The effort expended in speech, *G* (Equation 1),
can be approximated from knowledge about muscle dynamics [16]. Qualitatively, our effort term
behaves like the physiological effort: it is zero if muscles are
stationary in a neutral position, and increases as motions become
faster and stronger. Minimizing *G*
tends to make the pitch curve smooth and continuous, because it
minimizes the magnitude of the first and second derivatives of the
pitch.

The error term, *R* (Equations
2 and 3), behaves like a communications error
rate: it is zero if the prosody exactly matches an ideal tone
template, and it increases as the prosody deviates from the
template. The choice of template encodes the lexical information
carried by the tones. The speaker tries to minimize the deviation,
because if it becomes too large, the speaker will expect the
listener to mis-classify the tone and possibly misinterpret the
utterance.

Figure 1 shows how the
*G* (effort) term depends on the
shape of *e*. The curves we show all
go through the same set of pitch targets (dashed circles). The
*G* values increase with the RMS
curvature and slope of *e*. In this
case, optimal pitch curve has the smallest value of *G*, *G*_{1}.