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Augmented family: Difference between revisions

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Badness: 0.035554
Badness: 0.035554


; Music
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 Sad Like Winter Leaves] by [http://soundcloud.com/cityoftheasleep/sad-like-winter-trees Igliashon Jones]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 Sad Like Winter Leaves] by [http://soundcloud.com/cityoftheasleep/sad-like-winter-trees Igliashon Jones]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 Galticeran Sonatina] by [http://soundcloud.com/joelgranttaylor/galticeran_sonatina Joel Taylor]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 Galticeran Sonatina] by [http://soundcloud.com/joelgranttaylor/galticeran_sonatina Joel Taylor]


== Inflated ==
== Inflated ==
Comma list: 28/27, 128/125
Subgroup: 2.3.5.7
 
[[Comma list]]: 28/27, 128/125


POTE generator: ~3/2 = 722.719
[[Mapping]]: [{{val|3 0 7 -6}}, {{val|0 1 0 3}}]


Map: [<3 0 7 -6|, <0 1 0 3|]
{{Multival|legend=1|3 0 9 -7 6 21}}


Wedgie: <<3 0 9 -7 6 21||
[[POTE generator]]: ~3/2 = 722.719


EDOs: 3d, 15, 48bc, 63bc, 78bc
{{Val list|legend=1| 3d, 15, 48bc, 63bbc, 78bbc }}


Badness: 0.054729
[[Badness]]: 0.054729


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 28/27, 55/54, 128/125
Comma list: 28/27, 55/54, 128/125
Mapping: [{{val|3 0 7 -6 -4}}, {{val|0 1 0 3 3}}]


POTE generator: ~3/2 = 722.663
POTE generator: ~3/2 = 722.663


Map: [<3 0 7 -6 -4|, <0 1 0 3 3|]
Vals: {{Val list| 3de, 15, 48bce, 63bbcee, 78bbcee }}


EDOs: 3de, 15, 48bce, 63bce, 78bce
Badness: 0.031171


Badness: 0.031171
== Deflated ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 21/20, 128/125


== Deflated  ==
[[Mapping]]: [{{val|3 0 7 13}}, {{val|0 1 0 -1}}]
Comma list: 21/20, 128/125


POTE generator: ~3/2 = 681.629
{{Multival|legend=1|3 0 -3 -7 -13 -7}}


Map: [<3 0 7 13|, <0 1 0 -1|]
[[POTE generator]]: ~3/2 = 681.629


Wedgie: <<3 0 -3 -7 -13 -7||
{{Val list|legend=1| 3, 9, 21d, 30bdd }}


EDOs: 3, 9, 21d, 30bd
[[Badness]]: 0.059079


Badness: 0.059079
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 21/20, 33/32, 128/125
Comma list: 21/20, 33/32, 128/125
Mapping: [{{val|3 0 7 13 15}}, {{val|0 1 0 -1 -1}}]


POTE generator: ~3/2 = 680.042
POTE generator: ~3/2 = 680.042


Map: [<3 0 7 13 15|, <0 1 0 -1 -1|]
Vals: {{Val list| 3, 9, 21de, 30bdde }}
 
Badness: 0.037183


EDOs: 3, 9, 21de, 30bde
== Hexe ==
Subgroup: 2.3.5.7


Badness: 0.037183
[[Comma list]]: 50/49, 128/125


== Hexe  ==
[[Mapping]]: [{{val|6 0 14 17}}, {{val|0 1 0 0}}]
Comma list: 50/49, 128/125


[[POTE_tuning|POTE generator]]: ~3/2 = 710.963
{{Multival|legend=1|6 0 0 -14 -17 0}}


Map: [<6 0 14 17|, <0 1 0 0|]
[[POTE generator]]: ~3/2 = 710.963


Wedgie: <<6 0 0 -14 -17 0||
{{Val list|legend=1| 6, 12, 30d, 42dd, 54cdd }}


EDOs: [[6edo|6]], [[12edo|12]], [[30edo|30d]], [[42edo|42d]], [[54edo|54cd]]
[[Badness]]: 0.057730


Badness: 0.057730
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 50/49, 56/55, 125/121
Comma list: 50/49, 56/55, 125/121
Mapping: [{{val|6 0 14 17 21}}, {{val|0 1 0 0 0}}]


