Marvel family
Marvel[edit]
The head of the marvel family is marvel, which tempers out 225/224, the septimal kleisma or marvel comma. Marvel has a normal list basis of [2, 3, 5]; hence a 5-limit scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by 197edo.
Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to catakleismic temperament. Another temperament which does little damage to tuning accuracy is compton temperament, for which 240edo may be used.
See also Marvel temperaments.
Vital statistics[edit]
Comma c = 225/224
Related linear temperament: catakleismic temperament
7-limit minimax: 3 and 5 1/4c flat, 7 just
[|1 0 0 0>, |5/4 1/2 -1/2 1/4>, |5/4 -1/2 1/2 1/4>, |0 0 0 1>]
Eigenmonzo subgroup: 2.5/3.7
9-limit minimax: 3 1/6c flat, 5 1/3c flat, 7 just
[|1 0 0 0>, |5/6 2/3 -1/3 1/6>, |5/3 -2/3 1/3 1/3>, |0 0 0 1>]
Eigenmonzo subgroup: 2.9/5.7
Lattice basis: secor length 1.256, 3/2 length 1.369
Angle(secor, 3/2) = 106.958 degrees
Map to lattice: [<0 0 -1 -2|, <0 1 -1 0|]
Map: [<1 0 0 -5|, <0 1 0 2|, <0 0 1 2|]
Generators: 2, 3, 5
EDOs: 10, 12, 19, 22, 31, 41,72, 197, 269c
Projection pairs: 7 225/32
Spectrum: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9
Scales: marvel9, marvel10, marvel11, marvel12, marvel19, marvel22, pump12_1, pump12_2, pump13, pump14, pump15, pump16, pump17, pump18
Minkowski blocks[edit]
{2, 3, 5} subgroup
8: 16/15, 250/243
9: 135/128, 128/125
10: 25/24, 2048/2025
11: 135/128, 2048/1875
12: 2048/2025, 128/125
15: 128/125, 32768/30375
17: 25/24, 2278125/2097152
19: 16875/16384, 81/80
21: 128/125, 273375/262144
22: 2048/2025, 3125/3072
29: 16875/16384, 32805/32768
31: 81/80, 34171875/33554432
41: 34171875/33554432, 3125/3072
Music[edit]
Semimarvelous Blue Drawf by Chris Vaisvil
notJoelTaylorsTreeSpirit-Marvel10-2 by Billy Stiltner
11-limit (Unimarv)[edit]
Commas: 225/224, 385/384
Related linear temperament: catakleismic temperament
[|1 0 0 0 0>, |4/3 8/9 -1/3 0 -1/9>, |8/3 -2/9 1/3 0 -2/9>, |3 4/3 0 0 -2/3>, |8/3 -2/9 -2/3 0 7/9>]
Eigenmonzo subgroup: 2.9/5.11/9
Lattice basis: secor length 1.0364 5/4 length 1.0759
Angle(secor, 5/4) = 104.028 degrees
Map to lattice: [<0 -1 0 -2 1|, <0 -1 1 0 -2|]
Map: [<1 0 0 -5 12|, <0 1 0 2 -1|, <0 0 1 2 -3|]
Generators: 2, 3, 5
Edos: 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 269ce, 341ce
Badness: 0.000255
Projection pairs: 7 225/32 11 4096/375
Spectrum: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11
Scales: marvel22_11, unimarv19, unimarv22
Hobbit bases[edit]
{2, 3, 5} subgroup
12: 128/125, 2048/2025
15: 128/125, 32768/30375
19: 16875/16384, 81/80
22: 2048/2025, 2109375/2097152
31: 2109375/2097152, 81/80
41: 3125/3072, 34171875/33554432
13-limit[edit]
Commas: 225/224, 385/384, 351/350
13-limit eigenmonzo subgroup: 2.11/9.13/9
15-limit eigenmonzo subgroup: 2.15/11.15/13
Map: [<1 0 0 -5 12 -4|, <0 1 0 2 -1 -1|, <0 0 1 2 -3 4|]
EDOs: 19, 22, 31, 50, 53, 72, 103, 175f, 300cef, 403bcef
Badness: 0.000690
Spectrum: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11
Hecate[edit]
Commas: 225/224, 385/384, 325/324
13-limit eigenmonzo subgroup: 2.7.13/5
15-limit eigenmonzo subgroup: 2.7.15/13
Map: [<1 0 0 -5 12 2|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -2|]
EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef
Badness: 0.000721
Projection pairs: 7 225/32 11 4096/375 13 324/25
