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From: JJTHAD~ife.uams.edu
Date: Sat, 16 Sep 1995 03:18:49 -0500 (CDT)
Subject: Harp reed: Clamped bar or Siren? (was Differences in harps & blues melodies)

From Harvey Andrussen:
>>Woodwind? Percussion? Brass? What type of devices are these . . . ?
>I think . . . we'd virtually all say that the harmonica is in a class by itself for ~tone~.

Harmonicas don't leave musicologists in a quandary, I'm told. They are classified as "free reed" instruments, a class shared by harmonium, reed organ, accordion, jaw harp, and some but not all of the reed stops on a concert organ. This is in contrast with "striking reed" instruments, like
clarinet, sax, oboe (two reeds), and other of the organ reed stops, for which the reeds hit something during each swing. Harv continues [square brackets mine]:

> But why? It has more to do with the entire acoustical system than the reed . . . ; regarding just the reed now, it is from a family of instruments that use a ~clamped bar~ where the pitch is determined by:
> [math equations here]
When I read Helmholz' treatment of the clamped bar (which I believe is the classical source of these or similar equations), I too thought that this math certainly applied to harmonica reeds, which undoubtedly are clamped at one end. Now I am convinced otherwise. I'll explain why a little later.

>. . . [C]lamped reeds . . . produce overtones that are not harmonic (Douglas Tate notes some of this in his book, but then states that it is different for clarinets and saxes. This is not true if you believe Harry F. Olson [book reference]:
> The overtones produced by the fixed or clamped reed (at one end) are:
> [table here -- wild overtone series, also originally from Helmholz]
> . . . The reed organ, harmonica, clarinet, oboe, bassoon, saxophone and
> tuning fork are examples of instruments employing a bar or reed clamped
> at one end.

Harvey, is this list of instruments yours or Olson's? Does he use the phrase "clamped reeds", or only you? The seeds of chaos are sown here.

>Olson goes on to say in his book on p 223 that the . . . harmonica . . . is rich in overtones . . . into the ultrasonic region . . . [with] . . . both even and odd harmonics (this part is a bit mysterious to me, since they plot it, but don't correlate it back in hard numbers to the preceding chart, nor does he name the higher order overtones -- JT, DT help?!).

Help? I wish I had the test equipment to provide experimental help. I can only offer a hypothesis and why it might be reasonable:

Hypothesis: When powered by a stream of air, the free reed of a harmonica behaves less like a bar fixed at one end than like a siren.

A siren? Helmholz again, with equations and all. I think he also has a drawing -- a disk with a hole in it rotating in front of an air source. Puffs of air. Sure, the harp reed is a "clamped bar" (albeit a rather limber one) but consider where it is clamped! Right in the only route for a powerful stream of air to pass. Voila, puffs of air. Consider the harp's kissin' cousin, the jaw harp. How different and anemic it sounds if you don't breath in or out! Likewise a harmonica reed plucked with a thumbnail. In fact, Johnston (1987) illustrates that a harp reed so plucked actually has a different (higher) fundamental frequency than when played by the breath. I'd predict that the overtone series is also rather different, with the plucked reed being more like
a clamped bar, the blown reed more like a siren. But, you say, sirens sound nothing like harmonicas? I'd predict you could make one that did a fair job, by positioning, sizing, and shaping holes in a spun disk to imitate the periods that a played harmonica reed's passageway is open for the air.

So who has really looked at this supposed "witch's brew" of harmonica over-tones? If I recall my Helmholz, siren overtones are relatively simple. Remembering the shape of an isolated harp reed's sound (cover plates off) on a friend's oscilloscope some years ago, it seemed simple too.

--John Thaden