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 ==
== Beyla ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 3025/3024, 4375/4374
[[Comma list]]: 385/384, 4375/4374
 
[[Mapping]]: [{{val| 1 0 0 1 6 }}, {{val| 0 1 0 7 -6 }}, {{val| 0 0 1 -4 3 }}]


[[Mapping]]: [{{val|2 0 0 2 5}}, {{val|0 1 0 7 5}}, {{val|0 0 1 -4 -3}}]
Mapping generators: ~2, ~3, ~5


Mapping generators: ~99/70, ~3, ~5
{{Val list|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}
 
[[Badness]]: 0.721 × 10<sup>-3</sup>


[[Minimax tuning]]:
=== 13-limit ===
* [[11-odd-limit]] eigenmonzos: 2, 11/10, 8/7
Subgroup: 2.3.5.7.11.13


{{Val list|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
Comma list: 169/168, 325/324, 385/384


[[Badness]]: 0.0888 × 10<sup>-3</sup>
Mapping: [{{val| 1 0 0 1 6 2 }}, {{val| 0 1 0 7 -6 4 }}, {{val| 0 0 1 -4 3 -2 }}]


Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11
Mapping generators: ~2, ~3, ~5


=== Donar ===
Vals: {{Val list| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
Subgroup: 2.3.5.7.11.13


Comma list: 3025/3024, 4225/4224, 4375/4374
Badness: 0.840 × 10<sup>-3</sup>


Mapping: [{{val|2 0 1 -2 2 7}}, {{val|0 1 0 7 5 3}}, {{val|0 0 2 -8 -6 -5}}]
== Thor ==
Subgroup: 2.3.5.7.11


Mapping generators: ~99/70, ~3, ~220/117
[[Comma list]]: 3025/3024, 4375/4374


Map to lattice: [{{val|0 2 2 6 4 1}}, {{val|0 -1 -2 1 1 2}}]
[[Mapping]]: [{{val| 2 0 0 2 5 }}, {{val| 0 1 0 7 5 }}, {{val| 0 0 1 -4 -3 }}]


Lattice basis:  
Mapping generators: ~99/70, ~3, ~5
: 44/39 length = 0.3480, 6/5 length = 0.7828
: Angle (44/39, 6/5) = 85.3977°


Minimax tuning:
[[Minimax tuning]]:
* 13-odd-limit eigenmonzos: 2, 11/10, 8/7
* [[11-odd-limit]] eigenmonzos: 2, 11/10, 8/7
* 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 }}
{{Val list|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}


Badness: 0.322 × 10<sup>-3</sup>
[[Badness]]: 0.0888 × 10<sup>-3</sup>


Scales: [[Donar46]]
Projection pairs: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11


=== Thunor ===
=== Thunor ===
Line 106: Line 107:
Badness: 0.549 × 10<sup>-3</sup>
Badness: 0.549 × 10<sup>-3</sup>


== Vidar ==
=== Donar ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13
 
Comma list: 3025/3024, 4225/4224, 4375/4374
 
Mapping: [{{val| 2 0 1 -2 2 7 }}, {{val| 0 1 0 7 5 3 }}, {{val| 0 0 2 -8 -6 -5 }}]
 
Mapping generators: ~99/70, ~3, ~220/117
 
Map to lattice: [{{val| 0 2 2 6 4 1 }}, {{val| 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°


[[Comma list]]: 4375/4374, 100663296/100656875
Minimax tuning:
* 13-odd-limit eigenmonzos: 2, 11/10, 8/7
* 15-odd-limit eigenmonzos: 2, 8/7, 15/11


[[Mapping]]: [{{val| 1 0 0 1 5 }}, {{val| 0 1 -1 11 1 }}, {{val| 0 0 5 -20 -4 }}]
Vals: {{Val list| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}


Mapping generators: ~2, ~3, ~55/32
Badness: 0.322 × 10<sup>-3</sup>


{{Val list|legend=1| 46, 224, 270, 494, 764, 1395, 1889 }}
Scales: [[Donar46]]


=== 13-limit ===
== Heimdall ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11


Comma list: 4225/4224, 4375/4374, 6656/6655
[[Comma list]]: 4375/4374, 117649/117612


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 2 }}, {{val| 0 2 0 14 37 }}, {{val| 0 0 1 -4 -12 }}]


Mapping generators: ~2, ~3, ~55/32
Mapping generators: ~2, ~343/198, ~5


Vals: {{Val list| 46, 224, 270, 494, 764, 1395, 1889 }}
{{Val list|legend=1| 270, 342, 612, 954, 1547, 1817 }}


== Bragi ==
== Bragi ==
Line 139: Line 154:
{{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 165:
Vals: {{Val list| 19, 46, 224, 270, 494, 764 }}
Vals: {{Val list| 19, 46, 224, 270, 494, 764 }}


== Beyla ==
== Vidar ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 385/384, 4375/4374
[[Comma list]]: 4375/4374, 100663296/100656875


[[Mapping]]: [{{val| 1 0 0 1 6 }}, {{val| 0 1 0 7 -6 }}, {{val| 0 0 1 -4 3 }}]
[[Mapping]]: [{{val| 1 0 0 1 5 }}, {{val| 0 1 -1 11 1 }}, {{val| 0 0 5 -20 -4 }}]


Mapping generators: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~55/32


{{Val list|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}
{{Val list|legend=1| 46, 224, 270, 494, 764, 1395, 1889 }}
 
[[Badness]]: 0.721 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 169/168, 325/324, 385/384
Comma list: 4225/4224, 4375/4374, 6656/6655


Mapping: [{{val| 1 0 0 1 6 2 }}, {{val| 0 1 0 7 -6 4 }}, {{val| 0 0 1 -4 3 -2 }}]
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, ~5
Mapping generators: ~2, ~3, ~55/32


Vals: {{Val list| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
Vals: {{Val list| 46, 224, 270, 494, 764, 1395, 1889 }}
 
Badness: 0.840 × 10<sup>-3</sup>
 
== Heimdall ==
Subgroup: 2.3.5.7.11
 
[[Comma list]]: 4375/4374, 117649/117612
 
[[Mapping]]: [{{val| 1 0 0 1 2 }}, {{val| 0 2 0 14 37 }}, {{val| 0 0 1 -4 -12 }}]
 
Mapping generators: ~2, ~343/198, ~5
 
{{Val list|legend=1| 270, 342, 612, 954, 1547, 1817 }}


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 14:38, 23 October 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°

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

Vals: 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

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

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

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]]

Mapping generators: 2, ~3, ~14/13

Vals: 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]]

Mapping generators: ~2, ~3, ~55/32

Vals: Template:Val list

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