Natural rhythms of periodic temporal attention

The study asks whether the ability to flexibly focus attention in time (periodic temporal attention) is limited by an underlying rhythmic neural mechanism and whether such limits are modality- and motor-dependent. Prior work shows attention and perception exhibit rhythmic sampling, many paradigms use 1–2 Hz rhythms, and motor behaviors naturally operate near ~1.5–2 Hz. The authors hypothesize that temporal attention may have limited, sensory-specific optimal sampling rates and that overt motor activity might modulate attention differently across modalities due to intrinsic motor rhythms and sensorimotor timing constraints. They address this by quantifying performance across a broad range of beat frequencies (~0.3–3.8 Hz) in auditory and visual tasks, with and without finger-tapping, and by modeling the system with coupled oscillators.

Background work indicates: (1) attention and perception can be rhythmically entrained by low-frequency neural oscillations; (2) experimental paradigms frequently use 1–2 Hz rhythms, aligning with natural musical tempo; (3) motor behaviors (walking, tapping) exhibit preferred rates ~1.5–2 Hz and delta-band oscillations (0.5–4 Hz) shape motor dynamics; (4) visual sustained attention shows rhythmic sampling around theta (4–8 Hz). Together, these suggest potential modality-specific temporal constraints and a strong motor–attention link via active sensing, yet the limits and optimal sampling rate of periodic temporal attention had not been quantified.

Participants: 30, 20, 50, 30, 20, and 15 participants (ages 18–35, 69% female) for experiments 1–6, respectively; normal hearing/vision; no neurological/psychiatric disorders; no professional musicians. Ethics: Aix-Marseille University guidelines; informed consent.

Task paradigm (general): On each trial, three reference stimuli defined an isochronous beat (tempo), followed by a mixture of on-beat (targets) and off-beat (distractors). At trial end, a deviant stimulus occurred, and participants judged whether it was on- or off-beat (beat discrimination). Off-beat distractors introduced temporal interference, forcing continuous tracking of the beat. Beat frequencies spanned ~0.3–3.8 Hz (modality-dependent). Individual difficulty was titrated via a staircase that adjusted distractor density to reach ~75% performance at 2 Hz baseline.

Auditory experiments (1, 2, 6): Pure tones (44.1 kHz sampling; binaural; Sennheiser HD 250) presented in anechoic room with visual fixation. Exp 1 passive: tempi 0.6, 0.7, 1, 1.3, 1.7, 2.2, 2.9, 3.8 Hz; tone duration 10% of ISI. Exp 2: two sessions—passive (no movement) and tracking (index finger tapping in-phase on noiseless pad with microphone capture). Exp 6 control: fixed tone length 22.5 ms across tempi to orthogonalize tempo and duration. Trials lasted ~2–12 s and contained ≥4 targets; distractor density titrated; ISIs constrained to >9% of beat period. Feedback provided per trial and per block.

Visual experiments (4, 5): Centered visual gratings (5° extent; 60 Hz display), with continuous pink noise presented binaurally to equalize auditory background. Exp 4 passive: tempi 0.3, 0.4, 0.6, 0.7, 1, 1.3, 1.7, 2.2, 2.9, 3.8 Hz; grating duration 18% of ISI; trial durations ~2–20 s. Exp 5: passive and tracking (tapping) sessions with tempos 0.4, 0.7, 1, 1.3, 1.7, 2.2, 2.9, 3.8 Hz.

Free tapping experiment (3): Subset of BAASTA to assess spontaneous and range-limited tapping without cues: participants tapped at comfortable (60 s), slowest (60 s), and fastest (30 s) rates on the noiseless pad.

Motor timing metrics (tracking sessions): Inter-tap intervals yielded guided tapping precision and coefficient of variation (CV = relative standard deviation). Sensorimotor simultaneity was quantified as the phase difference between tap times and beat onsets, normalized to the beat period (radians), using absolute and signed indices (anticipation vs reaction).

