A Two-Process Model for Control of Legato Articulation across a Wide Range of Tempos during Piano Performance

The key overlap times (KOTs) required for legato articulation vary markedly with tempo. For scales/ arpeggios performed at interonset intervals (IOIs) of 100-1000 ms, prior reports show an increasing but nonlinear functional dependence of KOT on IOI. Because the major nonlinearity appears in the long-IOI (slow-tempo) region, the dependence of KOT on IOI is not attributable to gross biomechanical factors, such as finger inertias. Herein, we show that the dependence can arise from a neural circuit in which a predictive central process and a slow sensory feedback process cooperate to control articulation. An oscillating neural network is first constructed as an extension of the vector-integration-to-endpoint (VITE) model for voluntary control of movement. The resulting circuit exhibits volition-controlled oscillation rates. It also affords predictive control by continuously computing an internal estimate of the remaining " time-to-contact" (TTC) with a targeted integration level, the reaching of which triggers the oscillator's next half cycle. At fixed successive threshold values of this estimate of time remaining in the current half cycle, the performer first launches keystroke n + 1 and then lifts keystroke n. As tempo slows, the time required to pass between threshold crossings elongates, and KOT increases. However, if performers used only such a central process to control articulation, they would not show the bend seen in the slow tempo region of the KOT vs. IOI function. The bend emerges if performers lift keystroke n whenever they cross the second internal threshold or receive sensory feedback from stroke n + 1, whichever comes earlier. Empirical estimates of feedback delay times are consistent with this interpretation.