Jp. Jacobs et D. Bullock, A two-process model for control of legato articulation across a wide rangeof tempos during piano performance, MUSIC PERC, 16(2), 1998, pp. 169-199
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 d
ependence 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 th
at the dependence can arise from a neural circuit in which a predictive cen
tral process and a slow sensory feedback process cooperate to control artic
ulation. An oscillating neural network is first constructed as an extension
of the vector-integration-to-endpoint (VITE) model for voluntary control o
f movement. The resulting circuit exhibits volition-controlled oscillation
rates. It also affords predictive control by continuously computing an inte
rnal estimate of the remaining "time-to-contact" (TTC) with a targeted inte
gration level, the reaching of which triggers the oscillator's next half cy
cle. At fixed successive threshold values of this estimate of time remainin
g in the current half cycle, the performer first launches keystroke n + 1 a
nd then lifts keystroke n. As tempo slows, the time required to pass betwee
n threshold crossings elongates, and KOT increases. However, if performers
used only such a central process to control articulation, they would not sh
ow 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.