Modeling (coupled oscillators): Three delay-coupled noisy phase oscillators represented stimulus (S), attention (A), and motor (M) with equations: θ̇_A = ω_A + K_AM sin(θ_M(t−τ_AM)−θ_A) + K_AS sin(θ_S(t−τ_AS)−θ_A) + ξ_A; θ̇_M = ω_M + K_MA sin(θ_A(t−τ_MA)−θ_M) + K_MS sin(θ_S(t−τ_MS)−θ_M) + ξ_M. Natural frequencies set to ω_A = 1.5 Hz (auditory) or 0.7 Hz (visual), ω_M = 1.7 Hz; key parameters included coupling strengths K, time-delays τ, and noise D. Performance was approximated by the phase-locking value (PLV) between S and A. Simulations ran for 10,000 s at 25 ms sampling.

Analyses: Single-subject measures followed by group-level repeated-measures ANOVAs, paired/unpaired Welch t-tests, Spearman correlations; Bayes factors (AIC-based) to assess evidence for null vs effect hypotheses; third-order polynomial fits to estimate optimal tempos (local maxima/minima). A GLMM (R glmer) on exp 1 included predictors: deviant type (on/off-beat), deviant–beat distance, and beat frequency, with participant as random factor.

• Auditory passive (Exp 1): Performance varied with tempo (RM-ANOVA F(7,203)=15.3, p<0.001) with inverse U-shape (3rd-order fit R^2=0.86, p=0.002). Optimal tempo ~1.34 Hz (SD=0.80). Control with fixed tone duration replicated effects (F(7,98)=8.9, p<0.001; fit R^2=0.86; optimal ~1.32 Hz). GLMM showed independent contributions of deviant nature (χ^2=18.2), distance (χ^2=13.2), and beat frequency (χ^2=11.2), all p<0.001.
• Auditory motor contribution (Exp 2): Performance varied with tempo (F(7,133)=15.9, p<0.001). Tracking vs passive: main effect (F(1,19)=7.5, p=0.013) and interaction (F(7,133)=2.8, p=0.023). Motor tracking improved performance selectively at 1.3 Hz (t(19)=2.75, p=0.013), 1.7 Hz (t(19)=2.93, p=0.009), and 2.2 Hz (t(19)=3.59, p=0.002). Optimal tempo similar in both sessions (~1.47 Hz; no difference t(19)=0.02, p=0.99; Bayes factor=0.22). Guided tapping CV showed U-shape across tempi (F(7,133)=6.84, p<0.001; fit R^2=0.95), with optimal guided tapping tempo ~1.42 Hz, not different from attention optimal tempos (Bayes factors ~0.24–0.25 supporting null). Sensorimotor simultaneity was better on correct than incorrect trials (F(1,19)=23.4, p<0.001); trials with low vs high simultaneity showed higher performance for low-simultaneity (i.e., closer alignment) trials (F(1,19)=30.81, p<0.001), indicating closer beat tracking benefited auditory performance.
• Free tapping (Exp 3): Spontaneous tapping frequency M=1.67 Hz (SD=0.74). Slow tapping M=0.60 Hz (SD=0.30); fast tapping M=4.69 Hz (SD=1.13), spanning ~0.5–4+ Hz.
• Visual passive (Exp 4): Lower distractor density needed vs audition (M=0.28 vs 1.01; Welch t(56)=-5.52, p<0.001). Performance varied with tempo (F(9,243)=53.6, p<0.001) with inverse U-shape (fit R^2=0.93). Optimal visual attention tempo ~0.83 Hz (SD=0.34), significantly lower than auditory (Welch t(56)=3.18, p=0.003).
• Visual motor contribution (Exp 5): Performance varied with tempo (F(7,133)=62.9, p<0.001). No overall session main effect (F(1,19)=0.56, p=0.46) but session×tempo interaction (F(7,133)=2.8, p=0.03). Motor tracking impaired performance at 1.66 Hz (t(19)=-2.23, p=0.038) and 2.2 Hz (t(19)=-2.67, p=0.015). Optimal tempos similar across sessions (~0.83 vs ~0.65 Hz; t(19)=-1.47, p=0.16; Bayes factor=0.66). Guided tapping CV exhibited U-shape (fit R^2=0.78, p=0.007) with optimal tapping ~1.40 Hz (not differing from auditory guided tapping; Welch t(38)=0.12, p=0.91), but CV did not differ significantly across visual tempi (F(7,133)=0.88, p=0.48) and was overall higher (worse) than auditory (Welch t(38)=2.18, p=0.037). Sensorimotor timing in vision showed reactive tapping (later than beat), and better visual performance associated with lower simultaneity (i.e., less close alignment) on correct vs incorrect trials (F(1,19)=8.41, p=0.009). Splitting by simultaneity revealed worse performance when taps closely tracked the beat, especially at ~1–2.2 Hz (e.g., 1 Hz t(19)=-2.93, p=0.009).
• Modeling: A 3-oscillator model (S–A–M) reproduced passive and tracking profiles in both modalities with high accuracy (auditory R^2≈0.92–0.95; visual R^2≈0.95). Key parameters: attention natural frequency ω_A set to 1.5 Hz (auditory) vs 0.7 Hz (visual); motor ω_M=1.7 Hz; sensorimotor time-delay τ_S−M = 0.1 s (auditory) vs 0.35 s (visual). Motor–attention coupling K_M−A increased from 2 (passive) to 10 (tracking) to capture selective modulation near ~1.5–2 Hz. Short τ_S−M yielded beneficial motor influence (auditory), whereas longer τ_S−M produced disruptive effects (visual).

