In this article, we explore the use of Bayesian networks for identifying the timbre of musical instruments. Peak spectral amplitude in ten frequency windows is extracted for each of 20 time windows to be used as features. Over a large data set of 24,000 audio examples covering the full musical range of 24 different common orchestral instruments, four different Bayesian network structures, including naive Bayes, are examined and compared with two support vector machines and a k-nearest neighbor classifier. Classification accuracy is examined by instrument, instrument family, and data set size. Bayesian networks with conditional dependencies in the time and frequency dimensions achieved 98 percent accuracy in the instrument classification task and 97 percent accuracy in the instrument family identification task. These results demonstrate a significant improvement over the previous approaches in the literature on this data set. Additionally, we tested our Bayesian approach on the widely used Iowa musical instrument data set, with similar results.