Figure 1.
Transformation: from the score to perception.
Before the notes on the score can be perceived as music by the listener, the score must be rendered (e.g., by a performer) as an acoustic (pressure) signal which varies over time. Therefore, in a psychophysical sense, the score may be defined as the objective correlate of subjective perception. By manipulating the score, we can find out what features of the score correspond to features of perception, in this case syncopation.
Figure 2.
A schematic diagram illustrating the process of generating the stimuli; basic half-bar rhythm-components are paired to create one-bar rhythm-patterns, rhythm-patterns are used to produce a three-bar score (including metronome) and finally the score is rendered as a waveform. a shows ‘binary’ and ‘ternary’ grouped rhythm-components. Rhythm-components A, B, F, G and H feature ‘missing down-beats’. b shows example rhythm-pattern pairings. c shows example scores, including rhythm-patterns featuring missing down-beats and polyrhythms. d Shows an example waveform (for rhythm-pattern CJ), rendered using synthesis.
Figure 3.
Syncopation by rhythm-component. a
Matrix showing group mean syncopation ratings for rhythm-patterns which may be indexed as follows: the upper triangle of the matrix refers to rhythm-patterns where the horizontal axis denotes the first rhythm-component of the rhythm-pattern, and where the vertical axis denotes the second rhythm-component. For the lower triangle of the matrix the reverse is true. This provides a general way to compare the mean ratings between the two orders of presentation for any given pair of rhythm-components. Same rhythm-component pairs (e.g., BB) are shown in grey. Note that the pair AA is excluded because it represents a full bar of rests. b shows a ‘map’ of the matrix shown in panel a, broken down into regions corresponding to score features: polyrhythmic and monorhythmic patterns in both 4/4 and 6/8. This map illustrates how the data is categorized in the subsequent analyses. c shows group mean and 95% confidence intervals for pooled ratings, averaged for each listener, composed (selectively) for comparison of ratings for all stimuli categorized within the following paired conditions: monorhythms in 4/4 versus those in 6/8 (see map in panel b), polyrhythms versus monorhythms, down-beat missing versus down-beat present, strong-beat missing versus strong-beat present. * denotes significance (p<0.05, Wilcoxon Signed-Rank Test, uncorrected). d plots mean and 95% confidence intervals for ratings pooled by rhythm-component; For each distribution, all ratings for rhythm-patterns featuring each respective rhythm-component were selected and separated into groups by location of the rhythm-component within the rhythm-pattern (e.g., AB + AC + AD… versus BA + CA + DA….). * denotes significance (p<0.05, Wilcoxon Signed-Rank Test, uncorrected).
Figure 4.
Pair-wise changes in ratings when rhythm-component order was switched.
This figure plots (for each rhythm-pattern) the change in group mean rating caused by switching the rhythm-component order (i.e., this is equivalent to a subtraction of the lower-triangle ratings of Fig. 3a from the upper-triangle ratings of Fig. 3a). Triangles denote significance (p<0.05, Wilcoxon Signed-Rank Test, uncorrected). Interestingly, the significant changes (when order was switched) correspond to missing down-beat rhythm-patterns. The right-hand key shows the notations for each pair of rhythm-patterns that reached significance.