The study of biological symmetry continues to be an important and active area of research, yet in the hearing sciences there are no established quantitative methods for measuring auditory asymmetries and dissimilarities in threshold tuning curves (i.e. audiograms). Using a paired design and adopting methods from the analysis of fluctuating asymmetry, we describe methods for auditory researchers interested in delineating auditory asymmetries and comparing tuning curves, behavioral or neural. We illustrate the methods using audiograms of the prothoracic T-cell interneuron in a nocturnal katydid (Neoconocephalus ensiger). The results show that 87–92 % of T-cells had right-minus-left threshold asymmetries no larger than expected from measurement error alone. Thus, apart from small random fluctuating asymmetries, T-cell pairs in N. ensiger showed no sensory bias and were bilaterally symmetrical from 5 to 100 kHz. The sensitivity of the methods for detecting tuning curve dissimilarities was confirmed in a sound lateralization paradigm by comparing the ‘symmetry’ (i.e. similarity) of T-cell tuning curves measured at 0 degrees stimulation with tuning curves measured at 90 degrees stimulation for the same T-cell. The results show that T-cell thresholds measured frontally (0 degrees) were significantly higher than those measured laterally (90 degrees), particularly for ultrasonic frequencies. Statistically, the directional shift (increase) in auditory thresholds was detected as a directional asymmetry in T-cell tuning, whose origin and functional significance to an insect behaving normally are discussed. The paper discusses practical considerations for detecting auditory asymmetries and tuning curve dissimilarities in general, and closes by questioning the relevance of auditory symmetry for sound localization in both vertebrates and insects.