Topological properties of energy spectra of general one-dimensional quasiperiodic systems, describing Bloch electrons in magnetic fields, are studied for an infinity of irrational modulation frequencies corresponding to irrational numbers of flux quanta per unit cell. These frequencies include well-known ones considered in works on Fibonacci quasicrystals. It is shown that the spectrum for any such frequency exhibits a self-similar hierarchy of clusters characterized by universal (system-independent) values of Chern topological integers which are exactly determined. The cluster hierarchy provides a simple and systematic organization of all the spectral gaps, labeled by universal and exactly determinable values of topological numbers. The numbers for a gap give both the quantum Hall conductance of the system and the winding number of the edge states traversing the gap as a quasimomentum is varied. The universal organization of gaps should be compared with the usual system-dependent one based on successive rational approximants of the irrational frequency. For more details, see http://arxiv.org/abs/1310.7970 (submitted).