Synchronization and Continuation Tapping to Complex Meters

Joel S. Snyder1, Erin E. Hannon2, Edward W. Large3, & Morten H. Christiansen2

1The Rotman Research Institute, Baycrest Centre for Geriatric Care2Department of Psychology, Cornell University

3Center for Complex Systems and Brain Sciences, Florida Atlantic University

RPPW 2005: Bilzen, Belgium

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

Complex meters

500 500 750 500 500 750

250 ms

1750 ms

500/750 ms

7/8: 2-2-3

750 500 500 750 500 500

250 ms

1750 ms

500/750 ms

7/8: 3-2-2

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)

Questions1. 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?

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, present 3-2-2, mismatch, absent

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)

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

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)

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

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)

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?

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

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?