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.
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:
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.)