This paper presents scaling relations and fitting formulae for adiabatic cold dark matter (CDM) cosmologies that account for baryon effects in the matter transfer function with better than 10% accuracy in the large-scale structure regime. The formulae are based on a physically motivated separation of effects such as acoustic oscillations, Compton drag, velocity overshoot, baryon infall, adiabatic damping, Silk damping, and cold-dark-matter growth suppression. A simpler and more accurate form for the zero baryon transfer function is also introduced. These descriptions are used to quantify the amplitude and location of baryonic features in linear theory. Baryonic oscillations are prominent if the baryon fraction Ωb/Ω0 is greater than Ω0h² + 0.2, but in more conventional cosmologies, the main effect is a sharp suppression in the transfer function below the sound horizon. The paper provides a simple but accurate description of this effect, emphasizing that it is not well approximated by a change in the shape parameter Γ. The paper also discusses the physical effects that influence the transfer function, including the sound horizon, Silk damping scale, and the drag epoch. The paper presents fitting formulae for the transfer function in both the cold dark matter and baryon components, and discusses their performance in different cosmological parameters. The results show that the fitting formula works well for a range of parameters, with residuals under 10% for fully baryonic models and under 5% for lower baryon fractions. The paper also discusses the phenomenology of baryonic oscillations, including their location and amplitude, and the suppression of power below the sound horizon. The paper concludes that baryonic features in the matter power spectrum represent a valuable resource for cosmological information, but one that may be difficult to mine observationally.This paper presents scaling relations and fitting formulae for adiabatic cold dark matter (CDM) cosmologies that account for baryon effects in the matter transfer function with better than 10% accuracy in the large-scale structure regime. The formulae are based on a physically motivated separation of effects such as acoustic oscillations, Compton drag, velocity overshoot, baryon infall, adiabatic damping, Silk damping, and cold-dark-matter growth suppression. A simpler and more accurate form for the zero baryon transfer function is also introduced. These descriptions are used to quantify the amplitude and location of baryonic features in linear theory. Baryonic oscillations are prominent if the baryon fraction Ωb/Ω0 is greater than Ω0h² + 0.2, but in more conventional cosmologies, the main effect is a sharp suppression in the transfer function below the sound horizon. The paper provides a simple but accurate description of this effect, emphasizing that it is not well approximated by a change in the shape parameter Γ. The paper also discusses the physical effects that influence the transfer function, including the sound horizon, Silk damping scale, and the drag epoch. The paper presents fitting formulae for the transfer function in both the cold dark matter and baryon components, and discusses their performance in different cosmological parameters. The results show that the fitting formula works well for a range of parameters, with residuals under 10% for fully baryonic models and under 5% for lower baryon fractions. The paper also discusses the phenomenology of baryonic oscillations, including their location and amplitude, and the suppression of power below the sound horizon. The paper concludes that baryonic features in the matter power spectrum represent a valuable resource for cosmological information, but one that may be difficult to mine observationally.