Modeling Jazz Artist Influence MathematicallyA Preliminary Investigation

By Andres Calderon JaramilloMentor - 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 Rhythm

Velocity

Pitch Duration 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 D D CC E G E

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.

Simulation for Oscar Peterson

Simulation for Art Tatum

Methodology – Cont’d

Possible new measurement:

a2 a3 …a1 an

c2 c3 …c1 cn

DISTANCEFUNCTION

Potential

•Extension of results to other genres and instruments.

•Applicability:▫Learning styles by feedback.▫Recruitment of musicians.

Questions?