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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.10.16 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.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2017-02-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University