  In this work, we consider the modeling of signals that are almost, but not
quite, harmonic, i.e., composed of sinusoids whose frequencies are close to
being integer multiples of a common frequency. Typically, in applications, such
signals are treated as perfectly harmonic, allowing for the estimation of their
fundamental frequency, despite the signals not actually being periodic. Herein,
we provide three different definitions of a concept of fundamental frequency
for such inharmonic signals and study the implications of the different choices
for modeling and estimation. We show that one of the definitions corresponds to
a misspecified modeling scenario, and provides a theoretical benchmark for
analyzing the behavior of estimators derived under a perfectly harmonic
assumption. The second definition stems from optimal mass transport theory and
yields a robust and easily interpretable concept of fundamental frequency based
on the signals' spectral properties. The third definition interprets the
inharmonic signal as an observation of a randomly perturbed harmonic signal.
This allows for computing a hybrid information theoretical bound on estimation
performance, as well as for finding an estimator attaining the bound. The
theoretical findings are illustrated using numerical examples.
