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Scatology. Scatology. Study of output Also called coprology From what comes out you get a pretty good idea of what when in!!!!!. Allusion in Music. Beethoven and Mozart. Weber and Beethoven. Stravinsky and Lithuania. Stravinsky and Lithuania II. Bruckner and Schubert.
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Scatology • Study of output • Also called coprology • From what comes out you get a pretty good idea of what when in!!!!!
Finding allusions • Locating repeating patterns • Pattern matching a staple of artificial intelligence • Often called pattern recognition • Origins in set theory in mathematics • Finding patterns in math can be quite different than finding them in music.
Pattern Matching code • No user-given pattern • Segmentation (incremental) • Controllers (variables) • Too wide: noise • Types of variations? • Too narrow: no patterns • Self-adjusting??
Types of variations • Transposition • Inversion • Retrograde • Inversion-retrograde • Interpolated notes • Excised notes • Equivalent sets
Set Theory Pattern matching for contemporary music. Note that many musical/math set processes do not have corresponding counterparts!
Mathematical set theory • Set: {45,15,17} • Curly brackets • Typically unordered
Mathematical set theory • is an element of • is not an element of • is a proper subset of • is a subset of • is not a subset of • the empty set; a set with no elements • union • intersection
Mathematics and Sets Example of a set proof: A (B C) = (A B) (A C)
Musical set theory • Set: [9,3,5] • Brackets • Ordered or unordered • Modulo 12 (pitch classes) • Ordered version of above: [9,3,5] • Normal (unordered/smallest) version of above [3,5,9] • Prime version (unordered/invertible) of above [0,2,6]
Music and Sets • The same set • [0,3,7] [0,3,7] [0,3,7]
Cellular automata • An example rule set • 8 possible ways to set upper patterns (23) • 256 possible rule sets (28) • Follows Steven Wolfram’s model in a New Kind of Science (NKS)
Sequence of steps • Time downward (one dimensional?)
In color • Rule 30 • Rule 110