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Encyclopedia of Microtonal Music Theory

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magic

[Joe Monzo]

A family of musical temperament tunings.

. . . . . . . . .
[data from Gene Ward Smith, Yahoo tuning-math message 10917 (Sat Jul 17, 2004 5:28 pm)]

family name: magic, 19&22
period: octave
generator: flat major third
5-limit
name: magic, 19&22
comma: 3125/3072 ratio = 2,3,5-monzo |-10 -1, 5> "magic comma"
mapping: [<1 0 2|, <0 5 1|]
poptimal generator: 19/60-edo
TOP period: 1201.276744 cents
TOP generator: 380.795718 cents
MOS cardinalities: 7, 10, 13, 16, 19, 22, 41, 60

Below are Tonescape® Lattices of the 5-limit versions.

7-limit
name: magic, 19&22
wedgie: <<5 1 12 -10 5 25||
mapping: [<1 0 2 -1|, <0 5 1 12|]
7-limit poptimal generator: 13/41-edo
9-limit poptimal generator: 71/224-edo
TOP period: 1201.276744 cents
TOP generator: 380.795718 cents
TM basis: {225/224, 245/243} ratios
MOS cardinalities: 7, 10, 13, 16, 19, 22, 41
name: muggles 16&19
wedgie: <<5 1 -7 -10 -25 -19||
mapping: [<1 0 2 5|, <0 5 1 -7|]
7-limit poptimal generator: 62/197-edo
9-limit poptimal generator: 53/168-edo
TOP period: 1203.148010 cents
TOP generator: 379.393104 cents
TM basis: {126/125, 525/512} ratios
MOS cardinalities: 7, 10, 13, 16, 19, 35, 54
name: witch
wedgie: <<5 1 9 -10 0 18||
mapping: [<1 0 2 0|, <0 5 1 9|]
7-limit poptimal generator: 39/125-edo
9-limit poptimal generator: 6/19-edo
TOP period: 1193.274911 cents
TOP generator: 377.328028 cents
TM basis: {36/35, 1875/1792} ratios
MOS cardinalities: 7, 10, 13, 16, 19
11 limit
name: magic, 19&22
wedgie: <<5 1 12 -8 -10 5 -30 25 -22 -64||
mapping: [<1 0 2 -1 6|, <0 5 1 12 -8|]
poptimal generator: 33/104-edo
TOP period: 1200.749423 cents
TOP generator: 380.922404 cents
TM basis: {100/99, 225/224, 245/243} ratios
MOS cardinalities: 7, 10, 13, 16, 19, 22, 41, 63, 104
. . . . . . . . .

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