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We present a new method for musical genre classification based on high-level melodic features that are extracted directly from the audio signal of polyphonic music. The features are obtained through the automatic characterisation of pitch contours describing the predominant melodic line, extracted using a state-of-the-art audio melody extraction algorithm. Using standard machine learning algorithms the melodic features are used to classify excerpts into five different musical genres. We obtain a classification accuracy above 90% for a collection of 500 excerpts, demonstrating that successful classification can be achieved using high-level melodic features that are more meaningful to humans compared to low-level features commonly used for this task. We also compare our method to a baseline approach using low-level timbre features, and study the effect of combining these low-level features with our high-level melodic features. The results demonstrate that complementing low-level features with high-level melodic features is a promising approach.