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Modeling Jazz Artist Influence
Mathematically
A Preliminary Investigation
By Andres Calderon Jaramillo
Mentor - Larry Lucas, Ph.D.
University of Central Oklahoma
Presentation Outline
• Project description and literature review.
• Musical background.
• Mathematical background.
• Methodology and potential.
• Questions.
Project Description
• Markov chains as tools in the modeling of
influence between jazz artists (musical
resemblance).
• Choice of primary artists:
▫ Art Tatum (1909 – 1956).
▫ Oscar Peterson (1925 – 2007).
• Only piano melodies are considered.
Literature Review
• Music cognition and perception.
• Composer identification.
• Style recognition.
• Automatic composition.
▫ Improvising Jazz Using Markov Chains by Yuval
Marom.
Musical Background
Melody
Notes
Pitch
Rhythm
Duration
Velocity
Rests
Mathematical Background
• Stochastic process defined:
▫ Family of random variables defined on some
sample space .
• State space (S):
▫ Set of distinct values assumed by a stochastic
process.
Source:
Isaacson, D. L., & Madsen, R. W. (1976). Markov chains, theory and
applications. John Wiley & Sons, Inc.
Mathematical Background – Cont’d
• Discrete-time Markov chain:
▫ Discrete-time stochastic process.
▫ Countable or finite state space.
▫ Satisfies the Markov property.
• Transition probability matrix.
Source:
Isaacson, D. L., & Madsen, R. W. (1976). Markov chains, theory and
applications. John Wiley & Sons, Inc.
Mathematical Background – Cont’d
“Pop Goes the Weasel” fragment (pitches)
C
C
D
D
E
G
E
C
S = {C, D, E, G}
Methodology
• Main goal:
▫ A measure of musical resemblance.
• Building Markov chains for a piece:
▫ “Naive” approach.
▫ “Controlled” approach.
▫ “Multidimensional” approach.
Methodology – Cont’d
• Variation:
▫ Higher-order Markov chains.
▫ Markov chains for “macroscopic” parameters.
• Some measures of resemblance:
▫
▫
▫
▫
Distribution of the pitch.
Distribution of the velocity.
Distribution of the duration.
Distribution of note and rest runs.
Methodology – Cont’d
Possible new measurement:
a1
a2
a3
…
an
Simulation for Art Tatum
DISTANCE
FUNCTION
c1
c2
c3
…
Simulation for Oscar Peterson
cn
Potential
• Extension of results to other genres and
instruments.
• Applicability:
▫ Learning styles by feedback.
▫ Recruitment of musicians.
Questions?