In the quarter century since the development of geometric morphometrics the community of practitioners has largely been occupied with training issues and anatomy-based applications research in the biological sciences. However, just as the scope of geometry transcends comparative anatomy, the potential scope of morphometric analysis transcends investigations of the form and shape of organismal bodies. An important area of opportunity for morphometricians lies in the application of geometric methods to non-traditional form/shape analysis problems. To illustrate the potential of morphometric data analysis approaches to contribute to investigations outside its traditional base in (physical) morphology we report here results of an investigation into the morphometrics of bat echolocation calls. By treating Hanning windowed spectrograms of bat search echolocation calls as complex 3D surfaces, and by using a variant of eigensurface analysis to sample and compare these surfaces, it is possible to identify bat species to very high levels of accuracy (>90% for raw cross-validated training set identifications, >80% for jackknifed training set identifications), even for species (e.g., Myotis) whose spectrograms have resisted separation into species-specific clusters using traditional spectrogram descriptors. Moreover, the shape modeling capabilities of geometric morphometrics render the complex mathematical subspaces within which these spectrogram shape data reside - along with the discriminant functions used to separate training-set clusters - interpretable in a simple, intuitive, and biologically informative manner. These results demonstrate the rich source of species-specific information bioacoustic signal structures represent. They also illustrate the type of advances that can be made when morphometricians venture beyond the traditional confines of their field to address wider questions of significance in the biological and the physical sciences.