MIT Student Uses Math to Blend Musical Notes Seamlessly

The student invented an algorithm based on "optimal transport."

An MIT student has invented an algorithm that produces a portamento effect, the effect of gliding a note at one pitch into a note of a lower or higher pitch, between any two audio signals in real-time. In tests, the algorithm seamlessly merged various different audio clips. 

The algorithm is based on something called "optimal transport." It is a geometry-based framework formulated in the 1700s that determines the most efficient ways to move objects between multiple origin and destination configurations. 

"Optimal transport is used here to determine how to map pitches in one sound to the pitches in the other," said the algorithm's creator Trevor Henderson, now a graduate student in computer science. "If it's transforming one chord into a chord with a different harmony, or with more notes, for instance, the notes will split from the first chord and find a position to seamlessly glide to in the other chord."

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