Noise is one of the primary quality-of-life issues in urban environments. In addition to annoyance, noise negatively impacts public health and educational performance. While low-cost sensors can be deployed to monitor ambient noise levels at high temporal resolutions, the amount of data they produce and the complexity of these data pose significant analytical challenges. One way to address these challenges is through machine listening techniques, which are used to extract features in attempts to classify the source of noise and understand temporal patterns of a city's noise situation. However, the overwhelming number of noise sources in the urban environment and the scarcity of labeled data makes it nearly impossible to create classification models with large enough vocabularies that capture the true dynamism of urban soundscapes In this paper, we first identify a set of requirements in the yet unexplored domain of urban soundscape exploration. To satisfy the requirements and tackle the identified challenges, we propose Urban Rhapsody, a framework that combines state-of-the-art audio representation, machine learning, and visual analytics to allow users to interactively create classification models, understand noise patterns of a city, and quickly retrieve and label audio excerpts in order to create a large high-precision annotated database of urban sound recordings. We demonstrate the tool's utility through case studies performed by domain experts using data generated over the five-year deployment of a one-of-a-kind sensor network in New York City.