We have investigated the density of states (DOS) of the generalised Th
ue-Morse (GTM) lattice, and compared by that means the degrees of aper
iodicity and relevant electronic states of various GTM lattices. Furth
er, we have correlated the DOS of various GTM lattices with the corres
ponding energy spectrum. Among other things, we find that GTM lattices
with higher ratios of relevant exponents are likely to be more period
ic than other varieties of it.