When I wrote the first version of this page back in 2004, the opening paragraph went like this:
Considering the oft-repeated claim that the harmonica is the biggest selling commercially produced musical instrument in history, there have been surprisingly few studies into how it actually works. There have been published studies of free reeds in general, going all the way back to Wheatstone's research in the late 1820s, but only a few researchers have focused on the unique qualities of the harmonica.
In the decade since then, things have improved markedly, with scientists and harmonica players coming together to figure out just what goes on inside this favorite instrument of ours. Thankfully, a good proportion of these studies are also available online.
The earliest study of harmonicas of which I am aware was On the Physics of Harmonicas, published in The American Journal of Physics, Volume 20, Issue 6 back in 1952. Authored by A. W. Simon, the article can be previewed here and you can purchase the full article.
One particularly influential article was written by Robert "Johno" Jonston in 1987, during his studies at Monash University in Australia. Entitled Pitch Control in Harmonica Playing, it was originally published in Acoustics Australia, Volume 15, Issue 3 and was the first formal study of the physics of bending and overblowing. A copy of the article in .pdf form is available here.
A decade later, US researchers Henry Bahnson and James "Turbodog" Antaki collaborated on some research leading to the 1998 publication of the article Acoustical and Physical Dynamics of the Diatonic Harmonica. Originally published in the Journal of the Acoustical Society of America, Volume 103, Issue 4, a .pdf copy can be downloaded here. Follow-up papers include Physics, phonetics, and physiology of the diatonic harmonica by Turbodog and Hank Bahnson with Quinter C. Beery, published in the Journal of the Acoustical Society of America, Volume 106, Issue 4 (1999) (abstract available here) and Acoustic Coupling between Oral Tract and Diatonic Harmonica: Recent Observations, by Turbodog and Hank Bahnson, along with Greg Burgreen, published in Journal of the Acoustical Society of America, Volume 111 Issue 5 (2002) (abstract available here).
More recently, Turbodog partnered with Jeongho Kim, Abhinav Singhal, Greg Burgreen and Fangjun Shu to publish Aeroelastic Analysis of a Closing Reed of the Mouth Organ (Harmonica) in Journal of the Acoustical Society of America, Volume 130 Issue 4 (2011), abstract available here.
Additionally, Turbodog has made several computer simulations of the air flow around harmonica reeds as well as x-ray footage, boroscopic video and sonograms (some of which include internal footage of Howard Levy!) and assorted other good stuff, all gathered together on this page.
Turbodog has also had several harmonica-related patents granted, a couple of them having extremely useful information about the physics of the instrument. US Patent 6359204, issued in 2002 covers some innovations in harmonica reeds and reedplates. The patent documents can be studied online via Google Patents here. US Patent 6635814 was issued in 2003 and covers various aspect of comb design. It can be viewed online here.
The leading French researcher into harmonica physics is Laurent Millot. A collaboration with Christian Cuesta and Claude Valette lead to the publication of Experimental Results when Playing Chromatically on a Diatonic Harmonica, in the journal Acustica, Volume 87, Issue 2, in 2001. This article is not freely available online, but those interested in such things are advised to try to order a copy through the library system (the journal's ISSN is 0001-7884), or if you have more money than patience, you can buy a copy here.
A study by Laurent Millot and Vincent Debut entitled Time Domain Simulation of the Diatonic Harmonica was published in the same year by the Mosart Workshop on Current Research Directions in Computer Music. A .pdf file of this article is available here.
A more recent paper A Proposal for a Minimal Model of Free Reeds was authored by Laurent Millot and Clément Baumann, published in Acta Acustica united with Acustica Volume 93, Issue 1, in 2007. An abstract of this paper is available here.
If you read French, then you may be interested in earlier work by Laurent Millot, including Étude des Instabilites dés Valves: Application à l’Harmonica Diatonique and Étude De l’Aérodynamique De l’Harmonica Diatonique, published in the Laboratoire d'Acoustique Musicale Report of Activities 1997-2000, available as a .pdf file here.
If you read German, you may be interested in Schlagende Zungen: Physik der Mundharmonika, by Leopold Mathelitsch and Ivo Verovnik, published in Physik in Unserer Zeit 47(3), published in May 2016. You can read an abstract here.
Another paper by a German researcher, this time written in English, is Physics of Playing Bluesharp by Alfred Förtsch, presented at the Musikalische Akustik Zwischen Empirie und Theorie conference in Hamburg in 2015. A .pdf transcript of the proceedings is available here. Alfred Förtsch also runs the website bluesharpscience.de, devoted to the topic of harmonica physics.
With the assistance of noted harmonica teacher David Barrett, a group of researchers published a study with the self-explanatory title Real-time Magnetic Resonance Imaging of the Upper Airways During Harmonica Pitch Bends in a 2013 issue of Proceedings of Meetings on Acoustics an online journal published by the Acoustical Society of America. A .pdf file of this paper may be downloaded for free here.
A summary that is somewhat more accessible to the general reader was written by David Barrett and is available here. There are also a couple of related videos on YouTube: MRI Video Footage and Video Interview of Study.
