When two musical notes with simple frequency ratios are played simultaneously, the resulting musical chord is pleasing and evokes a sense of resolution or "consonance". Complex frequency ratios, on the other hand, evoke feelings of tension or "dissonance". Consonance and dissonance form the basis of harmony, a central component of Western music. In earlier work, we provided evidence that consonance perception is based on neural temporal coding in the brainstem (Bones et al., 2014). Here, we show that for listeners with clinically normal hearing, aging is associated with a decline in both the perceptual distinction and the distinctiveness of the neural representations of different categories of two-note chords. Compared with younger listeners, older listeners rated consonant chords as less pleasant and dissonant chords as more pleasant. Older listeners also had less distinct neural representations of consonant and dissonant chords as measured using a Neural Consonance Index derived from the electrophysiological "frequency-following response." The results withstood a control for the effect of age on general affect, suggesting that different mechanisms are responsible for the perceived pleasantness of musical chords and affective voices and that, for listeners with clinically normal hearing, age-related differences in consonance perception are likely to be related to differences in neural temporal coding.