  Social dynamics are shaped by each person's actions, as well as by collective
trends that emerge when individuals are brought together. These latter kind of
influences escape anyone's control. They are, instead, dominated by aggregate
societal properties such as size, polarization, cohesion, or hierarchy. Such
features add nuance and complexity to social structure, and might be present,
or not, for societies of different sizes. How do societies become more complex?
Are there specific scales at which they are reorganized into emergent entities?
In this paper we introduce the {\em social complexity spectrum}, a
methodological tool, inspired by theoretical considerations about dynamics on
complex networks, that addresses these questions empirically. We use as a probe
a sociolinguistic process that has unfolded over decades within the
north-western Spanish region of Galicia, across populations of varied sizes. We
estimate how societal complexity increases monotonously with population size;
and how specific scales stand out, at which complexity would build up faster.
These scales are noted as dips in our spectra, similarly to missing wavelengths
in light spectroscopy. Also, `red-' and `blue-shifts' take place as the general
population shifted from more rural to more urban settings. These shifts help us
sharpen our observations. Besides specific results around social complexity
build-up, our work introduces a powerful tool to be applied in further study
cases.
