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The baryon acoustic oscillations (BAO) provide an important bridge betweenthe early universe and the expansion history at late times. While the BAO hasprimarily been used as a standard ruler, it also encodes recombination eraphysics, as demonstrated by a recent measurement of the neutrino-induced phaseshift in the BAO feature. In principle, these measurements offer a novel windowinto physics at the time of baryon decoupling. However, our analyticunderstanding of the BAO feature is limited, particularly for the range ofFourier modes measured in surveys. As a result, it is unclear what the BAOphase teaches us about the early universe beyond what is already known from thecosmic microwave background (CMB). In this paper, we provide a more complete(semi-)analytic treatment of the BAO on observationally relevant scales. Inparticular, we compute corrections to the frequency and phase of the BAOfeature that arise from higher order effects which occur in the tight couplingregime and during baryon decoupling. The total phase shift we find iscomparable to a few percent shift in the BAO scale (frequency) and thusrelevant in current data. Our results include an improved analytic calculationof the neutrino induced phase shift template that is in close agreement withthe numerically determined template used in measurements of the CMB and BAO.

The Phase of the BAO on Observable Scales