Octagar temperaments: Difference between revisions

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__FORCETOC__
Octagar temperaments temper out the octagar comma, {{monzo|5 -4 3 -2}} = 4000/3969.
Octagar temperaments temper out the octagar comma, |5 -4 3 -2> = 4000/3969.


=Slendi=
Temperaments discussed elsewhere are [[Garibaldi temperament|garibaldi]], [[Augmented family #Augene|augene]], [[Tetracot family #Octacot|octacot]], [[Orwellismic temperaments #Quartonic|quartonic]], [[superkleismic]], [[Meantone family #Injera|injera]], [[Diaschismic family #Bidia|bidia]], [[Kleismic family #Hemikleismic|hemikleismic]], [[Mirkwai clan #Pluto|pluto]], [[Porcupine family #Nautilus|nautilus]], [[Ripple family|ripple]], and [[Amity family #Hamity|hamity]].
Commas: 4000/3969, 84035/82944


POTE generator: ~49/48 = 29.181
== Slendi ==
[[Comma list]]: 4000/3969, 84035/82944


Map: [<1 2 3 3|, <0 -17 -28 -8|]
[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -17 -28 -8}}]


Wedgie: <<17 28 8 5 -35 -60||
{{Multival|legend=1|17 28 8 5 -35 -60}}


EDOs: 41, 206, 247bc, 288bcd, 329bcd
[[POTE generator]]: ~49/48 = 29.181


Badness: 0.1429
{{Val list|legend=1| 41, 206, 247bc, 288bcd, 329bcd }}


==11-limit==
[[Badness]]: 0.142903
Commas: 100/99, 245/242, 46656/46585
 
=== 11-limit ===
Comma list: 100/99, 245/242, 46656/46585
 
Mapping: [{{val|1 2 3 3 4}}, {{val|0 -17 -28 -8 -22}}]


POTE generator: ~49/48 = 29.180
POTE generator: ~49/48 = 29.180


Map: [<1 2 3 3 4|, <0 -17 -28 -8 -22|]
Vals: {{Val list| 41, 206e }}


EDOs: 41, 206e
Badness: 0.063217


Badness: 0.0632
=== 13-limit ===
Comma list: 100/99, 144/143, 245/242, 343/338


==13-limit==
Mapping: [{{val|1 2 3 3 4 4}}, {{val|0 -17 -28 -8 -22 -1}}]
Commas: 100/99, 144/143, 245/242, 343/338


POTE generator: ~49/48 = 29.125
POTE generator: ~49/48 = 29.125


Map: [<1 2 3 3 4 4|, <0 -17 -28 -8 -22 -12|]
Vals: {{Val list| 41, 124ef, 165ef }}
 
Badness: 0.043644


EDOs: 41, 124ef, 165ef
== Slithy ==
[[Comma list]]: 4000/3969, 420175/419904


Badness: 0.0436
[[Mapping]]: [{{val|1 3 5 4}}, {{val|0 -19 -36 -16}}]


=Slithy=
{{Multival|legend=1|19 36 16 13 -28 -64}}
Commas: 4000/3969, 420175/419904


POTE generator: ~21/20 = 89.282
[[POTE generator]]: ~21/20 = 89.282


Map: [<1 3 5 4|, <0 -19 -36 -16|]
{{Val list|legend=1| 27, 94, 121, 215, 336d }}


EDOs: 27, 94, 121, 215, 336d
[[Badness]]: 0.107482


Badness: 0.1075
=== 11-limit ===
Comma list: 540/539, 2200/2187, 4375/4356


==11-limit==
Mapping: [{{val|1 3 5 4 8}}, {{val|0 -19 -36 -16 -61}}]
Commas: 540/539, 2200/2187, 4375/4356


POTE generator: ~21/20 = 89.291
POTE generator: ~21/20 = 89.291


Map: [<1 3 5 4 8|, <0 -19 -36 -16 -61|]
Vals: {{Val list| 94, 121, 215, 336de, 551bde }}


EDOs: 94, 121, 215, 336de, 551bde
Badness: 0.045895


Badness: 0.0459
=== 13-limit ===
Comma list: 325/324, 352/351, 540/539, 1575/1573


==13-limit==
Mapping: [{{val|1 3 5 4 8 4}}, {{val|0 -19 -36 -16 -61 -4}}]
Commas: 325/324, 352/351, 540/539, 1575/1573


POTE generator: ~21/20 = 89.286
POTE generator: ~21/20 = 89.286


Map: [<1 3 5 4 8 4|, <0 -19 -36 -16 -61 -4|]
Vals: {{Val list| 94, 121, 215, 336def }}


EDOs: 94, 121, 215, 336def
Badness: 0.028492


Badness: 0.0285
[[Category:Temperament collection]]
[[Category:Rank 2]]

Revision as of 22:08, 24 June 2021

Octagar temperaments temper out the octagar comma, [5 -4 3 -2⟩ = 4000/3969.

Temperaments discussed elsewhere are garibaldi, augene, octacot, quartonic, superkleismic, injera, bidia, hemikleismic, pluto, nautilus, ripple, and hamity.

Slendi

Comma list: 4000/3969, 84035/82944

Mapping: [⟨1 2 3 3], ⟨0 -17 -28 -8]]

Wedgie: ⟨⟨ 17 28 8 5 -35 -60 ]]

POTE generator: ~49/48 = 29.181

Template:Val list

Badness: 0.142903

11-limit

Comma list: 100/99, 245/242, 46656/46585

Mapping: [⟨1 2 3 3 4], ⟨0 -17 -28 -8 -22]]

POTE generator: ~49/48 = 29.180

Vals: Template:Val list

Badness: 0.063217

13-limit

Comma list: 100/99, 144/143, 245/242, 343/338

Mapping: [⟨1 2 3 3 4 4], ⟨0 -17 -28 -8 -22 -1]]

POTE generator: ~49/48 = 29.125

Vals: Template:Val list

Badness: 0.043644

Slithy

Comma list: 4000/3969, 420175/419904

Mapping: [⟨1 3 5 4], ⟨0 -19 -36 -16]]

Wedgie: ⟨⟨ 19 36 16 13 -28 -64 ]]

POTE generator: ~21/20 = 89.282

Template:Val list

Badness: 0.107482

11-limit

Comma list: 540/539, 2200/2187, 4375/4356

Mapping: [⟨1 3 5 4 8], ⟨0 -19 -36 -16 -61]]

POTE generator: ~21/20 = 89.291

Vals: Template:Val list

Badness: 0.045895

13-limit

Comma list: 325/324, 352/351, 540/539, 1575/1573

Mapping: [⟨1 3 5 4 8 4], ⟨0 -19 -36 -16 -61 -4]]

POTE generator: ~21/20 = 89.286

Vals: Template:Val list

Badness: 0.028492

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