1. A Perceptual Model of Pulse Salience and Metrical Accent in Musical Rhythms Richard Parncutt Presented by Zhenyao Mo

2. Overview Learning patterns (meters) Learning patterns (meters) Locating accents (downbeat) Locating accents (downbeat) Two experiments Two experiments A model A model –Perceptual –Quantitative –Computational

3. Experiment-1 : Pulse Salience Six Patterns Six Patterns –Pulse (1) –Waltz (2:1) –March (2:1:1) –Swing (3:2:1) –Skip (3:1:2) –Cross (2:1:1:2) Tempi Tempi –6 tempi Total : 6 * 6 = 36 trial Total : 6 * 6 = 36 trial 22 Listeners 22 Listeners To tap along with the underlying beat To tap along with the underlying beat Data Data –Pattern –Tempi –Period (time between taps) –Phase (start of the rhythm)

4. Experiment-1 : Conclusion Pulse sensation is quite ambiguous Pulse sensation is quite ambiguous Ambiguity increases as the pattern becomes more complex Ambiguity increases as the pattern becomes more complex Ambiguity increases as note rate increases Ambiguity increases as note rate increases –Small increase –inconsistent

5. Experiment-2 : Metrical Accent Six Patterns Six Patterns –Pulse (1) –Waltz (2:1) –March (2:1:1) –Swing (3:2:1) –Skip (3:1:2) –Cross (2:1:1:2) Tempi Tempi –Only 1 Along with basic patterns, target notes were played in another timbre Along with basic patterns, target notes were played in another timbre Total : 26 trial Total : 26 trial 22 Listeners 22 Listeners To judge whether the target was To judge whether the target was –Off the beats (sure) –Off the beats (not sure) –On the beats (not sure) –On the beats (sure) Conclusion: ambiguous Conclusion: ambiguous

6. Model : overview Phenomenal accent Pattern matching Pulse SalienceTempo DependenceMax Tactus Superposition Metrical Accent L.H. ’ s Model : begin at the start of a rhythm, then test hypothetical interpretations At each new event Present Model : look at a whole sequence at once

7. Model (continue) Phenomenal accent Pattern matching Pulse SalienceTempo DependenceMax Tactus Superposition Metrical Accent Either absolute time Or relative to a basic time Say, b = ¼ note beat Cycle: one duration of basic time

8. Model (continue) Phenomenal accent Pattern matching Pulse SalienceTempo DependenceMax Tactus Superposition Metrical Accent Each cycle is assign a phenomenal accent, which is calculated by SF : duration loudness timber pitch their interaction

9. Model (continue) Phenomenal accent Pattern matching Pulse SalienceTempo DependenceMax Tactus Superposition Metrical Accent Calculate the Pulse-match Salience S ’ m under period P and phase Q SF : a cycle S ’ m : a music paragraph S ’ m uses SF

10. Model (continue) Phenomenal accent Pattern matching Pulse SalienceTempo DependenceMax Tactus Superposition Metrical Accent Get rid of the dependence On tempo S ’ m -> Sm Normalize by basic time b

11. Model (continue) Phenomenal accent Pattern matching Pulse SalienceTempo DependenceMax Tactus Superposition Metrical Accent Pulse-period salience function Sp : based on distribution Overall salience S : a combination of Sm and Sp

12. Model (continue) Phenomenal accent Pattern matching Pulse SalienceTempo DependenceMax Tactus Superposition Metrical Accent A hypothesis with maximum salience is the Tactus

13. Model (continue) Phenomenal accent Pattern matching Pulse SalienceTempo DependenceMax Tactus Superposition Metrical Accent Metrical accent Am at time T in a period Am(T) Linear addition of the Saliences of T in all periods

14. Application of the Model Read the paper … Read the paper …