The mathematical basis for the earlier reported spectrum of discrete electromagnetic field (EMF) frequencies that were shown to affect health and disease is substantiated and generalized in the present paper. The particular EMF pattern was revealed by a meta-analysis of, now, more than 500 biomedical publications that reported life-sustaining as well as life-decaying EMF frequencies. These discrete eigenfrequency values can be related to supposed bio-resonance of solitons or polaron quasi particles in life systems. Bio-solitons are conceived as self-reinforcing solitary waves that are constituting local fields, being involved in intracellular geometric ordering and patterning, as well as in intra- and inter-cellular signalling. Literature search, revealed very similar frequency patterns for wave resonances of nucleotides in aqueous solution, for a candidate RNA-catalyst, as well as for sound-induced vibrations evoked in thin vibrating membranes. This collective evidence points at a generalized biophysical algorithm underlying complexity in nature, evidently manifest in both animate and non-animate modalities. The detected EMF eigenfrequencies could be arithmetically scaled according to an adapted Pythagorean tuning. The mathematical analysis shows that the derived arithmetical scale exhibits a sequence of unique products of integer powers of 2, 3 and a factor
. This generalized semi-harmonic frequency spectrum may reflect a discrete pilot-wave structure that can be interpreted as a, so called, hidden variable in Bohm’s causal interpretation of quantum field theory.