1. The Phase Correction Response in Sensorimotor Synchronization Bruno H. Repp Haskins Laboratories, New Haven, CT (now retired)

2. Preliminaries Apologies for focusing on my own research! The data I will show are for musicians as participants (“master tappers”). References can be found in Repp (2005) and Repp & Su (2013), two large review papers in Psychonomic Bulletin & Review.

3. Definitions Sensorimotor synchronization is the temporal coordination of a rhythmic movement with an external rhythm. Such coordination requires sensorimotor coupling, which gives rise to phase correction: temporal adjustments of the movement that improve and maintain synchronization. When both rhythms consist of discrete events (e.g., metronome ticks accompanied by finger taps), each external event elicits an adjustment of the subsequent movement event: a phase correction response (PCR). Coupling strength can be estimated from discrete time series with statistical methods. One convenient method, however, is to introduce perturbations in the external rhythm and to observe the PCRs elicited by them.

4. The Phase Shift Paradigm IOI = inter-onset interval PS = phase shift PCR = phase correction response (includes noise!) Calculation of the PCR: PCR i = a i - a i-1 = (t i - m i ) - (t i-1 - m i-1 ) = (t i - t i-1 ) - (m i - m i-1 ) = T i - M i a = asynchrony; t = time of tap; m = time of (metronome) tone T = inter-tap interval; M = metronome IOI

5. The PCR Function The PCR function is strongly linear for PSs within ~ ±10% of the IOI. Thus, PCR = α * PS The slope α is an estimate of sensorimotor coupling strength. The perceptual threshold for detecting a PS (~ ±5% of the IOI) seems irrelevant. (Schematic data for illustration)

6. The Complete PCR Function Phase Shift (ms) IOI = 500 ms (Repp, 2002, Human Movement Science) For PSs between ±50% of the IOI, the PCR function is nonlinear (sigmoid- shaped). There is also an asymmetry: Large negative PSs elicit smaller PCRs than do large positive PSs.

7. Intentional Suppression of the PCR The Event Onset Shift (EOS) Paradigm PCR i = a i - a i-1 - PS (Repp, 2002, Human Movement Science) IOI = 500 ms PCRs to EOSs larger than ±10% of the IOI can be suppressed, but a small residual PCR remains. It is immaterial whether the perturbation is an EOS or a PS. The steep linear slope of the PCR function within ±10% of the IOI is unaffected (?) by intentional suppression. EOS or PS (ms)

8. Does the Slope of the PCR Function Change at a Fixed Absolute or Relative Magnitude of the PS? Absolute (ms)Relative (% of IOI) (Repp, 2011, Journal of Motor Behavior) No clear answer

9. Alpha as a Function of IOI (Repp, 2008, Journal of Motor Behavior)(Repp, 2011, Journal of Motor Behavior) PSs within ±10% of IOIPSs within ±25 msPSs within ±10% of IOI

10. Enhancement of Alpha During the PCR (Repp, Keller, & Jacoby, 2012, Acta Psychologica)

11. What Triggers the PCR? Is it the preceding asynchrony? Perhaps, when an asynchrony is perceived. But can subliminal perception really trigger a PCR? Moreover, an asynchrony is not needed for a PCR! Indeed, the PCR tends to be larger in the absence of an asynchrony! (Repp, 2001, Journal of Experimental Psychology: Human Perception and Performance)

12. What Triggers the PCR? t i - m i Asynchrony (1) Perception C i - α * (t i - m i ) Phase correction No threshold? (2) mimi titi References α 1 - α (sensory) (motor) (sensorimotor) m i + C i t i + C i Phase resetting Persistence C i - α * (t i - m i ) Phase correction (inhibitory) t = time of tap; m = time of (metronome) tone; C = internal timekeeper interval Is it mixed phase resetting?

