I am looking for an equivalent word for gesture in reference to speech.
'Overture' came up in offline discussion but it isn't quite right.
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Utterance would be an equivalent for gesture in reference to speech.
Utterances are vocal expressions and the smallest units of speech in spoken language analysis. They communicate a particular message and differ from phonemes.
Gestures are physical expressions. They communicate a particular message also and differ from physical non-verbal communication.
Utterances are used for vocal communication and gestures are used for non-vocal communication.
Additionally, gestures are usually used in place of speech but they can be used along with speech as well. So, one gesture corresponds to one utterance:
Other spontaneous gestures used during speech production known as iconic gestures are more full of content, and may echo, or elaborate, the meaning of the co-occurring speech. They depict aspects of spatial images, actions, people, or objects.
For example, a gesture that depicts the act of throwing may be synchronous with the utterance, "He threw the ball right into the window." Such gestures that are used along with speech tend to be universal.
As a bonus, there is a book called "Gesture: Visible Action as Utterance" (by Adam Kendon) that compares gestures and utterances. (along with a detailed information about gestures.)