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The electronic-structural modulations of Ir$_{1-x}$Pt$_x$Te$_2$ (0 $\leqqx\leqq$ 0.12) have been examined by resonant elastic x-ray scattering (REXS)and resonant inelastic x-ray scattering (RIXS) techniques at both the Ir and Teedges. Charge-density-wave-like superstructure with wave vectors of$\mathbf{Q}$=(1/5 0 $-$1/5), (1/8 0 $-$1/8), and (1/6 0 $-$1/6) are observed onthe same sample of IrTe$_2$ at the lowest temperature, the patterns of whichare controlled by the cooling speeds. In contrast, superstructures around$\mathbf{Q}$=(1/5 0 $-$1/5) are observed for doped samples (0.02 $\leqq x\leqq$0.05). The superstructure reflections persist to higher Pt substitution thanpreviously assumed, demonstrating that a charge density wave (CDW) can coexistswith superconductivity. The analysis of the energy-dependent REXS and RIXSlineshape reveals the importance of the Te 5$p$ state rather than the Ir 5$d$states in the formation of the spatial modulation of these systems. The phasediagram re-examined in this work suggests that the CDW incommensurability maycorrelate the emergence of superconducting states as-like Cu$_x$TiSe$_2$ andLi$_x$TaS$_2$.

Commensurate vs incommensurate charge ordering near the superconducting dome in Ir$_{1-x}$Pt$_x$Te$_2$ revealed by resonant x-ray scattering