Valinorsmic clan: Difference between revisions

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Some cleanup; remove varda (covered by diaschismic family)
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The valinorsmic rank three temperaments temper out the [[valinorsma]], 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)
The valinorsmic rank three temperaments temper out the [[valinorsma]], 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)


== Rank four valinorsmic temperament  ==
== Valinorsmic ==
Comma: 176/175
Comma list: 176/175


Map: [<1 0 0 0 -4|, <0 1 0 0 0|, <0 0 1 0 2|, <0 0 0 1 1|]
Mapping: [<1 0 0 0 -4|, <0 1 0 0 0|, <0 0 1 0 2|, <0 0 0 1 1|]


EDOs: 22, 31, 46, 53, 58, 80, 111
EDOs: 22, 31, 46, 53, 58, 80, 111


== Manwe ==
== Manwe ==
Commas: 176/175, 1331/1323
Comma list: 176/175, 1331/1323


Map: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]
Mapping: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]


EDOs: 15, 31, 46, 77, 80, 111
EDOs: 15, 31, 46, 77, 80, 111
Line 18: Line 18:
Badness: 0.000679
Badness: 0.000679


=== 13-limit ===
=== 13-limit ===
Commas: 176/175, 1331/1323, 351/350
Comma list: 176/175, 1331/1323, 351/350


Map: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]
Mapping: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]


EDOs: 31, 46, 77, 80, 111
EDOs: 31, 46, 77, 80, 111
Line 27: Line 27:
Badness: 0.001147
Badness: 0.001147


== Varda  ==
== Mandos ==
Commas: 176/175, 896/891
Comma list: 176/175, 243/242


Map: [<2 0 11 0 14|, <0 1 -2 0 -4|, <0 0 0 1 1|]
Mapping: [<1 1 0 6 2|, <0 2 0 5 5|, <0 0 1 -2 0|]
 
EDOs: 12, 22, 46, 58, 80, 126
 
Badness: 0.000728
 
=== 13-limit  ===
Commas: 176/175, 352/351, 364/363
 
Map: [<2 0 11 0 14 24|, <0 1 -2 0 -4 -7|, <0 0 0 1 1 1|]
 
EDOs: 22, 46, 58, 80, 138cde, 242cde, 322bcde
 
Badness: 0.000970
 
== Mandos  ==
Commas: 176/175, 243/242
 
Map: [<1 1 0 6 2|, <0 2 0 5 5|, <0 0 1 -2 0|]


EDOs: 7, 24, 31, 58, 89
EDOs: 7, 24, 31, 58, 89
Line 54: Line 36:
Badness: 0.000751
Badness: 0.000751


=== 13-limit ===
=== 13-limit ===
Commas: 144/143, 176/175, 243/242
Comma list: 144/143, 176/175, 243/242


Map: [<1 1 0 6 2 4|, <0 2 0 5 5 -1|, <0 0 1 -2 0 0|]
Mapping: [<1 1 0 6 2 4|, <0 2 0 5 5 -1|, <0 0 1 -2 0 0|]


EDOs: 7, 24, 31, 58
EDOs: 7, 24, 31, 58
Line 63: Line 45:
Badness: 0.000923
Badness: 0.000923


== Ulmo ==
== Ulmo ==
Commas: 176/175, 2200/2187
Comma list: 176/175, 2200/2187


Map: [<1 0 0 1, -3|, <0 1 0 7 7|, <0 0 1 -4 -2|]
Mapping: [<1 0 0 1, -3|, <0 1 0 7 7|, <0 0 1 -4 -2|]


EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd
EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd
Line 72: Line 54:
Badness: 0.00123
Badness: 0.00123


=== 13-limit ===
=== 13-limit ===
Commas: 169/168, 176/175, 325/324
Comma list: 169/168, 176/175, 325/324


Map: [<1 0 0 1, -3 2|, <0 1 0 7 7 4|, <0 0 1 -4 -2 -2|]
Mapping: [<1 0 0 1, -3 2|, <0 1 0 7 7 4|, <0 0 1 -4 -2 -2|]


EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf
EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf
Line 81: Line 63:
Badness: 0.000932
Badness: 0.000932


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Valinorsmic]]
[[Category:Valinorsmic temperaments| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Rank 3]]

Revision as of 09:33, 15 June 2021

The valinorsmic rank three temperaments temper out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)

Valinorsmic

Comma list: 176/175

Mapping: [<1 0 0 0 -4|, <0 1 0 0 0|, <0 0 1 0 2|, <0 0 0 1 1|]

EDOs: 22, 31, 46, 53, 58, 80, 111

Manwe

Comma list: 176/175, 1331/1323

Mapping: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]

EDOs: 15, 31, 46, 77, 80, 111

Badness: 0.000679

13-limit

Comma list: 176/175, 1331/1323, 351/350

Mapping: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]

EDOs: 31, 46, 77, 80, 111

Badness: 0.001147

Mandos

Comma list: 176/175, 243/242

Mapping: [<1 1 0 6 2|, <0 2 0 5 5|, <0 0 1 -2 0|]

EDOs: 7, 24, 31, 58, 89

Badness: 0.000751

13-limit

Comma list: 144/143, 176/175, 243/242

Mapping: [<1 1 0 6 2 4|, <0 2 0 5 5 -1|, <0 0 1 -2 0 0|]

EDOs: 7, 24, 31, 58

Badness: 0.000923

Ulmo

Comma list: 176/175, 2200/2187

Mapping: [<1 0 0 1, -3|, <0 1 0 7 7|, <0 0 1 -4 -2|]

EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd

Badness: 0.00123

13-limit

Comma list: 169/168, 176/175, 325/324

Mapping: [<1 0 0 1, -3 2|, <0 1 0 7 7 4|, <0 0 1 -4 -2 -2|]

EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf

Badness: 0.000932

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