Porwell family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled
5,160 edits
adding parenthetical "(unchanged intervals)" to eigenmonzo lists
+semiporwell
Line 1: Line 1:
__FORCETOC__
The '''porwell family''' of rank-3 temperaments tempers out the porwell comma, {{monzo| 11 1 -3 -2 }} = [[6144/6125]].
The '''porwell family''' of rank three temperaments tempers out the porwell comma, {{monzo| 11 1 -3 -2 }} = [[6144/6125]].


== Hewuermity ==
== Hewuermity ==
Line 10: Line 9:


Mapping generators: ~2, ~3, ~35/32
Mapping generators: ~2, ~3, ~35/32
[[POTE generator]]s: ~3/2 = 702.3482, ~35/32 = 157.4677


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 29: Line 30:
[[Mapping]]: [{{val| 1 0 1 4 2 }}, {{val| 0 1 1 -1 1 }}, {{val| 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: [{{val| 0 1 -1 2 0 }}, {{val| 0 1 1 -1 1 }}]
Map to lattice: [{{val| 0 1 -1 2 0 }}, {{val| 0 1 1 -1 1 }}]
Line 36: Line 37:
: 11/10, 11/8
: 11/10, 11/8
: Angle (11/10, 11/8) = 87.464 degrees
: Angle (11/10, 11/8) = 87.464 degrees
[[POTE generator]]s: ~3/2 = 702.1530, ~11/10 = 157.0881


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 67: Line 70:


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


Map to lattice: [{{val| 0 1 -1 2 0 -3 }}, {{val| 0 1 1 -1 1 -2 }}]
Map to lattice: [{{val| 0 1 -1 2 0 -3 }}, {{val| 0 1 1 -1 1 -2 }}]
Line 75: Line 76:
: 11/10 length = 0.7898, 11/8 length = 1.002
: 11/10 length = 0.7898, 11/8 length = 1.002
: Angle (11/10, 11/8) = 106.7439 degrees
: Angle (11/10, 11/8) = 106.7439 degrees
POTE generators: ~3/2 = 701.8679, ~11/10 = 156.9582


Minimax tuning:  
Minimax tuning:  
Line 99: Line 102:


Mapping: [{{val| 1 0 1 4 2 2 }}, {{val| 0 1 1 -1 1 1 }}, {{val| 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 }}]
POTE generators: ~3/2 = 699.3420, ~11/10 = 155.3666


Vals: {{Val list| 7, 9, 15, 22f, 24, 31 }}
Vals: {{Val list| 7, 9, 15, 22f, 24, 31 }}
Line 104: Line 109:
Badness: 0.808 × 10<sup>-3</sup>
Badness: 0.808 × 10<sup>-3</sup>


== Jupiter ==
== Jupiter ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 540/539, 5632/5625
[[Comma list]]: 540/539, 5632/5625


[[Mapping]]: [{{val| 1 0 1 4 -5 }}, {{val| 0 1 1 -1 6 }}, {{val| 0 0 2 -3 8 }}]
[[Mapping]]: [{{val| 1 0 1 4 -5 }}, {{val| 0 1 1 -1 6 }}, {{val| 0 0 -2 3 -8 }}]
 
Mapping generators: ~2, ~3, ~35/32


{{Val list|legend=1| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }}
{{Val list|legend=1| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }}


[[Badness]]: 0.562 × 10<sup>-3</sup>
[[Badness]]: 0.562 × 10<sup>-3</sup>
== Semiporwell ==
Subgroup: 2.3.5.7.11
[[Comma list]]: 6144/6125, 9801/9800
[[Mapping]]: [{{val| 2 0 0 11 14 }}, {{val| 0 1 1 -1 -2 }}, {{val| 0 0 2 -3 -1 }}]
Mapping generators: ~99/70, ~3/2, ~128/99
[[POTE generator]]s: ~3/2 = 702.4613, ~128/99 = 442.4903
{{Val list|legend=1| 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee }}
[[Badness]]: 1.253 × 10<sup>-3</sup>
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3584/3575
Mapping: [{{val| 2 0 0 11 14 15 }}, {{val| 0 1 1 -1 -2 -1 }}, {{val| 0 0 2 -3 -1 -6 }}]
POTE generators: ~3/2 = 702.3964, ~128/99 = 442.5902
Vals: {{Val list| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }}
Badness: 1.220 × 10<sup>-3</sup>


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

Revision as of 11:57, 10 October 2021

The porwell family of rank-3 temperaments tempers out the porwell comma, [11 1 -3 -2⟩ = 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

POTE generators: ~3/2 = 702.3482, ~35/32 = 157.4677

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 (unchanged intervals): 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

POTE generators: ~3/2 = 702.1530, ~11/10 = 157.0881

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 (unchanged intervals): 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]]

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

POTE generators: ~3/2 = 701.8679, ~11/10 = 156.9582

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 (unchanged intervals): 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 (unchanged intervals): 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]]

POTE generators: ~3/2 = 699.3420, ~11/10 = 155.3666

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]]

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

Template:Val list

Badness: 0.562 × 10-3

Semiporwell

Subgroup: 2.3.5.7.11

Comma list: 6144/6125, 9801/9800

Mapping: [⟨2 0 0 11 14], ⟨0 1 1 -1 -2], ⟨0 0 2 -3 -1]]

Mapping generators: ~99/70, ~3/2, ~128/99

POTE generators: ~3/2 = 702.4613, ~128/99 = 442.4903

Template:Val list

Badness: 1.253 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 3584/3575

Mapping: [⟨2 0 0 11 14 15], ⟨0 1 1 -1 -2 -1], ⟨0 0 2 -3 -1 -6]]

POTE generators: ~3/2 = 702.3964, ~128/99 = 442.5902

Vals: Template:Val list

Badness: 1.220 × 10-3

Retrieved from "https://en.xen.wiki/index.php?title=Porwell_family&oldid=79314"