According to theoretical predictions the quasicrystalline (QC) electronic density of states (DOS) must have a rich and fine spiky structure which actually has resulted elusive. The problem with its absence may be related to poor structural characteristics of the studied specimens, and/or to the non-existence of this spike characteristic. Recent calculations have shown that the fine structure indeed exists, but only for two dimensional approximants phases. The aim of the present study is to show our recent experimental studies with point contacts tunnel junction spectroscopy performed in samples of very high quality. The studies were performed in icosahedral QC alloys with composition Tb 9 Mg 35 Zn 56 . We found the presence of a pseudogap feature at the Fermi level, small as compared to the pseudogap of other icosahedral materials. This study made in different spots on the QC shows quite different spectroscopic features, where the observed DOS was a fine non-spiky structure, distinct to theoretical predictions. In some regions of the specimens the spectroscopic features could be related to Kondo characteristics due to Tb magnetic atoms acting as impurities. Additionally, we observed that the spectroscopic features vanished under magnetic field.