Neural Entrainment to the Beat: The "Missing-Pulse" Phenomenon

Abstract

Most humans have a near-automatic inclination to tap, clap, or move to the beat of music. The capacity to extract a periodic beat from a complex musical segment is remarkable, as it requires abstraction from the temporal structure of the stimulus. It has been suggested that nonlinear interactions in neural networks result in cortical oscillations at the beat frequency, and that such entrained oscillations give rise to the percept of a beat or a pulse. Here we tested this neural resonance theory using MEG recordings as female and male individuals listened to 30 s sequences of complex syncopated drumbeats designed so that they contain no net energy at the pulse frequency when measured using linear analysis. We analyzed the spectrum of the neural activity while listening and compared it to the modulation spectrum of the stimuli. We found enhanced neural response in the auditory cortex at the pulse frequency. We also showed phase locking at the times of the missing pulse, even though the pulse was absent from the stimulus itself. Moreover, the strength of this pulse response correlated with individuals' speed in finding the pulse of these stimuli, as tested in a follow-up session. These findings demonstrate that neural activity at the pulse frequency in the auditory cortex is internally generated rather than stimulus-driven. The current results are both consistent with neural resonance theory and with models based on nonlinear response of the brain to rhythmic stimuli. The results thus help narrow the search for valid models of beat perception.SIGNIFICANCE STATEMENT Humans perceive music as having a regular pulse marking equally spaced points in time, within which musical notes are temporally organized. Neural resonance theory (NRT) provides a theoretical model explaining how an internal periodic representation of a pulse may emerge through nonlinear coupling between oscillating neural systems. After testing key falsifiable predictions of NRT using MEG recordings, we demonstrate the emergence of neural oscillations at the pulse frequency, which can be related to pulse perception. These findings rule out alternative explanations for neural entrainment and provide evidence linking neural synchronization to the perception of pulse, a widely debated topic in recent years.

Keywords: MEG; auditory rhythm; neural resonance theory; oscillations; pulse.

Figure 1.

Stimulus and paradigm. a, Notation of the auditory stimuli for the isochronous pattern (top), the syncopated pattern MP1 (middle), and the syncopated pattern MP2 (bottom) stimuli. b, Time course of a sample trial. In the passive listening period, the basic pattern (2 musical bars) was repeated eight times. Then, following a cue, a test item was played consisting of the same basic pattern but the tempo could be the same, 10% faster, or 10% slower. Participant performed a tempo-judgment task on the test item.

Figure 2.

Stimulus and MEG spectrum. a–d, The modulation spectra of each stimulus (top) and of the neural response it generated, averaged over 10% of the sensors with the highest 2 Hz amplitude (bottom). a, b, Syncopated patterns MP1 and MP2. There is no visible 2 Hz peak in the stimulus spectrum. However, pulse-frequency peaks (black arrows) are observed in the MEG spectrum for both syncopated rhythms. c, ISO condition: 2 Hz peaks and its harmonics are clear in both stimulus and MEG spectrum. d, RAND pattern: 2 Hz peaks are missing in both the stimulus and the MEG spectrum. e, Amplitude at 2 Hz versus the frequencies around it for each condition. Neural data are averaged over all MEG sensors. In the ISO and both syncopated conditions there was a significant difference between 2 Hz power and the frequencies around it, indicating a peak at the pulse frequency (Wilcoxon signed-rank test, *p < 0.05, **p < 0.01). In the RAND condition, there was no significant peak at 2 Hz. Error bars indicate SEM.

Figure 3.

Behavioral performance in the tapping task. a, TTT, the time elapsed from the beginning of the stimulus until subjects started tapping at the perceived pulse frequency. b, Blue, Synchronization coefficient for each subject. All subjects eventually managed to tap in synchrony with the beat. Red, Angle of the mean vector. Almost all subjects showed positive values indicating that tapping came earlier than the strong-beat positions. Error bars indicate SEM. The numbers on the bottom of the red trace indicate the average number of taps for each subject over the 10 syncopated rhythms during the behavioral task.

Figure 4.

MEG spectrum for individual subjects. The spectrum is shown averaged over both syncopated conditions and over seven channels (5% of the total number of channels) showing the highest 2 Hz power. a, A subject with low average TTT value, who perceived the pulse of the syncopated rhythms early on during the behavioral task. b, A subject with high TTT value. It took the subject >15 s to perceive the pulse. The MEG spectrum of the early pulse perceiver shows a clear 2 Hz peak that matches the expected pulse frequency of the stimulus while the late pulse perceiver failed to generate such oscillations. Note that both subjects showed peaks at frequencies present in the stimulus itself (e.g., 1.25 and 4 Hz). c, Correlation between 2 Hz amplitude and TTT for the two syncopated conditions. Subjects that showed higher 2 Hz amplitude during the MEG scans in the syncopated conditions perceived the pulse of the syncopated patterns and started tapping earlier during the subsequent behavioral task. Blue and red squares indicate the subjects shown in a and b respectively.

Figure 5.

Phase locking to the missing pulse for the two syncopated rhythms (MP1 and MP2; top two rows) and the RAND condition (bottom row). a, Illustration of the soundless strong-beat positions. Black dots mark the locations of each physical sound and, for the two syncopated rhythms, X's mark the strong-beat positions. Red X's denote strong-beat positions where no sounds were present, which served as t = 0 in this analysis. The bottom panels show averaged sound files time-locked to these positions, verifying that these were indeed quiet times. Similar soundless periods were selected from the RAND condition (depicted by the red X's), matched on their distance from previous sounds so as to control for carryover effects of evoked responses from previous sounds. b, MEG signals averaged over all participants for one representative MEG sensor. The signals were time-locked to the position of soundless strong beats (t = 0) in the syncopated conditions, or control epochs in the RAND condition, filtered between 1 and 40 Hz (blue) and between 0.5 and 3 Hz (red). c, Phase histograms at the time of the expected pulse, across all participants for the MEG sensor shown in b. d, Topography of the phase-locking values across MEG sensors. The colors indicate the Z value of the Rayleigh test. Significant sensors are indicated by an asterisk (p < 0.05, FDR corrected).

Figure 6.

Localization the missing-pulse response. a, Spectra of the neural response in response to the two syncopated rhythms in the right (blue) and left (red) hemisphere for each ROI. Inserts indicate the anatomical locations of the voxels used for each ROI (see Materials and Methods). b, Statistical comparison of 2 Hz amplitude (blue) versus amplitude in adjacent frequencies (red) in each ROI. Error bars indicate SEM. c, Whole-brain analysis of the missing-pulse response. The two clusters with the strongest missing-pulse responses were localized in the right and left STGs.