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How do humans discriminate emotion from non-emotion? The specific psychophysical cues and neural responses involved with resolving emotional information in sound are unknown. In this study we used a discrimination psychophysical-fMRI sparse sampling paradigm to locate threshold responses to happy and sad acoustic stimuli. The fine structure and envelope of auditory signals were covaried to vary emotional certainty. We report that emotion identification at threshold in music utilizes fine structure cues. The auditory cortex was activated but did not vary with emotional uncertainty. Amygdala activation was modulated by emotion identification and was absent when emotional stimuli were chance identifiable, especially in the left hemisphere. The right hemisphere amygdala was considerably more deactivated in response to uncertain emotion. The threshold of emotion was signified by a right amygdala deactivation and change of left amygdala greater than right amygdala activation. Functional sex differences were noted during binaural uncertain emotional stimuli presentations, where the right amygdala showed larger activation in females. Negative control (silent stimuli) experiments investigated sparse sampling of silence to ensure modulation effects were inherent to emotional resolvability. No functional modulation of Heschl's gyrus occurred during silence; however, during rest the amygdala baseline state was asymmetrically lateralized. The evidence indicates changing hemispheric activation and deactivation patterns between the left and right amygdala is a hallmark feature of discriminating emotion from non-emotion in music.