Nonlinear modeling of the "mitnahme-effekt" in coupled organ pipes

Two slightly mistuned organ pipes of the same nominal tone placed on neighboring holes of the same groove of the slider chest can synchronize if simultaneously sounded. The frequency difference between the two pipes disappears (mitnahme-effekt) giving up on a common frequency which is, in general, slightly higher than both natural frequencies of the pipes [Angster et al., ''Coupling between simultaneously sounded organ pipes,'' AES preprint 3534 (F1-2), Berlin (1993)]. A related phenomenon is observed when the separation between the two natural frequencies is bigger than 1%: this gives up on an increased difference frequency. This paper shows that a numerical simulation, where the two coupled pipes are modeled with a pair of coupled nonlinear oscillators, qualitatively obtains both these results. Furthermore the existence of a parameter range fitting all the experimental data is presented.