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Tempo Curves Considered Harmful

Not so long ago we decided to spend a Christmas holiday studying music and its performance. One of us is an amateur mathematician (M) and the other one likes to delve into old psychology textbooks (P), and because we enjoy impressing each other with new facts and insights, we often find ourselves in vehement discussions. Therefore we thought we might have a pleasant and peaceful time by putting our beloved hobby horses aside and embark upon a subject about which neither of us knew much: the timing aspects of music. We became interested in this field because we had noticed, while playing with the computer, our favourite toy, that adding just a bit of random timing noise to a program that played a score in an otherwise metronomically perfect way, made the music much more pleasant to listen to. It seemed as if we could make more sense of it. But we suspected that there was more to timing and expressive performance than adding bits of noise, so we invited a mutual friend who is a retired professional pianist to spend Christmas in our small but well equipped laboratory. Our friend has a great love for the piano and its music, but is completely ignorant of the advances of modern technology. To demonstrate to him our latest sequencer program we asked him to play the theme from the six variations composed by Ludwig van Beethoven on the duet Nel cor piu non mi sen/o, the score of which we had lying around (see Figure 1).