Pitch spelling: Investigating reductions of the search space

Pitch spelling addresses the question of how to derive traditional score notation from pitch classes or MIDI numbers. In this paper, we motivate that the diatonic notes in a piece of music are easier to spell correctly than the non-diatonic notes. Then we investigate 1) whether the generally used method of calculating the proportion of correctly spelled notes to evaluate pitch spelling models can be replaced by a method that concentrates only on the nondiatonic pitches, and 2) if an extra evaluation measure to distinguish the incorrectly spelled diatonic notes from the incorrectly spelled non-diatonic notes would be useful. To this end, we calculate the typical percentage of pitch classes that correspond to diatonic notes and check whether those pitch classes do indeed refer to diatonic notes in a piece of music. We explore extensions of the diatonic set. Finally, a good performing pitch spelling algorithm is investigated to see what percentage of its incorrectly spelled notes are diatonic notes. It turns out that a substantial part of the incorrectly spelled notes consist of diatonic notes, which means that the standard evaluation measure of pitch spelling algorithms cannot be replaced by a measure that only concentrates on non-diatonic notes without losing important information. We propose instead that two evaluation measures could be added to the standard correctness rate to be able to give a more complete view of a pitch spelling model.