Pitch Spelling Algorithms Author: David Meredith Presented by Jie Liu
About the author • Center for Computational Creativity, Department of Computing at CityUniversity,London • His research project focus on the development of algorithms for musical pattern recognition and extraction.
Concept of Pitch Spelling Algorithm • Pitch spelling algorithm attempts to compute the correct pitch names of the notes in a passage of tonal music • Onset-time, MIDI note number and duration(optional)
Practical Applications: • Required for MIDI-to-notation transcription • Required for audio-to-notation transcription • Useful in music information retrieval and musical pattern discovery
Example 1 • Different chromatic intervals. • Three occurrences of the same motive. • The three patterns have the same scale-step interval structures (-1,+1,+1) • Important for MIR
Example 2 • (a). G#4 leading note in A minor • (b) Ab4 subdominant in C minor
Pitch Spelling in common practice Western tonal music • Determined by the roles of notes in the harmonic, motivic and voice-leading structures of the passage. • Pitch spelling is not arbitrary. • The resulting score should represent the way that the music is perceived and interpreted.
Modelling the process of pitch spelling • What are the cognitive process involved when a musically trained individual do the pitch spelling • Using an algorithm to model it • Evaluated by authoritative published editions of scores
Three previous pitch spelling methods • Cambouropoulos (2002) • Longuet-Higgins (1993) • Temperley (2001) • Test Corpora: Bach’s music baroque and classical music
Longuet-Higgins’s algorithm • Input: (p (keyboard position),ton,toff) • Compute q (sharpness) for every note q is the position of the pitch name of the note on the line of fifths • Designed to be used only on monophonic melodies Db Ab Eb Bb F C G D A E B F# C# G# -5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
Longuet-Higgins’s algorithm • Assume every note is no more than 6 steps from tonic on the line of fifths • Assume first note is tonic or dominant of opening key • Assume consecutive notes always less than 12 steps apart on line of fifths. • more than 6 steps is the evidence of a change of key
Cambouropoulos’s algorithm • No priori knowledge, such as key signature, time signature, tonal centers and so on
Temperley’s algorithm • Pitch Variance Rule (L-H algorithm) Assume consecutive notes always less than 12 steps apart on line of fifths • Voice Leading Rule • Harmonic Feedback Rule (in good harmonic representations)
Temperley’s algorithm • Requires duration of each note and tempo---- it needs more information than other algorithms • Cannot deal with cases where two or more notes with the same pitch start at the same time
Ps 13 algorithm (improved on Temperley’s) • CNT (p,n)---Kpre, Kpost • Letter name L(p,n) • Set of tonic pitch classes X(n,l) • N(l,n)=sum CNT(p,n) (p is from X(n,l)) • n=max N(l,n)
Discussion on Kpre and Kpost • Best: Kpre=33, 23<=Kpost<=25 • Worst: Kpre = Kpost =1 • Mean number of errors 109.082 and mean accuracy 99.74% (1<=Kpre, Kpost<=50)
Conclusion and Future Work • Algorithms based on line of fifths (L-H and Templey) mis-spelt many more notes in the classical music than other algorithms • Algorithms should be tested on more varied corpus
Conclusion and Future Work • What is the best key-finding algorithm to use for pitch spelling (based on Krumhansl’s claim) • Need to determine whether or not algorithms are consistent with the perception and cognition process.