Spectrum: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11
17-limit[edit]
Commas: 225/224, 385/384, 325/324, 595/594
Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 -6|]
EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg
Badness: 0.000869
Enodia[edit]
Commas: 225/224, 385/384, 325/324, 375/374
Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 6|]
EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg
Badness: .000917
Marvelcat[edit]
Commas: 169/168, 225/224, 385/384
Map: [<1 0 0 -5 12 -|, <0 2 0 4 -2 3|, <0 0 1 2 -3 1|]
EDOs: 9, 10, 19, 44, 53, 72, 125f, 197ef, 269cef
Badness: 0.0009997
Marvell[edit]
Commas: 225/224, 385/384, 1573/1568
13-limit eigenmonzo subgroup: 2.9/5.11/9
15-limit eigenmonzo subgroup: 2.7.15/13
Map: [<1 0 0 -5 12 -29|, <0 1 0 2 -1 6|, <0 0 1 2 -3 10|]
EDOs: 9, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcef, 610bcef
Badness: 0.000862
Isis[edit]
Commas: 225/224, 385/384, 275/273
Map: [<1 0 0 -5 12 17|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -3|]
EDOs: 10, 22, 31, 41, 53, 94
Badness: 0.000866
Projection pairs: 7 225/32 11 4096/375 13 131072/10125
Deecee[edit]
Commas: 225/224, 385/384, 364/363
13-limit eigenmonzo subgroup: 2.9/5.13/9
15-limit eigenmonzo subgroup: 2.3.13/5
Map: [<1 0 0 -5 12 27|, <0 1 0 2 -1 -3|, <0 0 1 2 -3 -8|]
EDOs: 9, 22, 41, 63, 72, 185cf, 257cf
Badness: 0.000920
Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875
Mirage[edit]
Commas: 225/224, 243/242, 385/384
Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 0|, <0 0 0 0 0 1|]
EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef
Badness: 0.000738
Minerva[edit]
Commas: 99/98, 176/175
Related linear temperament: orwell
Eigenmonzo subgroup: 2.7/5.11/9
Lattice basis: 16/15 length 0.8997 5/4 length 1.0457
Angle(16/15, 5/4) = 98.6044 degrees
Map to lattice: [<0 -1 0 -2 -2|, <0 -1 1 0 2|]
Map: [<1 0 0 -5 -9|, <0 1 0 2 2|, <0 0 1 2 4|]
Generators: 2, 3, 5
EDOs: 9, 12, 21, 22, 31, 43, 53, 74, 75, 96, 127
Badness: 0.000381
Projection pairs: 7 225/32 11 5625/512
Scales: minerva12, minerva22x
Athene[edit]
Commas: 99/98, 176/175, 275/273
13-limit eigenmonzo subgroup: 2.11/9.13/7
15-limit eigenmonzo subgroup: 2.11/9.13/7
Map: [<1 0 0 -5 -9 -4|, <0 1 0 2 2 -1|, <0 0 1 2 4 4|]
EDOs: 22, 31, 53, 84e, 118d, 149df, 171de, 202def
Badness: 0.000818
Projection pairs: 7 225/32 11 5625/512 13 625/48
Other eleven limit marvel children[edit]
The second comma of the normal comma list defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.
Spectacle[edit]
Commas: 225/224, 243/242
Related linear temperament: marvo
[|1 0 0 0 0>, |1/5 0 0 0 2/5>, |2/5 -2 1 0 4/5>, |-19/5 -4 2 0 12/5>, |0 0 0 0 1>]
Eigenmonzo subgroup: 2.9/5.11
Map: [<1 1 0 -3 2|, <0 2 0 4 5|, <0 0 1 2 0|]
Generators: 2, 11/9, 5
EDOs: 10, 31, 41, 72, 240, 259b, 269ce, 310c, 331bc, 353c, 497bc, 569bc
Badness: 0.000499
Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9
Scales: spectacle31
13-limit[edit]
Commas: 225/224, 243/242, 351/350
Map: [<1 1 0 -3 2 -5|, <0 2 0 4 5 -2|, <0 0 1 2 0 4|]
EDOs: 31, 72, 103, 175f, 209, 240
Badness: 0.001009
Apollo[edit]
Commas: 100/99, 225/224
Related linear temperament: Magic
Eigenmonzo subgroup: 2.7/5.11/9
Map: [<1 0 0 -5 2|, <0 1 0 2 -2|, <0 0 1 2 2|]
EDOs: 12, 19, 22, 41, 104edo, 157ce, 198ce, 220ce, 261ce
Projection pairs: 7 225/32 11 100/9
13-limit[edit]
Commas: 100/99, 225/224, 245/243
Eigenmonzo subgroup: 2.11/9.13/9
