Porwell family: Difference between revisions

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Line 7: Line 7:
[[Comma list]]: [[6144/6125]]
[[Comma list]]: [[6144/6125]]


[[Mapping]]: [<1 0 1 4|, <0 1 1 -1|, <0 0 -2 3|]
[[Mapping]]: [{{val| 1 0 1 4 }}, {{val| 0 1 1 -1 }}, {{val| 0 0 -2 3 }}]


Mapping generators: ~2, ~3, ~35/32
Mapping generators: ~2, ~3, ~35/32


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit ]]
* 7- and [[9-odd-limit]]
: [|1 0 0 0>, |0 1 0 0>, |11/5 1/5 2/5 -2/5>, |11/5 1/5 -3/5 3/5>]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 11/5 1/5 2/5 -2/5 }}, {{monzo| 11/5 1/5 -3/5 3/5 }}]
: Eigenmonzos: 4/3, 7/5
: [[Eigenmonzo]]s: 4/3, 7/5


{{Val list|legend=1| 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 229, 251, 282, 381 }}
{{Val list|legend=1| 6, 7, 8, 9, 15, 16, 22, 23, 24, 31, 37, 38, 39, 40, 46, 47, 53, 55, 59, 68, 75, 77, 84, 99, 229, 251, 282, 381 }}
Line 27: Line 27:
[[Comma list]]: 121/120, 176/175
[[Comma list]]: 121/120, 176/175


[[Mapping]]: [<1 0 1 4 2|, <0 1 1 -1 1|, <0 0 -2 3 1|]
[[Mapping]]: [{{val| 1 0 1 4 2 }}, {{val| 0 1 1 -1 1 }}, {{val| 0 0 -2 3 1 }}]


Mapping generators: 2, 3, 11/10
Mapping generators: 2, 3, 11/10


Map to lattice: [<0 1 -1 2 0|, <0 1 1 -1 1|]
Map to lattice: [{{val| 0 1 -1 2 0 }}, {{val| 0 1 1 -1 1 }}]


Lattice basis:  
Lattice basis:  
Line 39: Line 39:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [|1 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0>, |22/9 2/9 1/3 -4/9 0>, |22/9 2/9 -2/3 5/9 0>, |10/3 2/3 0 -1/3 0>]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 10/9 -1/3 -2/9 0 }}, {{monzo| 22/9 2/9 1/3 -4/9 0 }}, {{monzo| 22/9 2/9 -2/3 5/9 0 }}, {{monzo| 10/3 2/3 0 -1/3 0 }}]
: [[Eigenmonzo]]s: 2, 9/7, 7/5
: [[Eigenmonzo]]s: 2, 9/7, 7/5


Line 66: Line 66:
Comma list: 121/120, 176/175, 351/350
Comma list: 121/120, 176/175, 351/350


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


Mapping generators: 2, 3, 11/10
Mapping generators: ~2, ~3, ~11/10


Map to lattice: [<0 1 -1 2 0 -3|, <0 1 1 -1 1 -2|]
Map to lattice: [{{val| 0 1 -1 2 0 -3 }}, {{val| 0 1 1 -1 1 -2 }}]


Lattice basis:  
Lattice basis:  
Line 78: Line 78:
Minimax tuning:  
Minimax tuning:  
* 13-odd-limit  
* 13-odd-limit  
: [|1 0 0 0 0 0>, |11/9 10/9 -1/3 -2/9 0 0>, |22/9 2/9 1/3 -4/9 0 0>, |22/9 2/9 -2/3 5/9 0 0>, |10/3 2/3 0 -1/3 0 0>, |14/3 -8/3 1 1/3 0 0>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 11/9 10/9 -1/3 -2/9 0 0 }}, {{monzo| 22/9 2/9 1/3 -4/9 0 0 }}, {{monzo| 22/9 2/9 -2/3 5/9 0 0 }}, {{monzo| 10/3 2/3 0 -1/3 0 0 }}, {{monzo| 14/3 -8/3 1 1/3 0 0 }}]
: Eigenmonzos: 2, 9/7, 7/5
: Eigenmonzos: 2, 9/7, 7/5
* 15-odd-limit
* 15-odd-limit
: [|1 0 0 0 0 0>, |0 1 0 0 0 0>, |11/5 1/5 2/5 -2/5 0 0>,|11/5 1/5 -3/5 3/5 0 0>, |13/5 3/5 1/5 -1/5 0 0>, |38/5 -12/5 1/5 -1/5 0 0>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 11/5 1/5 2/5 -2/5 0 0 }}, {{monzo| 11/5 1/5 -3/5 3/5 0 0 }}, {{monzo| 13/5 3/5 1/5 -1/5 0 0 }}, {{monzo| 38/5 -12/5 1/5 -1/5 0 0 }}]
: Eigenmonzos: 2, 4/3, 7/5
: Eigenmonzos: 2, 4/3, 7/5


Line 98: Line 98:
Comma list: 66/65, 121/120, 176/175
Comma list: 66/65, 121/120, 176/175


