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Musical variations from a chaotic mapping
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30.For interpreting the musical scores that demonstrate the results, nonmusicians might imagine the horizontal lines and intervening spaces on the scores as a kind of graph paper. The notes could be considered points on the graph. Then, pattern matching could alert the nonmusician to changes between the variation and the original piece.
31.The D4 in the soprano voice of m. 1 is prolonged, thus creating tension, until its relaxation or resolution on E4. Though the prolongation is not literally written out, the D4—clearly distinct from the lower voices (E3, G3, E3)—is heard as an accented unresolved dissonance until beat 4, when it resolves upwards by whole step.
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35.The D4 in beat 3 of m. 4 is interpreted as a prolonged appoggiatura, resolving to E4 on the last sixteenth of the measure. The G3 is analyzed as a lower neighbor to A3.
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