POTE generator: ~3/2 = 714.304
POTE generator: ~3/2 = 714.304


Map: [<6 0 14 17 21|, <0 1 0 0 0|]
Vals: {{Val list| 6, 12, 30de }}


EDOs: 6, 12, 30de
Badness: 0.038412


Badness: 0.038412
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 50/49, 56/55, 66/65, 105/104
Comma list: 50/49, 56/55, 66/65, 105/104
Mapping: [{{val|6 0 14 17 21 13}}, {{val|0 1 0 0 0 1}}]


POTE generator: ~3/2 = 710.005
POTE generator: ~3/2 = 710.005


Map: [<6 0 14 17 21 13|, <0 1 0 0 0 1|]
Vals: {{Val list| 6f, 12f }}


EDOs: 6f, 12f
Badness: 0.035946


Badness: 0.035946
== Hemiaug ==
Subgroup: 2.3.5.7


== Hemiaug  ==
[[Comma list]]: 128/125, 245/243
Comma list: 128/125, 245/243


[[POTE_tuning|POTE generator]]: ~28/27 = 45.118
[[Mapping]]: [{{val|3 1 7 -1}}, {{val|0 2 0 5}}]


Map: [<3 1 7 -1|, <0 2 0 5|]
{{Multival|legend=1|6 0 15 -14 7 35}}


Wedgie: <<6 0 15 -14 7 35||
[[POTE generator]]: ~28/27 = 45.118


EDOs: [[24edo|24]], [[27edo|27]], [[105edo|105bc]]
{{Val list|legend=1| 24, 27, 105bcc }}


Badness: 0.070463
[[Badness]]: 0.070463
 
=== 11-limit ===
Subgroup: 2.3.5.7.11


=== 11-limit  ===
Comma list: 56/55, 128/125, 245/243
Comma list: 56/55, 128/125, 245/243
Mapping: [{{val|3 1 7 -1 1}}, {{val|0 2 0 5 5}}]


POTE generator: ~28/27 = 45.788
POTE generator: ~28/27 = 45.788


Map: [<3 1 7 -1 1|, <0 2 0 5 5|]
Vals: {{Val list| 24, 27e, 51ce, 78cee }}


EDOs: 24, 27e, 51ce, 78ce
Badness: 0.038232


Badness: 0.038232
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 13-limit  ===
Comma list: 56/55, 91/90, 128/125, 245/243
Comma list: 56/55, 91/90, 128/125, 245/243
Mapping: [{{val|3 1 7 -1 1 13}}, {{val|0 2 0 5 5 -1}}]


POTE generator: ~28/27 = 46.250
POTE generator: ~28/27 = 46.250


Map: [<3 1 7 -1 1 13|, <0 2 0 5 5 -1|]
Vals: {{Val list| 24, 27e, 51ce, 78cee }}
 
EDOs: 24, 27e, 51ce, 78ce


Badness: 0.030159
Badness: 0.030159


== Triforce ==
== Triforce ==
Comma list: 49/48, 128/125
[[Comma list]]: 49/48, 128/125


[[POTE_tuning|POTE generator]]: ~7/6 = 247.049
[[POTE generator]]: ~7/6 = 247.049


Map: [<3 0 7 6|, <0 2 0 1|]
Map: [<3 0 7 6|, <0 2 0 1|]
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[[File:triforce9.jpg|alt=triforce9.jpg|triforce9.jpg]]
[[File:triforce9.jpg|alt=triforce9.jpg|triforce9.jpg]]


=== 11-limit ===
=== 11-limit ===
Comma list: 56/55, 77/75, 128/125
Comma list: 56/55, 77/75, 128/125


Line 299: Line 319:
Badness: 0.026152
Badness: 0.026152


==== Musical example ====
; Musical example
* [http://soundcloud.com/cityoftheasleep/the-triforce-of-courage15 The Triforce of Courage (tuned in 15edo)] by Igliashon Jones
* [http://soundcloud.com/cityoftheasleep/the-triforce-of-courage15 The Triforce of Courage (tuned in 15edo)] by Igliashon Jones


=== 13-limit ===
=== 13-limit ===
Comma list: 49/48, 56/55, 66/65, 77/75
Comma list: 49/48, 56/55, 66/65, 77/75


Line 315: Line 335:
[[triphi|Triforce(9) with L:s = phi]]
[[triphi|Triforce(9) with L:s = phi]]


=== Semitriforce ===
=== Semitriforce ===
Comma list: 49/48, 56/55, 77/75, 507/500
Comma list: 49/48, 56/55, 77/75, 507/500


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