Mapping: [<1 0 1 4 2 2|, <0 1 1 -1 1 1|, <0 0 -2 3 -1 -1|]
Mapping: [{{val| 1 0 1 4 2 2 }}, {{val| 0 1 1 -1 1 1 }}, {{val| 0 0 -2 3 -1 -1 }}]


Vals: {{Val list| 7, 9, 15, 24, 31, 77f, 108ef }}
Vals: {{Val list| 7, 9, 15, 24, 31, 77f, 108ef }}
Line 109: Line 109:
[[Comma list]]: 540/539, 5632/5625
[[Comma list]]: 540/539, 5632/5625


[[Mapping]]: [<1 0 1 4 -5|, <0 1 1 -1 6|, <0 0 2 -3 8|]
[[Mapping]]: [{{val| 1 0 1 4 -5 }}, {{val| 0 1 1 -1 6 }}, {{val| 0 0 2 -3 8 }}]


{{Val list|legend=1| 9, 22, 31, 53, 99e, 108, 121, 130, 152, 282, 434de, 465d, 617de, 747def, 899def }}
{{Val list|legend=1| 9, 22, 31, 53, 99e, 108, 121, 130, 152, 282, 434de, 465d, 617de, 747def, 899def }}

Revision as of 12:51, 14 June 2021

The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.

Hewuermity

Subgroup: 2.3.5.7

Comma list: 6144/6125

Mapping: [⟨1 0 1 4], ⟨0 1 1 -1], ⟨0 0 -2 3]]

Mapping generators: ~2, ~3, ~35/32

Minimax tuning:

[[1 0 0 0⟩, [0 1 0 0⟩, [11/5 1/5 2/5 -2/5⟩, [11/5 1/5 -3/5 3/5⟩]
Eigenmonzos: 4/3, 7/5

Template:Val list

Badness: 0.142 × 10-3

Projection pairs: 3 6125/2048 to 2.5.7

Zeus

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175

Mapping: [⟨1 0 1 4 2], ⟨0 1 1 -1 1], ⟨0 0 -2 3 1]]

Mapping generators: 2, 3, 11/10

Map to lattice: [⟨0 1 -1 2 0], ⟨0 1 1 -1 1]]

Lattice basis:

11/10, 11/8
Angle (11/10, 11/8) = 87.464 degrees

Minimax tuning:

[[1 0 0 0 0⟩, [11/9 10/9 -1/3 -2/9 0⟩, [22/9 2/9 1/3 -4/9 0⟩, [22/9 2/9 -2/3 5/9 0⟩, [10/3 2/3 0 -1/3 0⟩]
Eigenmonzos: 2, 9/7, 7/5

Template:Val list

Badness: 0.400 × 10-3

Projection pairs: 5 600/121 7 2662/375 11 120/11 to 2.3.11/5

Zeus11[22] hobbit transversal

33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,
11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,
11/6, 15/8, 64/33, 2

Zeus11[24] hobbit transversal

33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,
11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,
11/6, 15/8, 64/33, 2

Scales:

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 176/175, 351/350

Mapping: [⟨1 0 1 4 2 7], ⟨0 1 1 -1 1 -2], ⟨0 0 -2 3 -1 -1]]

Mapping generators: ~2, ~3, ~11/10

Map to lattice: [⟨0 1 -1 2 0 -3], ⟨0 1 1 -1 1 -2]]

Lattice basis:

11/10 length = 0.7898, 11/8 length = 1.002
Angle (11/10, 11/8) = 106.7439 degrees

Minimax tuning:

  • 13-odd-limit
[[1 0 0 0 0 0⟩, [11/9 10/9 -1/3 -2/9 0 0⟩, [22/9 2/9 1/3 -4/9 0 0⟩, [22/9 2/9 -2/3 5/9 0 0⟩, [10/3 2/3 0 -1/3 0 0⟩, [14/3 -8/3 1 1/3 0 0⟩]
Eigenmonzos: 2, 9/7, 7/5
  • 15-odd-limit
[[1 0 0 0 0 0⟩, [0 1 0 0 0 0⟩, [11/5 1/5 2/5 -2/5 0 0⟩, [11/5 1/5 -3/5 3/5 0 0⟩, [13/5 3/5 1/5 -1/5 0 0⟩, [38/5 -12/5 1/5 -1/5 0 0⟩]
Eigenmonzos: 2, 4/3, 7/5

Vals: Template:Val list

Badness: 0.934 × 10-3

Projection pairs: 5 600/121 7 2662/375 11 120/11 13 1280/99 to 2.3.11/5

Zeus13[22] hobbit transversal

260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2

Tinia

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 121/120, 176/175

Mapping: [⟨1 0 1 4 2 2], ⟨0 1 1 -1 1 1], ⟨0 0 -2 3 -1 -1]]

Vals: Template:Val list

Badness: 0.808 × 10-3

Jupiter

Subgroup: 2.3.5.7.11

Comma list: 540/539, 5632/5625

Mapping: [⟨1 0 1 4 -5], ⟨0 1 1 -1 6], ⟨0 0 2 -3 8]]

Template:Val list

Badness: 0.562 × 10-3

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