  The main goal of the spectroscopy program at COMPASS is to explore the
light-meson spectrum in the mass range below about $2\,\text{GeV}/c^2$ using
diffractive dissociation reactions. Our flagship channel is the production of
three charged pions in the reaction: $\pi^- + p \to \pi^-\pi^-\pi^+ +
p_\text{recoil}$, for which COMPASS has acquired the so far world's largest
dataset of roughly $50\,\text{M}$ exclusive events using an $190\,\text{GeV}/c$
$\pi^-$ beam.
  In order to extract the parameters of the $\pi_J$ and $a_J$ resonances that
appear in the $\pi^-\pi^-\pi^+$ system, we performed the so far most
comprehensive resonance-model fit, using Breit-Wigner parametrizations. This
method in combination with the high statistical precision of our data allows us
to study ground and excited states. We study the $a_4(2040)$ resonance in the
$\rho(770)\pi G$ and $f_2(1270)\pi F$ decays. In addition to the ground state
resonance $a_1(1260)$, we have found evidence for the $a_1(1640)$. We also
study the spectrum of $\pi_2$ states by simultaneously describing four
$J^{PC}=2^{-+}$ waves using three $\pi_2$ resonances, the $\pi_2(1670)$, the
$\pi_2(1880)$, and the $\pi_2(2005)$.
  Using a novel analysis approach, where the resonance-model fit is performed
simultaneously in narrow bins of the squared four-momentum transfer $t'$
between the beam pion and the target proton, allows us to study the $t'$
dependence of resonant and non-resonant components included in our model. We
observe that for most of the partial waves, the non-resonant components show a
steeper $t'$ spectrum compared to the resonances and that the $t'$ spectrum of
most of the resonances becomes shallower with increasing resonance mass. We
also study the $t'$ dependence of the relative phases between resonance
components. The pattern we observe is consistent with a common production
mechanism of these states.
