The $K\pi \pi$ spectrum in the reaction $K^{-}p\to K^{-}{\pi }^{+}{\pi }^{-}p$ at $12.6\frac{\mathrm{GeV}}{c}$ is analyzed, taking as a starting point the observation that the transverse momentum distributions are uniform throughout this spectrum and are restricted to small values. This behavior results in a threshold enhancement in the $K\pi \pi$ spectrum corresponding to every $K\pi$ mass value. With the exception of the $Q$ peak, and perhaps the $L$ meson, the $K\pi \pi$ mass spectrum can be regarded as a continuous sequence of such enhancements, which follow from phase-space distributions in the longitudinal momenta. A double-Regge-pole-exchange model for the $Q$ gives qualitative agreement with the data, but only if at least two exchange amplitudes are included; it does not give a correct description of the detailed correlations between the longitudinal and transverse momenta. A more successful description is given by a very simple resonance model. The similarities between the predictions of these two models—which are related by the concept of duality—are discussed in terms of the kinematic restrictions imposed by the condition of small transverse momenta.

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