1. Pitch Spelling Algorithms
Author: David Meredith
Presented by Jie Liu

2. Meredith: Pitch Spelling
ISE599: 2004: Liu Jie
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.

3. 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)

4. Practical Applications:
Required for MIDI-to-notation transcription
Required for audio-to-notation transcription
Useful in music information retrieval and musical pattern discovery

5. Example

6. 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

7. Example 2 (a). G#4 leading note in A minor
(b) Ab4 subdominant in C minor

8. 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.

9. 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

10. Three previous pitch spelling methods
Cambouropoulos (2002)
Longuet-Higgins (1993)
Temperley (2001)
Test Corpora:
Bach’s music
baroque and classical music

11. 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 –

12. 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

13. Cambouropoulos’s algorithm
No priori knowledge, such as key signature, time signature, tonal centers and so on

14. 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)

15. 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

16. 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)

17. Experimental Results (Bach’s music)
Algorithm
%notes correct
Number of errors
Cambouropoulos
93.74
2599
Longuet-Higgins
99.36
265
Temperley
99.71
122
Ps 13
Kpre=33,
Kpost(23,25)
99.81 81

18. Discussion on Kpre and Kpost
Best: Kpre=33, 23<=Kpost<=25
Worst: Kpre = Kpost =1
Mean number of errors and mean accuracy 99.74% (1<=Kpre, Kpost<=50)

19. Comparison of algorithms (baroque)
Notes
Ps13
(99.33%)
Camb
(98.71%)
Temp
(97.67%) LH
(97.65%)
Intervals
(99.45%)
(99.17%)
(99.16%)
(98.65%)
Ints and notes
(99.25%)
(98.68%)
(98.56%)
(98.41%)

20. 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

21. 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.

22. Thank you!