Acoustics of free-reed instruments, a review of the current info, by James Cottingham, is available online free this month in the March 2011 Physics Today, from the American Institute of Physics.

"This article looks at some of the main acoustical properties of Eastern and Western free-reed instruments. The research on them, both experimental and theoretical, has focused on three important areas: the basic mechanisms of reed oscillation and sound production, the influence of resonators on tone quality, and the influence of resonators on pitch. Of particular interest is pitch bending, especially notable in harmonica music."

This is a review, not research. Some highlights:

"The term 'free reed' and its definition may well be less familiar than the instruments themselves. What, then, is a free reed, and why is a harmonica reed 'free' and a clarinet reed not? ... a free reed is a vibrating tongue constructed or mounted in a way that allows it to vibrate back and forth through its reed plate or frame, much like a swinging door. In contrast, the so-called beating reed in an instrument such as the clarinet is slightly wider than the opening over which it is mounted."

"The principal acoustical difference between the Western and Asian free-reed instruments is in the design of the reeds. The Western instruments employ reeds in which a separately constructed tongue is mounted outside the reed plate or frame in such a way that the reed only sounds with one direction of airflow. Normally such a reed behaves like a so-called blown-closed reed—that is, a reed for which a musician's initial attack tends to decrease the distance between the reed and the frame. A clarinet reed mounted in its mouthpiece is an example of a blown-closed beating reed. Several theorists have developed models for the oscillation of the air-driven free reed, and the Western instruments have been subject to a number of experimental studies. For example, as will be discussed further below, musical acousticians have learned that the sounding frequency of the blown reed is somewhat below the natural vibrating frequency of the reed tongue.

"The Asian instruments, on the other hand, employ free reeds in which tongue and frame are cut from a single piece of material. Nowadays, metal is the usual choice, but other possibilities include bamboo or similar plant material. The reed tongue is positioned so that absent any pressure difference, it is in the closed position. Any initial pressure difference on the two sides of the reed will cause the reed opening to increase. Hence, reeds in Asian instruments are the blown-open type. In many instruments, including the khaen shown in figure 1d, a single reed functions with both directions of airflow. Because of their structure, the Eastern reeds must generally be coupled to a resonator, usually a pipe. For some very simple single-reed instruments, however, the player's vocal tract serves as a resonator. Theory predicts and experiment verifies that for the Eastern instruments, the sounding frequency of the reed–pipe combination is greater than both the natural frequency of the reed and the resonance frequency of the pipe."

"At a simple level of analysis, the sound production of a free reed is similar to that of a siren. As noted by Hermann von Helmholtz, 'The passage for the air being alternately closed and opened, its stream is separated into a series of individual pulses. This is effected on the siren . . . by means of a rotating disc pierced with holes.' For the free-reed instrument, the air stream is interrupted by the oscillating reed tongue."

"When the harmonica is played with straightforward blowing or drawing, the primary sounding reed is a blown-closed one coupled to the resonator, that is, the vocal tract of the musician. Johnston's groundbreaking study considered the volume of the oral cavity and the coupling between the two reeds that share a common chamber. He found that he could account for two common observations: The notes that can be bent are those for which the primary reed sounds a note higher in frequency than that sounded by the secondary reed, and the notes can be bent downward to pitches between those sounded by the two reeds. Figure 4c shows how the amplitudes of the primary and secondary reeds evolve as a harmonica player executes a draw bend.

"Unusually skilled players use what are called overblows and overdraws to bend notes beyond the frequencies of the chamber reeds. The technique involves more than just blowing or drawing much harder than usual. In particular, the configuration of the vocal tract, not just its volume, is an important and difficult-to-realize element. "

"An alternate route to pitch bending on the accordion involves modifying the accordion to include an additional resonating pipe or chamber for each of the instrument's keys. Thomas Tonon has recently developed, patented, and implemented a practicable pitch-bending instrument that gives its player a flexibility similar to that available to a harmonica player.15 By increasing the pressure on the key in the pitch-bending accordion, a musician can continuously bend the note downward about one semitone. "

(There's more info on non-western instruments.)

Also, as supplemental material:

A brief history of free-reed instruments
(Acoustics of free-reed instruments supplemental material)
James Cottingham

Asian free-reed instruments, scholars believe, originated in Southeast Asia. The details, however, are lost in the prehistory of the region's many ethnic groups. Nor do historians know the degree to which the invention of the Western free-reed instruments was inspired by familiarity with the Asian instruments, or the reason Western instruments used a different type of reed. Still, the eclectic sampling of dates below may be of interest.Circa 3000 BC—According to oral tradition, a female ruler named Nyn-Kwa creates the sheng.

    * 11th–12th centuries BC—Written references to the sheng appear in Chinese sources.
    * 1636—An instrument closely resembling the khaen is pictured in Marin Mersenne's Harmonie universelle, which indicates that Asian free-reed mouth organs were known in Europe by the time of the book's publication.
    * 1770—Christian Gottlieb Kratzenstein demonstrates his mechanical speaking machine, which uses a free reed as the sound source.
    * 1821—16-year-old German clockmaker Christian Friedrich Ludwig Buschmann creates an early version of what we know today as the harmonica.
    * 1820s—Versions of the harmonica, accordion, and reed organ (including the harmonium) are invented in Europe. Those instruments develop rapidly and are soon being mass produced.
    * 1828—Wilhelm Weber reports on his efforts to create a tuning standard that uses free reeds coupled to cylindrical pipes.
    * 1829—Piano and organ maker Cyrill Demian of Vienna patents the accordion. British physicist Charles Wheatstone, perhaps best known for the Wheatstone bridge, patents his version of the concertina. C Wheatstone & Co, Concertina Makers, is still in business in 2011 in the UK.
    * 1846—J. Estey & Co of Brattleboro, Vermont, begins manufacturing reed organs. The company builds some 520 000 organs before ceasing production in 1960.
    * 1857—The Matthias Hohner company of Trossingen, Germany, begins manufacturing harmonicas.
    * 1863—Hermann Helmholtz publishes the first edition of On the Sensations of Tone as a Physiological Basis for the Theory of Music. Chapter 5 of the book discusses free reeds as used in the harmonium.
    * 1868—As Japan introduces Western music into the school curriculum, small portable reed organs find common use in the classroom.
    * 1889—Torakusu Yamaha establishes Yamaha Organ Works. The company continues to manufacture reed organs into the 1970s.
    * 1925—American harmonica manufacturer William Kratt Sr, born in Trossingen, Germany, invents the familiar free-reed pitch pipe.
    * 1945—American composer and instrument inventor Harry Partch completes the chromelodeon, a pedal-pumped reed organ adapted to play the pitches of his 43-tone-per-octave scale.
    * 1998—The Center for the Study of Free-Reed Instruments was established at The City University of New York.
    * 2002—Lidia Kaminska earns the first doctoral degree granted by a US university in classical accordion performance.
    * 2005—The AIP Physics and Astronomy Classification Scheme (PACS) introduces a new category: Free reed instruments.

~ Becky in Tucson