13. What Triggers the PCR? (continued) The mixed phase resetting model bypasses the issue of subliminal perception. It readily accounts for the increased PCR in the absence of an asynchrony. It can explain the nonlinear PCR function and the increase of alpha with IOI. However, it cannot explain overcorrection at long IOIs. Also, it cannot explain why alpha is enhanced during the PCR. Is it the preceding perceptual asynchrony? e i - m i Asynchrony (3) C i – f(e i - m i ) Phase correction Neural dynamics (perceptual) e = expectation (of sound) This model allows for a nonlinear dynamic process that could lead to overcorrection or alpha enhancement. A dynamic approach avoids the issue of subliminal perception. (cf. Large & Jones, 1999, Psychological Review) ?

14. Perceptual Monitoring of Subdivisions (Baseline condition) Presence of a subdivision following the EOS reduces the PCR (relative to baseline). A shifted subdivision elicits a PCR (smaller than baseline). Insertion of a single “shifted” subdivision elicits a small PCR! (Repp, 2008, Psychological Research) All these effects become larger when the IOI is increased.

15. Temporal Evolution of the PCR The PCR takes 250-300 ms to evolve, regardless of IOI duration. Conditions B and C yield results similar to those of condition A. Condition A (Repp, 2011, Experimental Brain Research)

16. Does the PCR Increase with the Immediately Preceding IOI (> 300 ms)? (Repp, London, & Keller, 2008, Music Perception)(Repp, London, & Keller, 2011, Psychological Research) Sometimes it does (see Figure A on left), but more often it doesn’t. In two-interval rhythms, the PCR also does not increase systematically with cycle (IOI) duration (see figure below).

17. The PCR Is a Response to Violation of Temporal Expectations (Repp & Jendoubi, 2009, Advances in Cognitive Psychology) The PCR depends on the direction of change and may run counter to long-term changes in relative phase caused by subdivision timing.

18. Using the PCR to Investigate Auditory Streaming The PCR seemed to be insensitive to auditory streaming! (Repp, 2009a, Quarterly Journal of Experimental Psychology) IOI = 450 msIOI = 600 ms

19. Using the PCR to Investigate Auditory Streaming (continued) (Repp, 2009b, Quarterly Journal of Experimental Psychology) IOI = 450 msIOI = 600 ms Here the PCR was again insensitive to streaming at the slower tempo, but at the faster tempo a streaming effect was evident. Overall, the results suggest that perceptually segregated streams are often still integrated into a composite rhythm.

20. Anticipatory Phase Correction (APC) IOI (ms) (Repp & Moseley, 2012, Human Movement Science) Phase correction can be consciously controlled. Up to 1 s was needed for optimal use of cues. APC was generally conservative (< 80%). PCR to residual PS was like PCR without APC.

21. Kinematic Implementation of Phase Correction (Torre & Balasubramaniam, 2009, Experimental Brain Research)(Repp & Steinman, 2010, Human Movement Science) Phase correction occurs during the upward movement in tapping but evolves continuously (and is less vigorous) during the oscillation cycle

22. Summary The PCR elicited by perturbations is a manifestation of sensorimotor coupling. It is usually automatic but can be consciously controlled for purposes of intentional decoupling or anticipation (based on advance information). It does not require awareness of perturbations or asynchronies, not are sensorimotor asynchronies required to trigger it. It increases nonlinearly with perturbation magnitude but is a highly linear function of perturbation magnitude within a narrow range. It increases with metronome IOI duration, but not necessarily with preceding IOI duration or cycle duration in non-isochronous rhythms.* At long IOI durations (> 1 s), overcorrection occurs, for still unknown reasons.* Sensorimotor coupling (alpha) is increased immediately after a perturbation (i.e., during the PCR). Phase correction in rhythms containing perturbations seems to be distinct from phase correction in isochronous or continuously modulated rhythms.* The PCR may represent a neural system response to asynchronies between temporal predictions and the actual times of occurrence of rhythmic events.* *Further research is required!

23. Thank you for your attention! This research was supported by grants from the National Institute of Health and the National Science Foundation.