In this article, cognitive and musicological aspects of pitch and pitch interval representations are explored via computational modeling. The specific task under investigation is pitch spelling, that is, how traditional score notation can be derived from a simple unstructured 12-tone representation (e.g., pitch-class set or MIDI pitch representation). This study provides useful insights both into the domain of pitch perception and into musicological aspects of score notation strategies. A computational model is described that transcribes polyphonic MIDI pitch files into the Western traditional music notation. Input to the proposed algorithm is merely a sequence of MIDI pitch numbers in the order they appear in a MIDI file. No a priori knowledge such as key signature, tonal centers, time signature, chords, or voice separation is required. Output of the algorithm is a sequence of "correctly" spelled pitches. The algorithm is based on an interval optimization approach that takes into account the frequency of occurrence of pitch intervals within the major-minor tonal scale framework. The algorithm was evaluated on 10 complete piano sonatas by Mozart and had a success rate of 98.8% (634 pitches were spelled incorrectly out of a total of 54,418 notes); it was tested additionally on three Chopin waltzes and had a slightly worse success rate. The proposed pitch interval optimization approach is also compared with and tested against other pitch-spelling strategies.
On interval representations of graphs
