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Testing Different Modelsof Melodic Contour
Daniel Müllensiefen, Melanie Bonometti,Lauren Stewart, Geraint Wiggins
Goldsmiths, University of London
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This paper is about …
a comparison between different models of melodiccontour and their cognitive usefulness.
We present• some background and motivation,• the four contour theories compared,• the setup of the experiment, and• results
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Melodic Contour is importantfor …
• melody perception and melodic memory(White, 1960; Dowling & Fujitani, 1971; Dowling, 1978; Idson& Massaro, 1976, 1978; Edworthy, 1983; Dowling et al. 1995;Cutietta & Booth, 1996)
• composing and structuring melodies (Toch,1923; Jeppesen, 1935; Hindemith, 1940; Perricone, 2000;Kachulis, 2003; Bradford, 2005)
• analysing and classifying melodies (Meyer,1956; Rosen, 1971; de la Motte, 1993)
• similarity measurement and melody retrieval(Parsons, 1975; Jesser, 1990; Polansky, 1996; Kim et al.,2000; Zhou & Kankanhalli, 2003)
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Melodic Contour has beendefined formally …
• as contour classes (Huron, 1996)• as Fourier coefficients (Schmuckler, 1999)• as polynomial coefficients (Müllensiefen & Wiggins, submitted)• as interpolation lines (Steinbeck, 1982; Zhou & Kankanhalli,
2003)• as symbol sequences (Parson, 1975; Kim et al., 2000; Pauws,
2000; Müllensiefen & Frieler, 2004)• as step curves (Juhasz, 2000; Eerola & Toiviainen, 2004)• as matrix of interval relationships (Friedmann, 1985;
Marvin & Laprade, 1987; Quinn, 1999)
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Our motivation:
Compare different contour representations and find onethat:
• can be implemented in a computer program• has a level of abstraction comparable to what human
listeners extract• is useful for modelling human melody processing• allows for a compact representation as a feature to
characterise melodies and be part of the FANTASTIC*analysis toolbox
*http://www.doc.gold.ac.uk/isms/mmm/?page=Software%20and%20Documentation
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The compared models
• Huron’s Contour (Huron, 1996)• Interpolation Contour (Steinbeck, 1982; Müllensiefen &
Frieler, 2004)• Polynomial Contour (Müllensiefen & Wiggins, submitted)• Step Contour (Eerola & Toiviainen, 2004)
![Page 7: Testing Di erent Models of Melodic Contourmas03dm/papers/Slides_ESCOM09_Contour.pdf · Melodic Contour has been ... Step Curve Contour • n numerical parameter pairs (pitch, IOI)](https://reader030.vdocuments.mx/reader030/viewer/2022021514/5b1bb9117f8b9a32258ed400/html5/thumbnails/7.jpg)
Huron’s Contour
• 1 parameter (categorical, 9 classes)• Depends on: ordinal relation between p1, mean(p2,…,pn-1), pn
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Contour Categories
Melody 1
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Interpolation Contour
• A variable number of parameter pairs (line gradient, length),usually 1 to 5.
• Depends on: Number of reversals of pitch direction andexclusion of change notes
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Polynomial Contour
• 8 numerical parameters (polynomial coefficients)• Depends on: Capacity of pitch and onset data to be
approximated by polynomial shapes
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Step Curve Contour
• n numerical parameter pairs (pitch, IOI) for n notes• Depends on: pitch values and IOIs of all notes
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Experiment
• Paradigm: Audio-visual shape assignment task Assumption: Visual recoding of note sequence is inherent in
cognitive contour processing (e.g. Balch & Muscatelli, 1986; Princeet al., 2009)
4x10 practice trials 4x20 trials, including 5 repetition trials Complete randomisation, individual testing
• Participants: 85 adults (mean age: 21.2, normal vision, hearing) no selection for musical background (‘college population’)
• Dependent variables: Response Times Intra-subject consistency Inter-subject consistency Subject-Model consistency (i.e. accuracy)
• Independent Variable: Contour Representation (4-level factor)
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Experiment
• Working definition of melodic contour ininstructions:
“An image that represents the melody just heard”
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Example Trial
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Example Trial
1 2
3 4
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Results
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Results: Reaction Times
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Results: Subject-Model Accuracy
<.001***
<.001***
<.001*
Step
<.001*<.001***Line
.614Curve
Huron
Step
CurveHuron
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Results: Inter-Subject Agreement
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Results: Intra-Subject Agreement
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Summary
• Step Contour takes longest to process• Step Contour significantly better in terms of
Model-Subject Agreement Inter-Subject Agreement Proportion of correct ∧ identical responses
⇒supports assumption of contour as arepresentation for conscious processing (Dowlinget al., 1995)
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Next steps
• Look at individual differences• Implement features characterising step contour
curves (FANTASTIC): Global Variation Global Direction Local Variation
• Create Contour Space• Test: Distance in feature space ~ distance in
cognitive space?
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Testing Different Modelsof Melodic Contour
Daniel Müllensiefen, Melanie Bonometti, Lauren Stewart,Geraint Wiggins
Goldsmiths, University of London