Characterizing the link between small-scale chromatin structure and large-scale chromosome folding during interphase is a prerequisite for understanding transcription. Yet, this link remains poorly investigated. Here, we introduce a simple biophysical model where interphase chromosomes are described in terms of the folding of chromatin sequences composed of alternating blocks of fibers with different thicknesses and flexibilities, and we use it to study the influence of sequence disorder on chromosome behaviors in space and time. By employing extensive computer simulations, we thus demonstrate that chromosomes undergo noticeable conformational changes only on length-scales smaller than 105 basepairs and time-scales shorter than a few seconds, and we suggest there might exist effective upper bounds to the detection of chromosome reorganization in eukaryotes. We prove the relevance of our framework by modeling recent experimental FISH data on murine chromosomes.