1. Synchronization and Continuation Tapping to Complex Meters Joel S. Snyder 1, Erin E. Hannon 2, Edward W. Large 3, & Morten H. Christiansen 2 1 The Rotman Research Institute, Baycrest Centre for Geriatric Care 2 Department of Psychology, Cornell University 3 Center for Complex Systems and Brain Sciences, Florida Atlantic University RPPW 2005: Bilzen, Belgium

2. Complex meters “Western” meters contain beat levels that are isochronous and in simple integer ratios (e.g., 2:1, 3:1) within and between levels Complex meters contain one or more levels of non-isochronous beat levels with non-simple integer ratios within and between levels (e.g., 3:2) Appear in the folk music of several cultures, most notably in Balkan countries (Bulgaria, Macedonia, Greece) Used in music for dance, songs, children

3. Complex meters 500 750500 750 250 ms 1750 ms 500/750 ms 7/8: 2-2-3 750500 750500 250 ms 1750 ms 500/750 ms 7/8: 3-2-2

4. Are complex meters more difficult? North American adults have difficulty noticing temporal changes that disrupt complex (but not simple) meter beat structure… but Bulgarian and Macedonian adults and 6-month old North American infants notice disruptions for both (Hannon & Trehub, 2005) Experienced North American adult listeners stretch 3:2 ratios toward 2:1 during synchronization, mean = ~1.75 (Repp et al., in press)

5. Questions 1. To what extent can North American adults with a range of musical experience follow and represent the non-isochronous beat of complex meter stimuli? 2. To what extent does musical structure reinforce the non- isochronous beat structure and lower variability of tapping? 3. What is the relative influence of temporal grouping vs. metrical structure in determining tapping performance?

6. Method 24 undergraduate students (M=11,F=13); age=18-25 years; 0- 16 years of musical experience L interval = 750 ms, S interval = 500 ms, measure = 1750 ms Synchronization: Subjects tap to drum patterns (woodblock) in 2-2-3 or 3-2-2 accompanied by one of 24 melodies in 2-2-3 or 3-2-2 (flute) Continuation: Subjects continue tapping with or without melody with drum turned off (blocked) 2-2-3, match, present3-2-2, mismatch, absent

7. Data analysis Taps times (T) and stimulus times (S) normalized from 0-1 Ratio of long:short inter-tap interval indexes ability to follow and represent beat Coefficient of variation (CV) of tap position indexes overall difficulty Coefficient of delay (CDel) indexes tap timing relative to beat 3-way repeated measures ANOVA: Meter of drum (2) x match/mismatch (2) x present/absent melody during continuation (2)

8. Results: Bird’s eye view Continuation taps at beat 1 fixed to time 0

9. Results: Ratio Ratios fall between 1.5 and 2.0 (mean=1.679 for S and 1.732 for C) Synchronization: 3-2-2 is closer to complex ratio than 2-2-3 (p<.05)

10. Results: Ratio Ratios fall between 1.5 and 2.0 (mean=1.679 for S and 1.732 for C) Synchronization: 3-2-2 is closer to complex ratio than 2-2-3 (p<.05) Continuation: No main effect of meter Ratio is closer to complex meter when melody is present (p<.01) No correlations with musical experience

11. Results: Variability Synchronization: Higher CV in 3-2-2 (p<.001), despite better ratio Higher CV for mismatching melody in 3-2-2 but not 2-2-3 (p<.025)

12. Results: Variability Synchronization: Higher CV in 3-2-2 (p<.001), despite better ratio Higher CV for mismatching melody in 3-2-2 but not 2-2-3 (p<.025) Continuation (beats 2 & 3 only): No main effect of meter or match/mismatch Higher CV when melody is present (p<.005), due to error correction processes?

13. Results: Delay (Synchronization) Long<Short2<Short1 (p<.001) More negative CDel for 3-2-2 (p<.025) Meter x Beat interaction (p<.025), due to earlier tapping on Short2 in 3-2-2

14. Summary and conclusions North American adults with a range of experience with western music are able to produce ratios between 1.5 and 2.0 (cf. Hannon & Trehub, 2005; Repp et al., in press) Presence of melodies facilitate production of complex meters during continuation Tapping is less variable in 3-2-2 when the melody matches the meter (but not in 2-2-3) Pattern of negative asynchronies determined more by temporal grouping (Long<Short2<Short 1) than meter (Repp et al., in press Question: Do people raised with complex meters show similar types of biases in production?