Gamelismic family: Difference between revisions

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Cleanup with some info copied from gamelismic clan
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= Gamelan =
= Gamelan =
[[Comma list]]: c = 1029/1024
[[Comma list]]: 1029/1024


[[Mapping]]: [{{val| 1 1 0 3 }}, {{val| 0 3 0 -1 }},{{val| 0 0 1 0 }}]
[[Mapping]]: [{{val| 1 1 0 3 }}, {{val| 0 3 0 -1 }},{{val| 0 0 1 0 }}]
Line 12: Line 12:
: Angle (8/7, 5/4) = 90 degrees
: Angle (8/7, 5/4) = 90 degrees


[[Minimax tuning]]:  
[[Minimax tuning]]: c = 1029/1024
* 7-odd-limit: 3, 5, and 7 1/4c flat
* 7-odd-limit: 3, 5, and 7 1/4c flat
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 5/2 -1/4 1 -3/4 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 5/2 -1/4 1 -3/4 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
Line 24: Line 24:
{{Val list|legend=1| 5, 10, 15, 26, 31, 41, 72, 118, 159, 190 }}
{{Val list|legend=1| 5, 10, 15, 26, 31, 41, 72, 118, 159, 190 }}


Badness: 0.000176
[[Badness]]: 0.176 × 10<sup>-3</sup>


[[Projection pair]]: 3 1024/343 to 2.5.7
[[Projection pair]]: 3 1024/343 to 2.5.7


= Portent =
= Portent =
Portent has a [[Normal lists|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.
Portent has a [[Normal lists #normal interval list|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.


[[Comma]]s: c = 1029/1024, e = 385/384
Comma list: 385/384, 441/440


Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
Mapping: [{{val| 1 1 0 3 5 }}, {{val| 0 3 0 -1 4 }}, {{val| 0 0 1 0 -1 }}]


[|1 0 0 0 0&gt;, |10/7 6/7 0 -3/7 0&gt;,
Mapping generators: ~2, ~8/7, ~5
|39/14 4/7 1/2 -2/7 -1/2&gt;,
|20/7 -2/7 0 1/7 0&gt;,
|39/14 4/7 -1/2 -2/7 1/2&gt;]


[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7
Map to lattice: [{{val| 0 3 1 -1 3 }}, {{val| 0 0 1 0 -1 }}]


[[Minkowski_lattice_basis|Minkowski lattice basis]]: 8/7 length 0.46467, 12/11 length 1.931
Minkowski lattice basis:
: 8/7 length = 0.46467, 12/11 length = 1.931
: Angle (8/7, 12/11) = 86.657 degrees


Angle(8/7, 12/11) = 86.657 degrees
[[Minimax tuning]]: c = 1029/1024, e = 385/384
* [[11-odd-limit]]: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 39/14 4/7 1/2 -2/7 -1/2 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 39/14 4/7 -1/2 -2/7 1/2 }}]
: [[Eigenmonzo]]s: 2, 11/10, 9/7


Map to lattice: [&lt;0 3 1 -1 3|, &lt;0 0 1 0 -1|]
{{Val list|legend=1| 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190 }}


Map: [&lt;1 1 0 3 5|, &lt;0 3 0 -1 4| &lt;0 0 1 0 -1|]
Badness: 0.234 × 10<sup>-3</sup>
 
[[generator|Generators]]: 2, 8/7, 5
 
EDOs: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190
 
Badness: 0.000234


Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7
Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7


== Portending ==
== Portending ==
Commas: 325/324, 364/363, 441/440
Comma list: 325/324, 364/363, 441/440


Map: [&lt;1 1 0 3 5 6|, &lt;0 3 0 -1 4 12| &lt;0 0 1 0 -1 -2|]
Mapping: [{{val| 1 1 0 3 5 6 }}, {{val| 0 3 0 -1 4 12 }}, {{val| 0 0 1 0 -1 -2 }}]


EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf
{{Val list|legend=1| 15, 26, 41, 46, 72, 87, 159, 477cdf }}


Badness: 0.000627
Badness: 0.627 × 10<sup>-3</sup>


== Portentous ==
== Portentous ==
Commas: 385/384, 441/440, 625/624
Comma list: 385/384, 441/440, 625/624


Map: [&lt;1 1 0 3 5 -5|, &lt;0 3 0 -1 4 -3| &lt;0 0 1 0 -1 4|]
Mapping: [{{val| 1 1 0 3 5 -5 }}, {{val| 0 3 0 -1 4 -3 }}, {{val| 0 0 1 0 -1 4 }}]


EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef
{{Val list|legend=1| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }}


