This study adopts a multiple-methods approach to the investigation of prosody, drawing on insights from a quantitative methodology (experimental prosody research) as well as a qualitative one (conversation analysis). We use a k-means cluster analysis to investigate prosodic patterns in conversational sequences involving lexico-semantic contrastive structures. This combined methodology demonstrates that quantitative/statistical methods are a valuable tool for making relatively objective characterizations of acoustic features of speech, while qualitative methods are essential for interpreting the quantitative results. We find that in sequences that maintain global prosodic characteristics across contrastive structures, participants orient to interactional problems, such as determining who has the right to the floor, or avoiding disruption of an ongoing interaction. On the other hand, in sequences in which the global prosody is different across contrastive structures, participants do not generally appear to be orienting to such problems of alignment. Our findings expand the interpretation of "contrastive prosody" that is commonly used in experimental prosody approaches, while providing a way for conversation-analytic research to improve quantification and generalizability of findings.