  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.
