  Through analytic techniques verified by numerical calculations, we establish
general relations between the matter and cosmic microwave background (CMB)
power spectra and their dependence on cosmological parameters on small scales.
Fluctuations in the CMB, baryons, cold dark matter (CDM), and neutrinos receive
a boost at horizon crossing. Baryon drag on the photons causes alternating
acoustic peak heights in the CMB and is uncovered in its bare form under the
photon diffusion scale. Decoupling of the photons at last scattering and of the
baryons at the end of the Compton drag epoch, freezes the diffusion-damped
acoustic oscillations into the CMB and matter power spectra at different
scales. We determine the dependence of the respective acoustic amplitudes and
damping lengths on fundamental cosmological parameters. The baryonic
oscillations, enhanced by the velocity overshoot effect, compete with CDM
fluctuations in the present matter power spectrum. We present new exact
analytic solutions for the cold dark matter fluctuations in the presence of a
growth- inhibiting radiation {\it and} baryon background. Combined with the
acoustic contributions and baryonic infall into CDM potential wells, this
provides a highly accurate analytic form of the small-scale transfer function
in the general case.
