We propose an audio fingerprinting method that adapts findings from the field of blind astrometry to define simple, efficiently representable characteristic feature combinations called quads. Based on these, an audio identification algorithm is described that is robust to noise and severe time-frequency scale distortions and accurately identifies the underlying scale transform factors. The low number and compact representation of content features allows for efficient application of exact fixed-radius near-neighbor search methods for fingerprint matching in large audio collections. We demonstrate the practicability of the method on a collection of 100,000 songs, analyze its performance for a diverse set of noise as well as severe speed, tempo and pitch scale modifications, and identify a number of advantages of our method over two state-of-the-art distortion-robust audio identification algorithms.