Map: [<1 0 0 -5 2 7|, <0 1 0 2 -2 -5|, <0 0 1 2 2 2|]
EDOs: 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef
Projection pairs: 7 225/32 11 100/9 13 3200/243
Potassium[edit]
Commas: 45/44, 56/55
Eigenmonzo subgroup: 2.9/7.11
Map: [<1 0 0 -5 -2|, <0 1 0 2 2|, <0 0 1 2 1|]
EDOs: 9, 10, 12, 19, 31e, 50e
Badness: 0.000464
Projection pairs: 7 225/32 11 45/4
13-limit[edit]
Commas: 45/44, 56/55, 78/77
13-limit eigenmonzo subgroup: 2.9/7.13/9
15-limit eigenmonzo subgroup: 2.9/7.13/9
Map: [<1 0 0 -5 -2 -8|, <0 1 0 2 2 3|, <0 0 1 2 1 3|]
EDOs: 9, 10, 19, 31e, 50e
Badness: 0.000733
Projection pairs: 7 225/32 11 45/4 13 3375/256
Fantastic[edit]
Commas: 225/224, 4375/4356
Map: [<2 0 0 -10 -7|, <0 1 0 2 0|, <0 0 1 2 3|]
EDOs: 12, 22, 50, 72, 166, 238c, 310c
Badness: 0.000743
Catakleismoid[edit]
Commas: 225/224, 4375/4374
Map: [<1 0 1 -3 0|, <0 6 5 22 0|, <0 0 0 0 1|]
EDOs: 19, 53, 72, 197e, 269ce
Badness: 0.001275
13-limit[edit]
Commas: 169/168, 225/224, 325/324
Map: [<1 0 1 -3 0 0|, <0 6 5 22 0 14|, <0 0 0 0 1 0|]
EDOs: 19, 53, 72, 125f, 197ef, 269cef
Badness: 0.000916
Hestia[edit]
Commas: 225/224, 125000/124509
Map: [<1 0 0 -5 9|, <0 2 0 4 -7|, <0 0 1 2 0|]
EDOs: 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce
Badness: 0.00154
13-limit[edit]
Commas: 169/168, 225/224, 1001/1000
Map: [<1 0 0 -5 9 -1|, <0 2 0 4 -7 3|, <0 0 1 2 0 1|]
EDOs: 19, 29, 43, 53, 72, 125f, 197ef, 269cef
Badness: 0.001062
Malcolm[edit]
Commas: 225/224, 2200/2187
Map: [<1 0 0 -5 -3|, <0 1 0 2 7|, <0 0 1 2 -2|]
EDOs: 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce
Badness: 0.001250
13-limit[edit]
commas: 225/224, 275/273, 325/324
Map: [<1 0 0 -5 -3 2|, <0 1 0 2 7 4|, <0 0 1 2 -2 -2|]
EDOs: 41, 53, 94, 429cdef, 523cdef
Badness: 0.001075
Tripod[edit]
Commas: 105/104, 144/143, 196/195
13-limit eigenmonzo subgroup: 2.9/7.13/11
15-limit eigenmonzo subgroup: 2.5/3.13/11
Map: [<1 0 0 -5 12 -8|, <0 1 0 2 -1 3|, <0 0 1 2 -3 3|]
EDOs: 9, 10, 19, 31, 41, 72f, 81, 91, 122f, 163df
Badness: 0.000745
Projection pairs: 7 225/32 11 4096/375 13 3375/256
Prodigy[edit]
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to miracle temperament. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.
Commas: 225/224, 441/440
Related linear temperament: miracle
[|1 0 0 0 0>, |13/12 1/2 -1/4 0 1/12>, |13/6 -1 1/2 0 1/6>, |3/2 -1 1/2 0 1/2>, |0 0 0 0 1>]
Eigenmonzo subgroup: 2.9/5.11
Lattice basis: secor length 0.9111, 3/2 length 0.9477
Angle(secor, 3/2) = 65.933
Map to lattice: [<0 0 -1 -2 -3|, <0 1 -1 0 3|]
Map: [<1 0 0 -5 -13|, <0 1 0 2 6|, <0 0 1 2 3|]
Generators: 2, 3, 5
EDOs: 10, 12, 29, 31, 41, 72, 247c, 319bcde, 391bcde, 463bcde
Badness: 0.000344
Projection pairs: 7 225/32 11 91125/8192
Scales: prodigy11, prodigy12, prodigy29
Hobbit bases[edit]
{2, 3, 5} subgroup
31: 81/80, 34171875/33554432
41: 34171875/33554432, 32805/32768
13-limit[edit]
Commas: 105/104, 196/195, 352/351
Map: [<1 0 0 -5 -13 -8|, <0 1 0 2 6 3|, <0 0 1 2 3 3|]
EDOs: 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef
Badness: 0.000736
Prodigious[edit]
Commas: 225/224, 441/440, 364/363
Map: [<1 0 0 -5 -13 -23|, <0 1 0 2 6 11|, <0 0 1 2 3 4|]
EDOs: 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf
Badness: 0.000900
Prodigal[edit]
Commas: 225/224, 441/440, 351/350
Map: [<1 0 0 -5 -13 -4|, <0 1 0 2 6 -1|, <0 0 1 2 3 4|]
EDOs: 31, 72, 103, 175f
Badness: 0.000889