The ps13 pitch spelling algorithm

Abstract

In the ps13 pitch spelling algorithm, the pitch name of a note is assumed to depend on the local key and voice-leading. In the first stage of ps13, the pitch name implied for a note by a tonic is assumed to be the one that lies closest to that tonic on the line of fifths. The strength with which a pitch name is implied for a note is assumed to be proportional to the sum of the frequencies of occurrence, within a context around the note, of the tonics that imply that pitch name. In the second stage of ps13, certain neighbour-note and passing-note errors in the output of the first stage are corrected. An implementation of ps13, called PS13, spelt correctly 99.31% of the notes in a 195972 note test corpus, . A post-processing phase was added to PS13 in which the pitch names computed by PS13 are transposed by a diminished second if this brings them closer on the line of fifths to the pitch names of the notes in their vicinity. This version of the algorithm spelt 99.43% of the notes in correctly. When the second stage was removed altogether from PS13, 99.44% of the notes in were spelt correctly. The ps13-based algorithms achieved higher note accuracies than the algorithms of Temperley, Longuet-Higgins, Cambouropoulos and Chew and Chen on both and a “noisy” version of containing temporal deviations similar to those that occur in MIDI files derived from human performances.

Acknowledgements

The work reported here was funded by EPSRC grant number GR/S17253/02. I am grateful to Geraint Wiggins and the other members of the ISMS group at Goldsmiths College, University of London, for their support during this project. I would also like to thank Alan Marsden for providing detailed feedback on an earlier draft of this paper.

Notes

¹Available online at http://www.musedata.org

²There was, in fact, just one occurrence in of a black note not spelt as either a single flat or a single sharp. This was a single Bx in the first movement of Haydn's String Quartet in A major, Hob. III:60 (Op. 55, No. 1).

³I am grateful to Alan Marsden for pointing out that the fact that FixedLOFRange performed best over with ℓ_min = −2 is not surprising, since, during the period over which the music in was composed, the ‘wolf fifth’ in any regular mean-tone temperament (Oldham and Lindley, 2006) was commonly placed between G♯ and E♭ – that is, the two pitch name classes at the limits of the range permitted by FixedLOFRange when ℓ_min = −2.

⁴The Melisma system is available online at <http://www.link.cs.cmu.edu/music-analysis/>