Fig. 1.

Quantifying the effects of rhythmic entrainment in infant-directed singing. (A) Still images from audio–video recordings of infant-directed singing. (B) Lyrics and musical notation for the first two phrases of “Twinkle, Twinkle, Little Star.” (C) Audio amplitude waveform for the song phrases in B sung by the actress pictured in A. (D) Schematic sine wave with peaks aligned to the beat of the audio as sung. One cycle (−π to +π) is marked by vertical lines, with the beat centered. Note that the interbeat interval, true to natural singing, varies and is not perfectly isochronous. (E) Schematic beat markings for strong beats (large black bars) and weak beats (small black bars). (F and G) Raster plots of archetypal response data that are either unaligned (F) or aligned (G) in time with the beat of infant-directed singing. Horizontal lines in each raster plot represent response events (hypothetical looking response when a line is plotted, not looking when not); each row corresponds to a single beat cycle. (H and I) Peristimulus time histograms summarizing raster data for archetypal responses that are either unaligned (H) or aligned (I) in time with the beat. Dotted horizontal lines are 95% confidence intervals for response variation expected by chance alone (one-sided); solid horizontal line is median expected by chance. (J and K) Phase portraits of archetypal responses either unaligned (J) or aligned (K) in time with the beat; each circle represents the phase of an individual’s looking response at the timing of the beat. (L) Lissajous curves also quantify synchrony between two time-varying signals: from no synchrony (as would be expected for data in F, H, and J), to higher-order synchrony with phase shift (here, two periods of output signal correspond to one period of modulating signal), to 1:1 phase synchrony (synchronized with 1:1 periods but with phase shift in timing), and complete synchrony (1:1 synchrony with 0 phase shift, as would be expected for data in G, I, and K).