Conductivity measurements are reported in the organic linear-chain compound (TMTSF${)}_{2}$${\mathrm{PF}}_{6}$, in both the metallic and spin-density-wave states. The components of the complex conductivity were established by measurements in the radio-frequency, micro- and millimeter wave, and infrared spectral ranges. At temperatures above the spin-density-wave transition, a Drude-like metallic behavior was found together with a temperature-independent feature at higher frequencies. An observed Drude scattering rate of 3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ was found, placing the material well into the clean limit. In the spin-density-wave state, the low-field dc resistivity shows an activated behavior similar to a standard semiconductor with a gap value 2\ensuremath{\Delta}/${\mathit{k}}_{\mathit{B}}$\ensuremath{\approxeq}45 K. The ac response shows a strong frequency dependence, and most importantly, we observe two subgap modes: a very broad one in the radio frequency range, due to internal deformations of the spin density wave, and a narrow mode near 0.1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, which we interpret as the response of the q=0 phason. Furthermore, as expected for a material in the clean limit, we do not see evidence for a single particle gap in the infrared spectral range. In this paper, we will compare our experimental results with the various models of spin-density-wave dynamics and comment on the current status of the understanding of the dynamical response of spin density waves.