This paper presents a principled method for detecting the 'abnormal' content in vibration spectra obtained from rotating machinery. We illustrate the use of the method in detecting abnormalities in jet engine vibration spectra corresponding to unforeseen engine events. We take a novelty detection approach, in which a model of normality is constructed from the typically large numbers of examples of 'normal' behaviour that exist when monitoring jet engines. Abnormal spectral content is then detected by comparing new vibration spectra to the model of normality. The use of novelty detection allows us to take an engine-specific approach to modelling, in which the engine under test becomes its own model rather than relying on a model that is generic to a large population of engines. A probabilistic approach is taken that employs extreme value theory to determine the boundaries of normal behaviour in a principled manner. We also describe a novel visualisation technique that highlights significant spectral content that would otherwise be too low in magnitude to see in a standard plot of spectral power.