1. Rhythm and Time Two ways of viewing time Time as an endless stream, continuously flowing Heraclitus: “Time is a river into which we can never step into the same place twice” Sir Isaac Newton: “absolute, true and mathematical time, of itself and from its own nature … flows equably without relation to anything external.” Time as divided into discrete units Problem of how we demarcate units Analogy to units for space Time is intangible

2. Rhythm and Time Three aspects of time: Duality Time has dual modes of structure 1 st is clocklike 2 nd relies on experience for demarcation Hierarchy Both modes are hierarchic Motion Motion as the essence of time Time itself as moving Problematic to describe Quantitative mode Qualitative mode

3. Time in Music Properties of time in music Duality Distinction between meter and rhythm Hierarchy Both meter and rhythm can be viewed at increasingly broader time spans Motion Tempo as example of motion in music

4. The Experience of Time The Psychological Present The temporal span of attention, or one’s window on experience How long is the psychological present? Psychological Pace Is there a spontaneous tempo to the pace of psychological events?

5. Rhythm in Music What is meant by rhythm in music? The problem of a definition of rhythm Working definition A response to music of sound sequences of certain characteristics, comprising experiential as well as behavioral aspects

6. Rhythm vs. Non-rhythm Grouping Accent Regularity Psychological present

7. Descriptions of Musical Rhythms Are there descriptive systems for classifying musical rhythms? Classification with regard to meter Ex., Duple (2 beat) and Triple (3 beat) meters Compound meters: Quadruple (4 beat) and Sextuple (6 beat)

8. Descriptions of Musical Rhythms Are there descriptive systems for classifying musical rhythms? Classified in analogy to prosody Ex. Cooper & Meyer (1960) Iamb  - Trochee-  Dactyl-  Amphibrach  -  Anapest  - - accented  unaccented

9. The Metrical Hierarchy │x x x x│x x x x│x x x x│x x x x│ Level 1 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Level 2 ● ● ● ● ● ● ● ● Level 3 ● ● ● ● Level 4 ● ● Hierarchy 4 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1

10. Multidimensional Approaches to Musical Rhythms Gabrielsson (1973a, b, c)

11. Multidimensional Approaches to Musical Rhythms, con’t Gabrielsson (1973a, b, c)

12. Polyrhythms Two Component Polyrhythms: 2 x 3: │x x │x x │x x │ │x x x│x x x│x x x│ 3 x 4: │x x x│x x x│x x x│ │x x x x│x x x x│x x x x│ Three Component Polyrhythms: 3 x 4 x 5: │x x x│x x x│ │x x x x│x x x x│ │x x x x x│x x x x x│

13. Pitch and Rhythm Interactions Palmer & Krumhansl (1987a, 1987b) Pitch Condition: Temporal Condition: Melody Condition:

14. Pitch and Rhythm Interactions, con’t Palmer & Krumhansl (1987a, 1987b) Additive Model: Melody = α Pitch + β Temporal + c Interactive Model: Melody = α Pitch + β Temporal + ρ PT+ c PT = A pitch x temporal interaction (e.g., Pitch x Temporal; Pitch / Temporal).

15. Pitch and Rhythm Interactions, con’t Joint accent structure (Mari Jones, Marilyn Boltz)

16. Pitch and Rhythm Interactions, con’t Joint Accent Structure (Mari Jones, Marilyn Boltz)

17. Pitch and Rhythm Interactions, con’t Joint Accent Structure (Mari Jones, Marilyn Boltz)