The frequency distributions of the lineal energy, y, of 160 MeV proton, 150 MeV/u helium, and 490 MeV/u silicon ion beams were measured using a wall-less tissue equivalent proportional counter (TEPC) with a site size of 0.72 µm. The measured frequency distributions of y as well as the dose-mean values, y(D), agree with the corresponding data calculated using the microdosimetric function of the particle and heavy ion transport code system PHITS. The values of y(D) increase in the range of LET below ~10 keV µm(-1) because of discrete energy deposition by delta rays, while the relation is reversed above ~10 keV µm(-1) as the amount of energy escaping via delta rays increases. These results indicate that care should be taken with the difference between y(D) and LET when estimating the ionization density that usually relates to relative biological effectiveness (RBE) of energetic heavy ions.