Gamelismic family: Difference between revisions
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= Gamelan = | = Gamelan = | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 26: | Line 14: | ||
: 8/7 length = 0.5192, 5/4 length = log<sub>2</sub>5 | : 8/7 length = 0.5192, 5/4 length = log<sub>2</sub>5 | ||
: Angle (8/7, 5/4) = 90 degrees | : Angle (8/7, 5/4) = 90 degrees | ||
[[POTE generator]]s: ~8/7 = 233.6875, ~5/4 = 385.1853 | |||
[[Minimax tuning]]: c = 1029/1024 | [[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 }}] | ||
: | : [[Eigenmonzo]]s: 2, 7/6, 6/5 | ||
* 9-odd-limit: 3 1/7c flat, 5 and 7 2/7c flat | * [[9-odd-limit]]: 3 1/7c flat, 5 and 7 2/7c flat | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 10/7 -1/7 1 -3/7 }}, {{monzo| 20/7 -2/7 0 1/7 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 10/7 -1/7 1 -3/7 }}, {{monzo| 20/7 -2/7 0 1/7 }}] | ||
: | : [[Eigenmonzo]]s: 2, 6/5, 9/7 | ||
[[TE tuning]] map: {{val| 1200.486 1901.833 2786.314 3367.676 }} | [[TE tuning]] map: {{val| 1200.486 1901.833 2786.314 3367.676 }} | ||
| Line 43: | Line 33: | ||
[[Projection pair]]: 3 1024/343 to 2.5.7 | [[Projection pair]]: 3 1024/343 to 2.5.7 | ||
Scales: [[portent26]] | |||
= 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. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 385/384, 441/440 | [[Comma list]]: 385/384, 441/440 | ||
Mapping: [{{val| 1 1 0 3 5 }}, {{val| 0 3 0 -1 4 }}, {{val| 0 0 1 0 -1 }}] | [[Mapping]]: [{{val| 1 1 0 3 5 }}, {{val| 0 3 0 -1 4 }}, {{val| 0 0 1 0 -1 }}] | ||
Mapping generators: ~2, ~8/7, ~5 | Mapping generators: ~2, ~8/7, ~5 | ||
| Line 73: | Line 51: | ||
: 8/7 length = 0.46467, 12/11 length = 1.931 | : 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 | ||
[[POTE generator]]s: ~8/7 = 233.6884, ~5/4 = 385.1618 | |||
[[Minimax tuning]]: c = 1029/1024, e = 385/384 | [[Minimax tuning]]: c = 1029/1024, e = 385/384 | ||
| Line 81: | Line 61: | ||
{{Val list|legend=1| 10, 15, 26, 31, 41, 72, 118, 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 | [[Projection pair]]s: 3 1024/343 11 131072/12005 to 2.5.7 | ||
Scales: [[portent26]] | |||
== Portending == | == Portending == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 106: | Line 74: | ||
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 }}] | ||
POTE generators: ~8/7 = 233.9128, ~5/4 = 384.7278 | |||
{{Val list|legend=1| 15, 26, 41, 46, 72, 87, 159, 477cdf }} | {{Val list|legend=1| 15, 26, 41, 46, 72, 87, 159, 477cdf }} | ||
Badness: 0.627 × 10<sup>-3</sup> | Badness: 0.627 × 10<sup>-3</sup> | ||
== Portentous == | == Portentous == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 132: | Line 88: | ||
Mapping: [{{val| 1 1 0 3 5 -5 }}, {{val| 0 3 0 -1 4 -3 }}, {{val| 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 }}] | ||
POTE generators: ~8/7 = 233.6843, ~5/4 = 384.9830 | |||
{{Val list|legend=1| 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: 0.662 × 10<sup>-3</sup> | Badness: 0.662 × 10<sup>-3</sup> | ||
== Ominous == | == Ominous == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 158: | Line 102: | ||
Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 0 -1 4 -10 }}, {{val| 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 }}] | ||
POTE generators: ~8/7 = 233.4088, ~5/4 = 385.3825 | |||
{{Val list|legend=1| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }} | {{Val list|legend=1| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }} | ||
Badness: 0.751 × 10<sup>-3</sup> | Badness: 0.751 × 10<sup>-3</sup> | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 192: | Line 124: | ||
: 8/7 length = 0.3859, 6/5 length = 1.1303 | : 8/7 length = 0.3859, 6/5 length = 1.1303 | ||
: Angle (8/7, 6/5) = 98.6015 | : Angle (8/7, 6/5) = 98.6015 | ||
POTE generators: ~8/7 = 233.4313, ~5/4 = 385.2890 | |||
Minimax tuning: | 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 }}] | : [{{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 | : Eigenmonzos: 2, 13/11, 11/9 | ||
| Line 201: | Line 135: | ||
Badness: 0.612 × 10<sup>-3</sup> | Badness: 0.612 × 10<sup>-3</sup> | ||
== Momentous == | == Momentous == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 223: | Line 143: | ||
Mapping: [{{val| 1 1 0 3 5 7 }}, {{val| 0 3 0 -4 1 -5 }}, {{val| 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 }}] | ||
POTE generators: ~8/7 = 233.4088, ~5/4 = 385.3825 | |||
{{Val list|legend=1| 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: 0.832 × 10<sup>-3</sup> | Badness: 0.832 × 10<sup>-3</sup> | ||
== Foreboding == | == Foreboding == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 249: | Line 157: | ||
Mapping: [{{val| 1 1 0 3 5 1 }}, {{val| 0 3 0 -1 4 2 }}, {{val| 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 }}] | ||
POTE generators: ~8/7 = 233.3664, ~5/4 = 382.3425 | |||
{{Val list|legend=1| 5, 10, 15, 26, 31, 41, 72f, 185cf }} | {{Val list|legend=1| 5, 10, 15, 26, 31, 41, 72f, 185cf }} | ||
Badness: 0.873 × 10<sup>-3</sup> | Badness: 0.873 × 10<sup>-3</sup> | ||
= Gamel = | = Gamel = | ||
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 }}] | |||
[[POTE generator]]s: ~8/7 = 233.2909, ~5/4 = 384.2120 | |||
{{Val list|legend=1| 10, 31, 41, 72 }} | {{Val list|legend=1| 10, 31, 41, 72 }} | ||
Badness: 0.853 × 10<sup>-3</sup | [[Badness]]: 0.853 × 10<sup>-3</sup> | ||
[[Category:Theory]] | [[Category:Theory]] | ||