Pitch Spelling Algorithms

Author: David MeredithPresented by Jie Liu

About the author

Center for Computational Creativity, Department of Computing at City University, 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 transcriptionRequired for audio-to-notation transcriptionUseful in music information retrieval and musical pattern discovery

Example

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 spellingUsing an algorithm to model itEvaluated 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 fifthsDesigned 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 fifthsAssume first note is tonic or dominant of opening keyAssume 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 RuleHarmonic 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, KpostLetter 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)

Experimental Results (Bach’s music)Algorithm %notes

correctNumber of errors

Cambouropoulos

93.74 2599

Longuet-Higgins

99.36 265

Temperley 99.71 122

Ps 13Kpre=33,Kpost(23,25)

99.81 81

Discussion on Kpre and Kpost

Best: Kpre=33, 23<=Kpost<=25Worst: Kpre = Kpost =1

Mean number of errors 109.082 and mean accuracy 99.74% (1<=Kpre, Kpost<=50)

Comparison of algorithms (baroque)

Notes Ps13(99.33%)

Camb(98.71%)

Temp(97.67%)

LH(97.65%)

Intervals

Temp(99.45%)

Ps13(99.17%)

LH(99.16%)

Camb(98.65%)

Ints and notes

Ps13(99.25%)

Camb(98.68%)

Temp(98.56%)

LH(98.41%)

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.

Thank you!