Speech is easily produced with regular periodic patterns—as if spoken to a metronome. If we ask what it is that is periodically spaced, the answer is a perceptual ‘beat’ that occurs near the onset of vowels (especially stressed ones). Surprisingly, when periodically produced speech is studied it exhibits attractors at harmonic fractions (especially halves and thirds) of the basic periodicity. It is shown that the Haken–Kelso–Bunz model provides conceptual tools to account for the frequency histogram of acoustic beats in the speech. Why might there be attractors at periodically spaced phase angles? It is hypothesized that there are neural oscillations producing a pulse on every cycle, and that these pulses act as attractors for the beats at the onsets of syllables. Presumably these periodic time locations are generated by the same physiological mechanism as the periodic attentional pulse studied for some years by Jones (Psychol. Rev. 96 (1989) 459; Psychol. Rev. 106 (1999) 119). We propose that neurocognitive oscillators produce periodic pulses that apparently do several things: (1) they attract perceptual attention; (2) they influence the motor system (e.g., when producing speech) by biasing motor timing so that perceptually salient events line up in time close to the neurocognitive pulses. The consequent pattern of integer-ratio timings in music and speech is called meter. Speakers can control the degree to which they allow these metrical vector fields to constrain their timing.