Effort is ultimately measured in physical units, while the communication error probability is dimensionless. Since one can only sensibly add numbers with the same units (e.g., 1 kilogram + 1 meter = ?), a scale factor is needed to convert one into the units of the other. This scale factor, sk (in Equation 2), can vary from word to word, and we identify it with the prosodic strength, or importance of each word.
If a word's strength is large, the Stem-ML pitch contour will closely approximate the tone's template and the communication error probability will be small. In other words, a large strength indicates that the speaker is willing to expend enough effort to produce precise intonation. On the other hand, if the word is unimportant and its strength is small, the produced pitch will be controlled by other factors: neighboring words and ease of production. For prosodically weak words, minimizing the effort term will have the most effect: when sk is small, smoothness becomes more important than accuracy.
The concept that strength is related to how carefully speech is articulated was discussed by Browman and Goldstein , in the context of phoneme changes in casual speech. Flemming [4,3] discusses optimization models with continuous parameters (into which class this model falls), and their relationship with Optimality Theory .
If one relates this model to conventional views of accents and intonation, strength should be considered as a continuous parameter associated with a word or syllable. We suggest that listeners might treat strong tones as categorically different from weak tones, so these strength measurements might be equivalent to the presence or absence of accents (strong implies present). The strength numbers are associated with a particular rendition of the sentence. They vary somewhat even among utterances that were spoken with the same intent, but they seem to vary more between utterances where the sentence focus, the intonation type, or other prosodic features differ.
The prosodic strength of a word, sk, controls the interaction of its accent with its neighbors by way of the smoothness requirement, G. Stronger words will realize their pitch targets accurately, and affect the pitch in neighboring words. On the other hand, if the word is unimportant and its strength is small, the produced pitch will be controlled by other factors: neighboring words and ease of production.Greg Kochanski, Chilin Shih 2002-08-03