Physical modeling of flue instruments: A review of lumped models

Physical modeling of flue instruments is a challenge that has been stimulated by interesting sound synthesis obtained by simple lumped models. Those models are based on a strange mixture of ad-hoc assumptions, theories and fit of experimental results. On the other hand, more formal integral models have also been proposed. They rely on drastic simplifications and are limited to a linear behavior such as expected during the initial phase of a slow attack transient. The sophisticated mathematics involved and the modest results of the more formal models have formed a barrier between the two approaches. Initially, lumped models were simplified to the point that they became numerical oscillators with control parameters having no relationship with the physics. While researchers are now trying to use more realistic lumped models, it would be a goal to use the formal integral models to provide a more solid theoretical basis to lumped models. The issue of such an approach is however still uncertain.