Discovery of retrograde and inverted themes for indexing musical scores

This paper describes extensions to a musical score indexing program that enable it to discover sequences of notes that appear in retrograde and/or inverted form. The program was tested over a set of 50 orchestral movements by several composers of the Baroque, Classical, and Romantic periods. The retrograde and inversion discovery algorithm added an average of 3.76 patterns per movement to the index, increasing the number of notes in the index by 6.5%, and the number of entries by 8.2%. Among the patterns added to the index were variations of 3 themes in retrograde, 5 themes in inversion, and 3 themes in retrograde inversion.