Successive Pluck Collision Detection

As discussed above, in a simple 1D plucking model, the plectrum comes up and engages the string when $y_e(t) \ge y(t)$ , and above some maximum force the plectrum releases the string. At this point, it is ``above'' the string. To pluck again in the same direction, the collision-detection must be disabled until we again have $y_e< y$ , requiring one bit of state to keep track of that.<sup>10.16</sup> The harpsichord jack plucks the string only in the ``up'' direction due to its asymmetric behavior in the two directions [144]. If only ``up picks'' are supported, then engagement can be suppressed after a release until $y_e(t)$ comes back down below the envelope of string vibration (e.g., $y_e(t)<-y_{\mbox{\small max}}$ ). Note that intermittent disengagements as a plucking cycle begins are normal; there is often an audible ``buzzing'' or ``chattering'' when plucking an already vibrating string.

When plucking up and down in alternation, as in the tremolo technique (common on mandolins), the collision detection alternates between $y_e< y$ and $y_e > y$ , and again a bit of state is needed to keep track of which comparison to use.