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Much research in music information retrieval has focused on query-by-humming systems, which search melodic databases using sung queries. The database retrieval aspect of such systems has received considerable attention, but query processing and the melodic representation have not been examined as carefully. Common methods for query processing are based on musical intuition and historical momentum rather than specific performance criteria; existing systems often employ rudimentary note segmentation or coarse quantization of note estimates. In this work, we examine several alternative query processing methods as well as quantized melodic representations. One common difficulty with designing query-by-humming systems is the coupling between system components. We address this issue by measuring the performance of the query processing system both in isolation and coupled with a retrieval system. We first measure the segmentation performance of several note estimators. We then compute the retrieval accuracy of an experimental query-by-humming system that uses the various note estimators along with varying degrees of pitch and duration quantization. The results show that more advanced query processing can improve both segmentation performance and retrieval performance, although the best segmentation performance does not necessarily yield the best retrieval performance. Further, coarsely quantizing the melodic representation generally degrades retrieval accuracy.