Gamelismic family: Difference between revisions

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= Gamelan =
= Gamelan =
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.6875, ~5/4 = 385.1853
EDO generator: [[31edo|(6, 10)\31]], [[41edo|(8, 13)\41]], [[46edo|(9, 15)\46]]
Scales (Scala files): [[portent26]]
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7
[[Comma list]]: 1029/1024
[[Comma list]]: 1029/1024


Line 27: Line 42:


[[Projection pair]]: 3 1024/343 to 2.5.7
[[Projection pair]]: 3 1024/343 to 2.5.7
</div></div>


= Portent =
= Portent =
Portent has a [[Normal lists #normal interval list|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.
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.6884, ~5/4 = 385.1618
EDO generator: [[31edo|(6, 10)\31]], [[41edo|(8, 13)\41]], [[46edo|(9, 15)\46]]
Scales (Scala files): [[portent26]]
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11


Comma list: 385/384, 441/440
Comma list: 385/384, 441/440
Line 48: Line 79:
: [[Eigenmonzo]]s: 2, 11/10, 9/7
: [[Eigenmonzo]]s: 2, 11/10, 9/7


{{Val list|legend=1| 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190 }}
{{Val list|legend=1| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}


Badness: 0.234 × 10<sup>-3</sup>
Badness: 0.234 × 10<sup>-3</sup>


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


== Portending ==
== Portending ==
Comma list: 325/324, 364/363, 441/440
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~8/7 = 233.9128, ~5/4 = 384.7278
 
EDO generator: [[41edo|(8, 13)\41]], [[46edo|(9, 15)\46]], [[72edo|(14, 23)\72]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 364/363, 385/384


Mapping: [{{val| 1 1 0 3 5 6 }}, {{val| 0 3 0 -1 4 12 }}, {{val| 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 }}]
Line 62: Line 110:


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


== Portentous ==
== Portentous ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.6843, ~5/4 = 384.9830
EDO generator: [[31edo|(6, 10)\31]], [[72edo|(14, 23)\72]], [[87edo|(17, 28)\87]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 441/440, 625/624
Comma list: 385/384, 441/440, 625/624


Line 71: Line 136:


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


== Ominous ==
== Ominous ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.4088, ~5/4 = 385.3825
EDO generator: [[31edo|(6, 10)\31]], [[46edo|(9, 15)\46]], [[72edo|(14, 23)\72]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384, 441/440
Comma list: 351/350, 385/384, 441/440


Line 80: Line 162:


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


=== 17-limit ===
=== 17-limit ===
Comma list: 273/272, 351/350, 441/440, 561/560
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~8/7 = 233.4313, ~5/4 = 385.2890
 
EDO generator: [[31edo|(6, 10)\31]], [[46edo|(9, 15)\46]], [[72edo|(14, 23)\72]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 273/272, 351/350, 385/384, 441/440


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 }}]
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 }}]
Line 102: Line 201:


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


== Momentous ==
== Momentous ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.4088, ~5/4 = 385.3825
EDO generator: [[31edo|(6, 10)\31]], [[41edo|(8, 13)\41]], [[46edo|(9, 15)\46]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384
Comma list: 196/195, 352/351, 385/384


Line 111: Line 227:


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


== Foreboding ==
== Foreboding ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.3664, ~5/4 = 382.3425
EDO generator: [[10edo|(3, 6)\10]], [[15edo|(5, 9)\15]], [[31edo|(6, 10)\31]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 275/273
Comma list: 105/104, 144/143, 275/273


Line 120: Line 253:


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


= Gamel =
= Gamel =
Comma list: 1029/1024, 540/539
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~8/7 = 233.2909, ~5/4 = 384.2120
 
EDO generator: [[31edo|(6, 10)\31]], [[36edo|(7, 12)\36]], [[72edo|(14, 23)\72]]
 
Scales (Scala files):
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 1029/1024


Mapping: [{{val| 1 1 0 3 -1 }}, {{val| 0 3 0 -1 11 }}, {{val| 0 0 1 0 1 }}]
Mapping: [{{val| 1 1 0 3 -1 }}, {{val| 0 3 0 -1 11 }}, {{val| 0 0 1 0 1 }}]
Line 129: Line 279:


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


[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Gamelan]]
[[Category:Gamelismic]]
[[Category:Gamelismic]]
[[Category:Rank 3]]
[[Category:Rank 3]]
[[Category:Gamelan]]
[[Category:Portent]]

Revision as of 08:34, 13 March 2021

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

Gamelan

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.6875, ~5/4 = 385.1853

EDO generator: (6, 10)\31, (8, 13)\41, (9, 15)\46

Scales (Scala files): portent26

Technical data

Subgroup: 2.3.5.7

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.

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.6884, ~5/4 = 385.1618

EDO generator: (6, 10)\31, (8, 13)\41, (9, 15)\46

Scales (Scala files): portent26

Technical data

Subgroup: 2.3.5.7.11

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

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.9128, ~5/4 = 384.7278

EDO generator: (8, 13)\41, (9, 15)\46, (14, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 385/384

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

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.6843, ~5/4 = 384.9830

EDO generator: (6, 10)\31, (14, 23)\72, (17, 28)\87

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

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

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.4088, ~5/4 = 385.3825

EDO generator: (6, 10)\31, (9, 15)\46, (14, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

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

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.4313, ~5/4 = 385.2890

EDO generator: (6, 10)\31, (9, 15)\46, (14, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 351/350, 385/384, 441/440

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

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.4088, ~5/4 = 385.3825

EDO generator: (6, 10)\31, (8, 13)\41, (9, 15)\46

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

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

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.3664, ~5/4 = 382.3425

EDO generator: (3, 6)\10, (5, 9)\15, (6, 10)\31

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

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

Period: 1\1

Optimal (POTE) generators: ~8/7 = 233.2909, ~5/4 = 384.2120

EDO generator: (6, 10)\31, (7, 12)\36, (14, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1029/1024

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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