1. Modeling Jazz Artist Influence Mathematically A Preliminary Investigation By Andres Calderon Jaramillo Mentor - Larry Lucas, Ph.D. University of Central Oklahoma

2. Presentation Outline Project description and literature review. Musical background. Mathematical background. Methodology and potential. Questions.

3. 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.

4. Literature Review Music cognition and perception. Composer identification. Style recognition. Automatic composition. ▫Improvising Jazz Using Markov Chains by Yuval Marom.

5. Musical Background Melody Notes Rhythm Velocity Pitch Duration Rests

6. 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.

7. 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.

8. Mathematical Background – Cont’d “Pop Goes the Weasel” fragment (pitches) C C D D D D C C C C E E G G E E S = {C, D, E, G}

9. Methodology Main goal: ▫A measure of musical resemblance. Building Markov chains for a piece: ▫“Naive” approach. ▫“Controlled” approach. ▫“Multidimensional” approach.

10. 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.

11. Simulation for Oscar Peterson Simulation for Art Tatum Methodology – Cont’d Possible new measurement: a2a2 a2a2 a3a3 a3a3 … … a1a1 a1a1 anan anan c2c2 c2c2 c3c3 c3c3 … … c1c1 c1c1 cncn cncn DISTANCE FUNCTION DISTANCE FUNCTION

12. Potential Extension of results to other genres and instruments. Applicability: ▫Learning styles by feedback. ▫Recruitment of musicians.

13. Questions?