  Recent studies of the gravito-electromagnetic frequency spectra of
Kerr-Newman (KN) black holes have revealed two families of quasinormal modes
(QNMs), namely photon sphere modes and near-horizon modes. However, they can
only be unambiguously distinguished in the Reissner-Nordstr\"om (RN) limit, due
to a phenomenon called eigenvalue repulsion (also known as level repulsion,
avoided crossing or the Wigner-Teller effect), whereby the two families can
interact strongly near extremality. We find that these features are also
present in the QNM spectra of a scalar field in KN, where the perturbation
modes are described by ODEs and thus easier to explore. Starting from the RN
limit, we study how the scalar QNM spectra of KN dramatically changes as we
vary the ratio of charge to angular momentum, all the way until the Kerr limit,
while staying at a fixed distance from extremality. This scalar field case
clarifies the (so far puzzling) relationship between the QNM spectra of RN and
Kerr black holes and the nature of the eigenvalue repulsions in KN, that
ultimately settle the fate of the QNM spectra in Kerr. We study not just the
slowest-decaying QNMs (both for $\ell=m=0$ and $\ell=m=2$), but several
sub-dominant overtones as well, as these turn out to play a crucial role
understanding the KN QNM spectra. We also give a new high-order WKB expansion
of KN QNMs that typically describes the photon sphere modes beyond the eikonal
limit, and use a matched asymptotic expansion to get a very good approximation
of the near-horizon modes near extremality.