Badness: 0.000662
Badness: 0.662 × 10<sup>-3</sup>


== Ominous ==
== Ominous ==
Commas: 351/350, 385/384, 441/440
Comma list: 351/350, 385/384, 441/440


Map: [&lt;1 1 0 3 5 1|, &lt;0 3 0 -1 4 -10| &lt;0 0 1 0 -1 2|]
Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 0 -1 4 -10 }}, {{val| 0 0 1 0 -1 2 }}]


EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef
{{Val list|legend=1| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }}


Badness: 0.000751
Badness: 0.751 × 10<sup>-3</sup>


=== 17-limit ===
=== 17-limit ===
Commas: 273/272, 351/350, 441/440, 561/560
Comma list: 273/272, 351/350, 441/440, 561/560
 
Minimax tuning
 
[|1 0 0 0 0 0 0&gt;,
|7/4 9/10 0 0 -3/10 -3/20 0&gt;,
|5/2 7/5 0 0 -4/5 1/10 0&gt;,
|11/4 -3/10 0 0 1/10 1/20 0&gt;,
|7/2 -1/5 0 0 2/5 -3/10 0&gt;,
|7/2 -1/5 0 0 -3/5 7/10 0&gt;,
|4 2/5 0 0 -4/5 3/5 0&gt;]
 
Eigenmonzos: 2, 13/11, 11/9
 
Lattice basis: 8/7 0.3859 6/5 1.1303


Angle(8/7, 6/5) = 98.6015
Mapping: [{{val| 1 1 0 3 5 1 1 }}, {{val| 0 3 0 -1 4 -10 -8 }}, {{val| 0 0 1 0 -1 2 2 }}]


Map to lattice: [&lt;0 1 1 0 0 -1 0|, &lt;0 -1 -1 0 -1 2 1|]
Mapping generators: 2, 8/7, 5


Map: [&lt;1 1 0 3 5 1 1|, &lt;0 3 0 -1 4 -10 -8|,
Map to lattice: [{{val| 0 1 1 0 0 -1 0 }}, {{val| 0 -1 -1 0 -1 2 1 }}]


&lt;0 0 1 0 -1 2 2|]
Lattice basis:
: 8/7 length = 0.3859, 6/5 length = 1.1303
: Angle (8/7, 6/5) = 98.6015


Generators: 2, 8/7, 5
Minimax tuning:  
* [[17-odd-limit]]:
: [{{monzo| 1 0 0 0 0 0 0 }}, {{monzo| 7/4 9/10 0 0 -3/10 -3/20 0 }}, {{monzo| 5/2 7/5 0 0 -4/5 1/10 0 }}, {{monzo| 11/4 -3/10 0 0 1/10 1/20 0 }}, {{monzo| 7/2 -1/5 0 0 2/5 -3/10 0 }}, {{monzo| 7/2 -1/5 0 0 -3/5 7/10 0 }}, {{monzo| 4 2/5 0 0 -4/5 3/5 0 }}]
: Eigenmonzos: 2, 13/11, 11/9


EDOs: 26, 31, 46, 72, 103, 149, 175f, 221ef
{{Val list|legend=1| 26, 31, 46, 72, 103, 149, 175f, 221ef }}


Badness: 0.000612
Badness: 0.612 × 10<sup>-3</sup>


== Momentous ==
== Momentous ==
Commas: 196/195, 352/351, 385/384
Comma list: 196/195, 352/351, 385/384


Map: [&lt;1 1 0 3 5 7|, &lt;0 3 0 -4 1 -5|, &lt;0 0 1 0 -1 -1|]
Mapping: [{{val| 1 1 0 3 5 7 }}, {{val| 0 3 0 -4 1 -5 }}, {{val| 0 0 1 0 -1 -1 }}]


EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def
{{Val list|legend=1| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }}


Badness: 0.000832
Badness: 0.832 × 10<sup>-3</sup>


== Foreboding ==
== Foreboding ==
Commas: 105/104, 144/143, 275/273
Comma list: 105/104, 144/143, 275/273


Map: [&lt;1 1 0 3 5 1|, &lt;0 3 0 -1 4 2|, &lt;0 0 1 0 -1 1|]
Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 0 -1 4 2 }}, {{val| 0 0 1 0 -1 1 }}]


[[EDO|EDOs]]: 5, 10, 15, 26, 31, 41, [[72edo|72f]], [[185edo|185cf]]
{{Val list|legend=1| 5, 10, 15, 26, 31, 41, 72f, 185cf }}


