨0 -1 -2 1 1 2]]
Lattice basis:
- 44/39 length = 0.3480, 6/5 length = 0.7828
- Angle (44/39, 6/5) = 85.3977°
Minimax tuning:
- 13-odd-limit eigenmonzos: 2, 11/10, 8/7
- 15-odd-limit eigenmonzos: 2, 8/7, 15/11
Vals: Template:Val list
Badness: 0.322 × 10-3
Scales: Donar46
Thunor
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3025/3024
Mapping: [⟨2 0 0 2 5 -3], ⟨0 1 0 7 5 15], ⟨0 0 1 -4 -3 -8]]
Mapping generators: ~99/70, ~3, ~5
Map to lattice: [⟨0 -1 -2 -3 -2 -7], ⟨0 -1 -2 1 1 1]]
Lattice basis:
- 10/9 length = 0.4234, 6/5 length = 0.8426
- Angle (10/9, 6/5) = 84.126°
Minimax tuning:
- 13- and 15-odd-limit eigenmonzos: 2, 16/13, 9/7
Vals: Template:Val list
Badness: 0.341 × 10-3
Rym
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 4096/4095, 4375/4374
Mapping: [⟨2 0 0 2 5 22], ⟨0 1 0 7 5 -9], ⟨0 0 1 -4 -3 3]]
Mapping generators: ~99/70, ~3, ~5
Vals: Template:Val list
Badness: 0.549 × 10-3
Vidar
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 100663296/100656875
Mapping: [⟨1 0 0 1 5], ⟨0 1 -1 11 1], ⟨0 0 5 -20 -4]]
Mapping generators: ~2, ~3, ~55/32
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 4225/4224, 4375/4374, 6656/6655
Mapping: [⟨1 0 0 1 5 6], ⟨0 1 -1 11 1 2], ⟨0 0 5 -20 -4 -7]]
Mapping generators: ~2, ~3, ~55/32
Vals: Template:Val list
Bragi
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 2097152/2096325
Mapping: [⟨1 0 2 -7 8], ⟨0 1 0 7 -3], ⟨0 0 3 -12 2]]
Mapping generators: 2, ~3, ~320/297
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4375/4374, 10985/10976
Mapping: [⟨1 0 2 -7 8 -6], ⟨0 1 0 7 -3 7], ⟨0 0 3 -12 2 -13]]
Mapping generators: 2, ~3, ~14/13
Vals: Template:Val list
Beyla
Subgroup: 2.3.5.7.11
Comma list: 385/384, 4375/4374
Mapping: [⟨1 0 0 1 6], ⟨0 1 0 7 -6], ⟨0 0 1 -4 3]]
Mapping generators: ~2, ~3, ~5
Badness: 0.000721
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 385/384
Mapping: [⟨1 0 0 1 6 2], ⟨0 1 0 7 -6 4], ⟨0 0 1 -4 3 -2]]
Mapping generators: ~2, ~3, ~5
Vals: Template:Val list
Badness: 0.840 × 10-3
Heimdall
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 117649/117612
Mapping: [⟨1 0 0 1 2], ⟨0 2 0 14 37], ⟨0 0 1 -4 -12]]
Mapping generators: ~2, ~343/198, ~5