What is the cadence in one’s voice called when speaking parenthetically?

1) There is no single, agreed-upon term for the prosodic pattern of parenthetical constituents.
2) The most common and theory-neutral term is comma intonation (e.g. Emonds 1976, Culicover 1992, Brinton 2002, Huddleston & Pullum 2002, etc.).
3) Some researchers, especially those working on the interaction between syntax and prosody, use the term parenthetical dip following work by Dutch linguist Carla Schelfhout (e.g. Heringa 2012). I find this term quite adequate.
4) Scholars who are interested mainly in the semantics of parentheticals tend to have a more fanciful terminology (e.g. the introduction of a comma operator or comma feature in Potts 2007, the rule Align R and so-called comma phrases and lower order prosodic constituents in Selkirk 2005, etc.).
5) The actual phonetic realization of parentheticals is remarkably complex. Scientists working on the different phonetic attributes of parenthetical intonation (e.g. for artificial speech) tend to not have one comprehensive term for the phenomenon because they dissect it into its constituent parts, such as 'maximum and minimum pitch levels', 'high and low tones' (see ToBI), 'length of pauses' or 'intonational phrasing' etc. (For a summary see for instance Bodenbender 1999.)
6) Irrespective of the syntactic pattern involved, the following collocates are commonly used to describe intonation: intonational contour, intonational pattern, prosodic cue and prosodic structure.