  Measurements of jet cross-section ratios between inclusive bins of jet
multiplicity are performed in 140 fb$^{-1}$ of proton--proton collisions with
$\sqrt{s}=13$ TeV center-of-mass energy, recorded with the ATLAS detector at
CERN's Large Hadron Collider. Observables that are sensitive the energy-scale
and angular distribution of radiation due to the strong interaction in the
final state are measured double-differentially, in bins of jet multiplicity,
and are unfolded to account for acceptance and detector-related effects.
Additionally, the scalar sum of the two leading jets' transverse momenta is
measured triple-differentially, in bins of the third jet's transverse momentum
as well as bins of jet multiplicity. The measured distributions are used to
construct ratios of the inclusive jet-multiplicity bins, which have been shown
to be sensitive to the strong coupling $\alpha_{\textrm S}$ while being less
sensitive than other observables to systematic uncertainties and parton
distribution functions. The measured distributions are compared with
state-of-the-art QCD calculations, including next-to-next-to-leading-order
predictions. Studies leading to reduced jet energy scale uncertainties
significantly improve the precision of this work, and are documented herein.