The same team also collaborated on Digital Fabrication of Vocal Tract Models from Magnetic Resonance Imaging During Expert Pitch Bending on the Harmonica, published in a 2013 issue of the Journal of The Acoustical Society of America. The full version is not available online, but you can view an abstract here.
A somewhat different approach to the study of harmonica playing is taken by Carl J Weber in his article Harmonica Phonetics and the Harmonica Syllable, published in Harmonica Educator magazine in January 2014. A .pdf file of this article may be downloaded here.
Carl Weber's work inspired Hamid Eghbal-zadeh and Markus Schedl of the Department of Computational Perception at Johannes Kepler University to do further studies of bent notes on the harmonica, resulting in the paper Formant Analysis of Altered Notes in a Diatonic Harmonica, presented at the 2014 International Symposium on Musical Acoustics, held in Le Mans, France. A .pdf file of the article can be downloaded here.
Tom Tonon is the inventor of the BluesBox and hold several patents on free reed designs. His article Reed Cavity Design and Resonance was originally published in the Papers of the International Concertina Association and can be read online here. Although mostly concerned with chamber design in bellows-driven free reed instruments, some of the points he covers apply equally well to harmonicas.
Associate Professor of Physics at Coe College, Iowa, James Cottingham has done substantial research into free reeds, particularly those used in reed organs. Some of his studies have relevance for those interested in how harmonica reeds work. Theoretical And Experimental Investigation Of The Air-Driven Free Reed was published in Proceedings of the International Congress on Acoustics 1998 and is available in .pdf format here; The Motion of Air-Driven Free Reeds was published the following year in Collected Papers of the 137th Meeting of The Acoustical Society of America. It can be downloaded as a .pdf file here. The article Variation Of Frequency With Blowing Pressure For An Air-Driven Free Reed was published in the same collection and is available in .pdf format here.
More recently, Cottingham's Pitch Bending and Anomalous Behavior in a Free Reed Coupled to a Pipe Resonator and Reed Vibration in Western Free-Reed Instruments were published in Proceedings of the International Symposium on Musical Acoustics (2007). The former is available in .pdf format here and the latter is available here. His Modes of Reed Vibration and Transient Phenomena in Free Reed Instruments was published in Proceedings of the International Congress on Acoustics (2013) and a .pdf copy is available here.
Perhaps a little more accessible to the average reader, is an article by James Cottingham published in the March 2001 issue of Physics Today. A .pdf copy of the article can be downloaded here.
Cottingham's work in the field of free reed research and his position on the Technical Committee on Musical Acoustics of the Acoustical Society of America has encouraged the publication of several free reed studies in the Journal of the Acoustical Society of America (JASA). Here are links to abstracts of the more harmonica relevant of those papers:
Detailed Analysis of Free Reed Initial Transients, by Daniel M. Wolff, Spencer Henessee and James P. Cottingham, JASA Volume 136, Issue 4 (2014).
Attack Transients In Free Reed Instruments, Jennifer Biernat and James P. Cottingham, JASA Volume 134, Issue 5 (2014).
The Diatonic Harmonica, Pipe Resonators, and the Siren, Casey N. Brock and James P. Cottingham, JASA Volume 130, Issue 4 (2011).
Pitch Bending and Higher-Mode Reed Vibration in Mechanically Blown Free Reed Instruments, James P. Cottingham, JASA Volume 127, Issue 3 (2010).
Free Reeds Coupling With Either a Vocal Tract or Rather Small Pipe, Laurent Millot, JASA Volume 126, Issue 4 (2009).
Very-Low Frequency Range Influence for Free Reed Instruments Physical Modeling, Laurent P. Millot, JASA Volume 123, Issue 5 (2008).
Source-resonator modeling: a rough paradox, Laurent P. Millot, JASA Volume 123, Issue 5 (2008).
Reed Vibration, Pressure, and Airflow in Western Free-Reed Instruments, Edward L. Toussaint and James P. Cottingham, JASA Volume 122, Issue 5 (2007).
Sound Production in Asian and Western Free-Reed Instruments, James P. Cottingham, JASA Volume 120, Issue 5 (2006).
An Inward Striking Free Reed Coupled to a Cylindrical Pipe, Justin Vines, Ammon Paquette and James P. Cottingham, JASA Volume 114, Issue 4 (2003).
Modeling Free Reed Behavior Using Calculated Reed Admittance, James P. Cottingham and Casey A. Fetzer, JASA Volume 102, Issue 5 (1997).
Effects of Reed Cell Geometry on the Vibration Frequency and Spectrum of a Free Reed, James P. Cottingham, JASA Volume 101, Issue 5 (1997).
The animated image at the top of this page is a computer simulation of the airflow at the tip of a harmonica reed operating in its "normal" closing mode, ie. not taking part in a bend or overblow. Red represents areas of high velocity airflow, blue represents areas of low airflow.
For more information please visit www.turboharp.com/research and "Buy More TurboHarps!"
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