  We revisit the calculation of the average jet multiplicity in high-energy
collisions. First, we introduce a new definition of (sub)jet multiplicity based
on Lund declusterings obtained using the Cambridge jet algorithm. We develop a
new systematic resummation approach. This allows us to compute both the Lund
and the Cambridge average multiplicities to next-to-next-to-double (NNDL)
logarithmic accuracy in electron-positron annihilation, an order higher in
accuracy than previous works in the literature. We match our resummed
calculation to the exact NLO ($\mathcal{O}(\alpha_s^2)$) result, showing
predictions for the Lund multiplicity at LEP energies with theoretical
uncertainties up to $50\%$ smaller than the previous state-of-the-art. Adding
hadronisation corrections obtained by Monte Carlo simulations, we also show a
good agreement with existing Cambridge multiplicity data. Finally, to highlight
the flexibility of our method, we extend the Lund multiplicity calculation to
hadronic collisions where we reach next-to-double logarithmic accuracy for
colour singlet production.
