Similarities among Transformed Melodies: The Abstraction of Invariants

In studying the abstraction of musical ideas from diverse invariants, six-note melodies of varying note durations and note intensities were used as prototypes. Four types of transformations on a prototype distorted each of four musical components: contour, interval, loudness, and duration. In an acquisition phase, listeners heard simple transformations on a single prototype, but in recognition heard both simple and compound transformations as well as the prototype, which had been unheard in acquisition. Predictions were borne out, namely, that both prototypes and simple transformations were falsely recognized with greater certainty than any other transformed melodies; and latencies of recognition of the prototypes, an alternative measure of certainty, were shorter than latencies of recognition of any other transformed melodies. It is argued that the methods used enable the examination of the properties of musical transformation spaces.