The findings demonstrate that periodic temporal attention has limited sampling capacities with distinct modality-specific optimal rates: ~1.3–1.5 Hz in audition and ~0.7–0.8 Hz in vision. These constraints align with natural motor rhythms (~1.7 Hz) and suggest attentional sampling is governed by intrinsic oscillatory mechanisms within large-scale sensory-attention networks. Overt motor actions selectively modulate temporal attention near natural motor frequencies: improving auditory attention when motor and attentional fluctuations align temporally, but impairing visual attention where sensorimotor timing is delayed and reactive. Trial-level analyses show that close temporal alignment between taps and beat improves performance in audition but harms it in vision, indicating that sensorimotor simultaneity is a key determinant of the direction of motor influence. The coupled-oscillator model captures these dynamics by embodying sensory-specific attention oscillators (different natural frequencies) and modality-dependent sensorimotor delays, revealing structural constraints on motor–attention temporal alignment that explain the opposite motor effects across modalities.

This work quantifies natural sampling rates of periodic temporal attention and reveals sensory-specific optimal tempos (~1.5 Hz audition; ~0.7 Hz vision). It shows that motor engagement impacts temporal attention through temporal alignment: beneficial in audition and detrimental in vision around natural motor rhythms. A simple three-oscillator model explains these patterns via sensory-specific intrinsic attention rhythms and modality-dependent sensorimotor delays. Future research should test whether these constraints generalize beyond periodic temporal attention to other temporal expectation forms and investigate neural correlates and network mechanisms that implement these intrinsic rhythms and delays across sensory systems.

• Covert motor/premotor involvement could not be eliminated in passive sessions, potentially influencing attention even without overt movement.
• Visual tasks used transient stimuli and concurrent pink noise; ecological suitability differs across modalities, which may affect overall performance levels and interpretation of modality differences.
• Findings are specific to periodic temporal attention; generalization to aperiodic or symbolically cued temporal expectations remains untested.
• Modeling approximates behavior via phase-locking in simplified phase-oscillator dynamics and fixed parameters; real neural systems may involve additional complexity and adaptive changes.