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 Care
2Department 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
7/8: 2-2-3
250 ms
500/750 ms
500
500
750
500
500
750
1750 ms
7/8: 3-2-2
250 ms
500/750 ms
1750 ms
750
500
500
750
500
500
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)
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?
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?