Second-order topological photonic crystals support localized corner modes that deviate from the conventional bulk-edge correspondence. However, the frequency shift of corner modes spanning the photonic band gap has not been experimentally reported. Here, we observe the gapless corner modes of photonic crystal slabs within a parameter space by considering translation as an additional synthetic dimension. These corner modes, protected by topological pumping in synthetic translation dimensions, are found to exist independently of the specific corner configuration. The gapless corner modes are experimentally imaged via the near-field scanning measurement and validated numerically by full-wave simulations. We propose a topological rainbow with gradient translation, demonstrating the ability to extract and separate specific frequency components of light into different spatial locations. Our work contributes to the advancement of topological photonics and provides valuable insights into the exploration of gapless corner modes in synthetic dimensions.