ABSTRACT
In several places in this book, the topic of rhythm similarity has been mentioned brie y in dierent contexts. In this chapter, this topic is considered in greater detail. Before examining the complex problem of measuring sequence similarity, let us look at the simpler problem of comparing only two shapes. Consider the three pairs of shapes ordered le to right in Figure 33.1. Everyone would without doubt agree that the two shapes on the le are very hard to distinguish from each other, and that the two in the center are more similar to each other than the pair on the right. We are all experts at judging shape similarity. Even newly born infants can distinguish between squares and circles, and they can tell the dierence between the faces of their mother and father. e similarity between two objects is one of the most important features for distinguishing between them and for pattern recognition in general. Indeed, the survival of the human species depends crucially on this skill, and therefore it is not surprising that humans are masters at telling the dierence between the myriad of shapes they encounter in the world, even when their dierences are quite subtle. Can we construct a mathematical formula for measuring the similarity between two shapes, and more importantly for the topic of this book, between two musical rhythms? e articial intelligence pioneer Marvin Minsky (1981) frames the question thus: “What are the rules of musical resemblance? I am sure that this depends a lot on how melodies are ‘represented’ in each individual mind.”* To give a more complete account of this eld of research, and because no single method works well in all applications, in this chapter, several popular methods used to measure rhythm similarity are compared and illustrated with examples. For pedagogical reasons, we begin with the simplest possible measure (the Hamming distance) and then move on to more complex measures, highlighting their strengths and weaknesses along the way.
