Word Strength

The strength of each word is derived strictly from its position in the phrase (marked for the speaker with a hyphen), its position in the utterance, and it's position relative to the strongly accented word, or the word that the speaker is seeking confirmation. Specifically,

$$\left\{\vphantom{ \begin{array}{ll} S_{\mbox{accent}} & \mbox{If ... ...\gamma \beta X} & \mbox{Other words after the accent.} \end{array} }\right. \begin{array}{ll} S_{\mbox{accent}} & \mbox{If the word is accent... ...\cdot e^{\gamma \beta X} & \mbox{Other words after the accent.} \end{array}$$ (8)

where S_accent, S_pre-accent, S_L, S_post-accent, S_R are strength factors shared by all accented words, all words before the accent, all other words before the accent, all words just after the accent, and all other words after the accent, respectively.

Then, x is the position of the word in its phrase, changing smoothly from zero at the beginning to 1 at the end of the phrase, and $\alpha$ gives the slope that controls how the strength of words varies inside a phrase. Normally, $\alpha$ < 0, to give phrasing with more emphasis (higher pitch) at the beginning; $\alpha$ = 0 implies no phrasing.

Similarly, X is the position of the word in the utterance, changing smoothly from zero at the beginning to 1 at the end of the utterance, and $\beta$ gives the slope that controls how the strength of words changes across the utterance. Declination is equivalent to $\beta$ < 0, no declination to $\beta$ = 0, and a rising intonation can be obtained with $\beta$ > 0.

Finally, $\gamma$ controls how strongly the phrasing is suppressed after the accent: $\gamma$ = 0 means no phrasing or declination, and $\gamma$ = 1 implies equally strong phrasing on both sides of the accent. Each of these parameters affects from tens to hundreds of words.

Boundary tones have a strength that is calculated from the strength of the first or last word (as appropriate):

$$\nu \eta$$ (9)

where $\nu$ sets the ratio of boundary tone strength to the underlying word strength, and $\eta$ defines how much the boundary tone strength varies if the underlying word's strength changes. For $\eta$ = 0, the boundary tone strength is independent of the underlying word; for $\eta$ > 0, the boundary tone will be stronger when placed on stronger words; and for $\eta$ < 0, the boundary tone would be weaker on top of a stronger word.