Essays - Blues Harp Science (en)

Blues Harp
Physics
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On this site, essays written by me on the physics of the blues harp are offered for download in pdf format. Just like my website, the essays "live" - they are revised as needed (the creation date of the current version is indicated where appropriate).

Linear stability analysis: Historical - Updated - Put up for discussion

While looking for research papers on the physics of the blues harp, I first came across a 1987 publication by Robert B. Johnston, "Pitch control in harmonica playing". The theoretical part of this work is based on a 1979 paper by Neville H. Fletcher: "Excitation mechanisms in woodwind and brass instruments." The theoretical parts of both papers relevant to the blues harp are presented in a "student friendly" way in the following two essays. In addition, there are some outlooks as well as critical additions:
The role of the resonator when playing the blues harp is taken over by the vocal tract of the player. In contrast to the saxophone or clarinet, there are no data available to date (as of 2023) on the admittance of the resonator when playing the blues harp. Therefore, Johnston had to leave it at qualitative statements about possible playing frequencies on the blues harp. Quantitative predictions, according to Johnston, should follow from a phase condition when the admittance of the vocal tract is known.

In the meantime, the investigations carried out by Fletcher and Johnston will be placed in the framework of Linear Stability Analysis of self-excited systems, as it can be found for example in the textbooks of Chaigne and Kergomard or of Rienstra and Hirschberg (see my web page Literature). With this in mind, I derived updated formulas for the admittance of the reed system in the channel of a blues harp, and used them to perform a stringent linear stability analysis with a "toy model" for the resonator. In order to get realistic values for the reed admittance, effective parameters of formal 1-point oscillators for channel #4 of a C-Harp were calculated from own measurements. Possible playing frequencies and corresponding drawing or blowing pressures were predicted by comparing complex numerical values (a consideration of phase shifts proved unsatisfactory):
I could present a short version of this essay at the annual conference DAGA 2023 of the German Acoustic Society in Hamburg. The conclusions were based on a more realistic “toy model” in which impedance measurements were applied to the vocal tract of saxophone players bending and playing in the altissimo range. One result was that a drawbend and an overblow on channel #4 of a C-harp should be possible alternately with the same resonator frequency (in accordance with playing practice):

At the DAGA 2024 annual conference of the German Acoustical Society in Hannover, I presented my own measurements on the transient response of a drawbend (see also the essays on my own measurements linked below). The oscillation frequency of the overall system consisting of both reeds in the channel and the air in the vocal tract acts as a kind of “attractor”. Whether a linear stability analysis in the frequency range (which a priori assumes a common playing frequency) makes any sense at all seems rather questionable. It would probably make more sense to analyze the transient response in the time domain:

Essays about own measurements



Miscellaneous

  • 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.
  • The essay Comparison of forces on a blues harp reed shows that blues harp reeds oscillate "almost by themselves".
  • A brief bibliography Literature (uploaded as a web page) supplements the references listed in the essays.
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