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Pitch Spelling Algorithms. Author: David Meredith Presented 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. - PowerPoint PPT Presentation
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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!