Ragismic family: Difference between revisions

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GPV sequences
Line 50: Line 50:
Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~5


Vals: {{Val list| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
Optimal GPV sequence: {{Val list| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}


Badness: 0.840 × 10<sup>-3</sup>
Badness: 0.840 × 10<sup>-3</sup>
Line 90: Line 90:
* 13- and 15-odd-limit eigenmonzos: 2, 16/13, 9/7
* 13- and 15-odd-limit eigenmonzos: 2, 16/13, 9/7


Vals: {{Val list| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}
Optimal GPV sequence: {{Val list| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}


Badness: 0.341 × 10<sup>-3</sup>
Badness: 0.341 × 10<sup>-3</sup>
Line 103: Line 103:
Mapping generators: ~99/70, ~3, ~5
Mapping generators: ~99/70, ~3, ~5


Vals: {{Val list| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}
Optimal GPV sequence: {{Val list| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}


Badness: 0.549 × 10<sup>-3</sup>
Badness: 0.549 × 10<sup>-3</sup>
Line 126: Line 126:
* 15-odd-limit eigenmonzos: 2, 8/7, 15/11
* 15-odd-limit eigenmonzos: 2, 8/7, 15/11


Vals: {{Val list| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}
Optimal GPV sequence: {{Val list| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}


Badness: 0.322 × 10<sup>-3</sup>
Badness: 0.322 × 10<sup>-3</sup>
Line 141: Line 141:
Mapping generators: ~2, ~343/198, ~5
Mapping generators: ~2, ~343/198, ~5


{{Val list|legend=1| 270, 342, 612, 954, 1547, 1817 }}
{{Val list|legend=1| 72, 198, 270, 342, 612, 954, 1205, 1475, 1547, 1817, 2159, 4660, 4930, 6819, 7089, 9590d, 11749d }}


== Bragi ==
== Bragi ==
Line 150: Line 150:
[[Mapping]]: [{{val| 1 0 2 -7 8 }}, {{val| 0 1 0 7 -3 }}, {{val| 0 0 3 -12 2 }}]
[[Mapping]]: [{{val| 1 0 2 -7 8 }}, {{val| 0 1 0 7 -3 }}, {{val| 0 0 3 -12 2 }}]


Mapping generators: 2, ~3, ~320/297
Mapping generators: ~2, ~3, ~320/297


{{Val list|legend=1| 46, 224, 270, 494, 764, 1053, 1547 }}
{{Val list|legend=1| 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee }}


=== 13-limit ===
=== 13-limit ===
Line 161: Line 161:
Mapping: [{{val| 1 0 2 -7 8 -6 }}, {{val| 0 1 0 7 -3 7 }}, {{val| 0 0 3 -12 2 -13 }}]
Mapping: [{{val| 1 0 2 -7 8 -6 }}, {{val| 0 1 0 7 -3 7 }}, {{val| 0 0 3 -12 2 -13 }}]


Mapping generators: 2, ~3, ~14/13
Optimal GPV sequence: {{Val list| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}
 
Vals: {{Val list| 19, 46, 224, 270, 494, 764 }}


== Vidar ==
== Vidar ==
Line 174: Line 172:
Mapping generators: ~2, ~3, ~55/32
Mapping generators: ~2, ~3, ~55/32


{{Val list|legend=1| 46, 224, 270, 494, 764, 1395, 1889 }}
{{Val list|legend=1| 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894 }}


=== 13-limit ===
=== 13-limit ===
Line 183: Line 181:
Mapping: [{{val| 1 0 0 1 5 6 }}, {{val| 0 1 -1 11 1 2 }}, {{val| 0 0 5 -20 -4 -7 }}]
Mapping: [{{val| 1 0 0 1 5 6 }}, {{val| 0 1 -1 11 1 2 }}, {{val| 0 0 5 -20 -4 -7 }}]


Mapping generators: ~2, ~3, ~55/32
Optimal GPV sequence: {{Val list| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}
 
Vals: {{Val list| 46, 224, 270, 494, 764, 1395, 1889 }}


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Ragismic family| ]] <!-- main article -->
[[Category:Ragismic family| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Rank 3]]

Revision as of 16:18, 11 March 2022

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

Mapping 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°

Minimax tuning:

Template:Val list

Projection pair: ~7 = ~4374/625

Scales: Ragismic19

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

Template:Val list

Badness: 0.721 × 10-3

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

Optimal GPV sequence: Template:Val list

Badness: 0.840 × 10-3

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

Minimax tuning:

Template:Val list

Badness: 0.0888 × 10-3

Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11

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

Mapping 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.549 × 10-3

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

Mapping 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

Optimal GPV sequence: Template:Val list

Badness: 0.322 × 10-3

Scales: Donar46

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

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

Template:Val list

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]]

Optimal GPV sequence: Template:Val list

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

Template:Val list

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]]

Optimal GPV sequence: Template:Val list

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