Why is the three-nucleon force so odd?

By considering a class of diagrams which has been overlooked also in the most recent literature on three-body forces, we extract a new contribution to the three-nucleon interaction which specifically acts on the triplet odd states of the two-nucleon subsystem. In the static approximation, this $3N$-force contribution is fixed by the underlying $2N$ interaction, so in principle there are no free parameters to adjust. The $2N$ amplitude however enters in the $3NF$ diagram in a form which cannot be directly accessed or constrained by $\mathrm{NN}$ phase-shift analysis. We conclude that this new $3N$-force contribution provides a mechanism which implies that the presence of the third nucleon modifies the p-wave (and possibly the f-wave) components of the $2N$ subsystem in the triplet-isotriplet channels.