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Bell chiming is a folk music tradition that involves performers playing rhythmic patterns on church bells. The paper presents a method for automatic transcription of bell chiming recordings, where the goal is to detect the bells that were played and their onset times. We first present an algorithm that estimates the number of bells in a recording and their approximate spectra. The algorithm uses a modified version of the intelligent k-means algorithm, as well as some prior knowledge of church bell acoustics to find clusters of partials with synchronous onsets in the time-frequency representation of a recording. Cluster centers are used to initialize non-negative matrix factorization that factorizes the time-frequency representation into a set of basis vectors (bell spectra) and their activations. To transcribe a recording, we propose a probabilistic framework that integrates factorization and onset detection data with prior knowledge of bell chiming performance rules. Both parts of the algorithm are evaluated on a set of bell chiming field recordings.