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An  essay on the Physics of the Blues Harp has been published in the  conference paper of the FAMA (in Deutsche Gesellschaft für Akustik e. V.  DEGA) workshop in October 2015: Alfred Förtsch, Physics of playing bluesharp in: Musikalische Akustik zwischen Empirie und Theorie, Berlin 2016, p. 35-38.
A free download of the whole conference paper is offered here.
Erratum: On p. 35 (right column) read: "For air flowing through a series of appropriately chosen volumes this phase shift can be derived without referring to standing waves or inertia, presupposing ..."

Robert B. Johnston was probably the first to deal with bends and overblows on blues harps from a physical point of view. In the theoretical part of his 1987 paper "Pitch control in harmonica playing" he applies formulas from the 1979 paper  "Excitation mechanisms in woodwind and brass instruments" by Neville H. Fletcher. Johnston treats both reeds in the same channel of a blues harp as a "parallel circuit" and applies Fletcher's formula for the admittance of closing resp. opening reeds. Adopting Fletcher's criteria for sound excitation to the admittance of this parallel circuit bend notes and overbends are predicted in accordance to playing experience. We will have a closer look at Johnston's paper in the near future. As a first step a hopefully reader-friendly version of Fletcher's 1979 paper can be found here.
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