  The ringdown portion of a binary black hole merger consists of a sum of
modes, each containing an infinite number of tones that are exponentially
damped sinusoids. In principle, these can be measured as gravitational-waves
with observatories like LIGO/Virgo/KAGRA, however in practice it is unclear how
many tones can be meaningfully resolved. We investigate the consistency and
resolvability of the overtones of the quadrupolar $\ell = m = 2$ mode by
starting at late times when the gravitational waveform is expected to be
well-approximated by the $\ell m n = 220$ tone alone. We present a Bayesian
inference framework to measure the tones in numerical relativity data. We
measure tones at different start times, checking for consistency: we classify a
tone as stably recovered if and only if the 95\% credible intervals for
amplitude and phase at time $t$ overlap with the credible intervals at all
subsequent times. We test a set of tones including the first four overtones of
the fundamental mode and the 320 tone and find that the 220 and 221 tones can
be measured consistently with the inclusion of additional overtones. The 222
tone measurements can be stabilised when we include the 223 tone, but only in a
narrow time window, after which it is too weak to measure. The 223 tone
recovery appears to be unstable, and does not become stable with the
introduction of the 224 tone. We find that $N=3$ tones can be stably recovered
simultaneously. However, when analysing $N \geq 4$ tones, the amplitude of one
tone is consistent with zero. Thus, within our framework, one can identify only
$N=3$ tones with non-zero amplitude that are simultaneously stable.