Badness: 0.000873
Badness: 0.873 × 10<sup>-3</sup>


= Gamel =
= Gamel =
Commas: 1029/1024, 540/539
Comma list: 1029/1024, 540/539


Map: [&lt;1 1 0 3 -1|, &lt;0 3 0 -1 11|, &lt;0 0 1 0 1|]
Mapping: [{{val| 1 1 0 3 -1 }}, {{val| 0 3 0 -1 11 }}, {{val| 0 0 1 0 1 }}]


EDOs: 10, 31, 41, 72
{{Val list|legend=1| 10, 31, 41, 72 }}


Badness: 0.000853
Badness: 0.853 × 10<sup>-3</sup>


[[Category:Theory]]
[[Category:Theory]]

Revision as of 10:38, 5 March 2021

The gamelismic family of temperaments are rank-3 temperaments tempering out 1029/1024.

Gamelan

Comma list: 1029/1024

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

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

Minkowski lattice basis:

8/7 length = 0.5192, 5/4 length = log25
Angle (8/7, 5/4) = 90 degrees

Minimax tuning: c = 1029/1024

  • 7-odd-limit: 3, 5, and 7 1/4c flat
[[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [5/2 -1/4 1 -3/4⟩, [5/2 -1/4 0 1/4⟩]
Eigenmonzos: 2, 7/6, 6/5
  • 9-odd-limit: 3 1/7c flat, 5 and 7 2/7c flat
[[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [10/7 -1/7 1 -3/7⟩, [20/7 -2/7 0 1/7⟩]
Eigenmonzos: 2, 6/5, 9/7

TE tuning map: ⟨1200.486 1901.833 2786.314 3367.676]

Template:Val list

Badness: 0.176 × 10-3

Projection pair: 3 1024/343 to 2.5.7

Portent

Portent has a normal comma list [1029/1024, 385/384] and also tempers out 441/440.

Comma list: 385/384, 441/440

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

Mapping generators: ~2, ~8/7, ~5

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

Minkowski lattice basis:

8/7 length = 0.46467, 12/11 length = 1.931
Angle (8/7, 12/11) = 86.657 degrees

Minimax tuning: c = 1029/1024, e = 385/384

  • 11-odd-limit: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat
[[1 0 0 0 0⟩, [10/7 6/7 0 -3/7 0⟩, [39/14 4/7 1/2 -2/7 -1/2⟩, [20/7 -2/7 0 1/7 0⟩, [39/14 4/7 -1/2 -2/7 1/2⟩]
Eigenmonzos: 2, 11/10, 9/7

Template:Val list

Badness: 0.234 × 10-3

Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7

Portending

Comma list: 325/324, 364/363, 441/440

Mapping: [⟨1 1 0 3 5 6], ⟨0 3 0 -1 4 12], ⟨0 0 1 0 -1 -2]]

Template:Val list

Badness: 0.627 × 10-3

Portentous

Comma list: 385/384, 441/440, 625/624

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

Template:Val list

Badness: 0.662 × 10-3

Ominous

Comma list: 351/350, 385/384, 441/440

Mapping: [⟨1 1 0 3 5 1], ⟨0 3 0 -1 4 -10], ⟨0 0 1 0 -1 2]]

Template:Val list

Badness: 0.751 × 10-3

17-limit

Comma list: 273/272, 351/350, 441/440, 561/560

Mapping: [⟨1 1 0 3 5 1 1], ⟨0 3 0 -1 4 -10 -8], ⟨0 0 1 0 -1 2 2]]

Mapping generators: 2, 8/7, 5

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

Lattice basis:

8/7 length = 0.3859, 6/5 length = 1.1303
Angle (8/7, 6/5) = 98.6015

Minimax tuning:

[[1 0 0 0 0 0 0⟩, [7/4 9/10 0 0 -3/10 -3/20 0⟩, [5/2 7/5 0 0 -4/5 1/10 0⟩, [11/4 -3/10 0 0 1/10 1/20 0⟩, [7/2 -1/5 0 0 2/5 -3/10 0⟩, [7/2 -1/5 0 0 -3/5 7/10 0⟩, [4 2/5 0 0 -4/5 3/5 0⟩]
Eigenmonzos: 2, 13/11, 11/9

Template:Val list

Badness: 0.612 × 10-3

Momentous

Comma list: 196/195, 352/351, 385/384

Mapping: [⟨1 1 0 3 5 7], ⟨0 3 0 -4 1 -5], ⟨0 0 1 0 -1 -1]]

Template:Val list

Badness: 0.832 × 10-3

Foreboding

Comma list: 105/104, 144/143, 275/273

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

Template:Val list

Badness: 0.873 × 10-3

Gamel

Comma list: 1029/1024, 540/539

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

Template:Val list

Badness: 0.853 × 10-3

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