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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 overbends on blues harps from a physical point of view. In his 1987 paper "Pitch control in harmonica playing" he builds on an electro-acoustic model by Neville N. Fletcher for woodwind and brass instruments from 1979 ("Excitation mechanisms in woodwind and brass instruments" ). In Fletcher's work one finds formulas for the admittance of closing and opening reeds and criteria for possible playing frequencies. Johnston interprets the two reeds in the channel of a blues harp as a parallel circuit and uses Fletcher's formulas to calculate their total admittance. From the result he reads possible playing frequencies, which he associates with playing normal notes, bending and oververbending.
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 as a pdf file.
Update: The essay "Fletcher 1979" has been revised and significantly extended by now (March 30, 2019).
 
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