The dielectric properties of noncrystalline hafnium silicon oxynitride ($\mathrm{HfSiON})$ films with a variety of atomic compositions were investigated. The films were deposited by reactive sputtering of Hf and Si in an O, N, and Ar mixture ambient. The bonding states, band-gap energies, atomic compositions, and crystallinities were confirmed by x-ray photoelectron spectroscopy (XPS), reflection electron energy loss spectroscopy (REELS), Rutherford backscattering spectrometry (RBS), and x-ray diffractometry (XRD), respectively. The optical (high-frequency) dielectric constants were optically determined by the square of the reflective indexes measured by ellipsometry. The static dielectric constants were electrically estimated by the capacitance of $\mathrm{Au}∕\mathrm{HfSiON}∕\mathrm{Si}(100)$ structures. It was observed that low N incorporation in the films led to the formation of only $\mathrm{Si}\text{\ensuremath{-}}\mathrm{N}$ bonds without $\mathrm{Hf}\text{\ensuremath{-}}\mathrm{N}$ bonds. An abrupt decrease in band-gap energies was observed at atomic compositions corresponding to the boundary where $\mathrm{Hf}\text{\ensuremath{-}}\mathrm{N}$ bonds start to form. By combining the data for the atomic concentrations and bonding states, we found that $\mathrm{HfSiON}$ can be regarded as a pseudo-quaternary alloy consisting of four insulating components: ${\mathrm{SiO}}_{2}$, ${\mathrm{HfO}}_{2}$, ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$, and ${\mathrm{Hf}}_{3}{\mathrm{N}}_{4}$. The optical and static dielectric constants for the films showed a nonlinear dependence on the N concentration, whose behavior can be understood in terms of abrupt $\mathrm{Hf}\text{\ensuremath{-}}\mathrm{N}$ bond formation.