Hard-x-ray spectroscopy relies on a suite of modern techniques for studies of vibrational, electronic, and magnetic excitations in condensed matter. At present, the energy resolution of these techniques can be improved only by decreasing the spectral window of the involved optics-monochromators and analyzers-thereby sacrificing the intensity. Here, we demonstrate hard-x-ray spectroscopy with greatly improved energy resolution without narrowing the spectral window by adapting principles of spectrographic imaging to the hard-x-ray regime. Similar to Newton's classical prism, the hard-x-ray spectrograph disperses different "colors"-i.e., energies-of x-ray photons in space. Then, selecting each energy component with a slit ensures high energy resolution, whereas measuring x-ray spectra with all components of a broad spectral window keeps the intensity. We employ the principles of spectrographic imaging for phonon spectroscopy. Here the new approach revealed anomalous soft atomic dynamics in α-iron, a phenomenon which was not previously reported in the literature. We argue that hard-x-ray spectrographic imaging also could be a path to discovering new physics in studies of electronic and magnetic excitations.