This paper aims at being a provocative guide to the future of asteroseismology from the perspective of the analysis of time series, where the fundamentals of harmonic analysis are subjected to stress tests. In this context, we give an annotated summary of our research over the last decades on harmonic analysis of A-F stars. We discuss and explore the consequences of our findings, which may extend to any kind of pulsators. As well, we analyse the impact of this reconsideration on future asteroseismic studies, which would entail a paradigm shift. This includes a discussion on the presence of fractal behavior in δ Sct stars, and how this can be used to develop a stopping criterion of the pre-whitening process, as an alternative to SNR (or significance) criterion. Drilling a scientific paradigm has its natural resilience, hence the path described here is being arduous, although fruitful at the same time. SF, JP-G, JR, ML-M, and RG acknowledges financial support from the State Agency for Research of the Spanish MCIU through the Center of Excellence Severo Ochoa award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709) and Spanish public funds for research under projects ESP2015-65712- C5-5-R. JS and AG acknowledge funding support from Spanish public funds for research under projects ESP2017-87676-C5-2- R. JS also acknowledges funding support from project RYC2012-09913 under the Ramón y Cajal program of the Spanish MINECO. AG acknowledges support from Universidad de Granada under project E-FQM-041-UGR18 from the Programa Operativo FEDER 2014–2020 programme by Junta de Andalucía regional Government.