Basic Facts Week 9

Woodwinds

A cylindrical pipe exhibits normal modes that are harmonically related. If the pipe is open at both ends then there is a pressure node at each end of the tube and the tube must hold an integral number of half-wavelengths. Thus the modes have the form Eqn1 and Eqn2.

If the pipe is closed at one end and open at the other then there is a pressure node at the open end and a pressure anti-node at the closed end. In this case the tube must hold an odd integral number of quarter-wavelengths. Thus the modes have the formEqn3 and Eqn4.
Note that the lowest note from a half-closed tube is 1 octave lower than that from an open tube of the same length. Note also that all the even harmonics are missing from a half-closed tube.

Reed Instruments

Reed is a thin strip of material mounted in or over a hole through which air is forced.
Reeds are divided into several classes:-

Free Reeds sit in an opening that is larger than the reed so that the reed never completely blocks the passage of air. Examples include Harmoniums, Accordions, and Mouth Organs.

Beating Reeds are mounted so that they can completely close the opening during some part of the cycle and so interrupt the flow of air completely.

Single beating reeds are mounted over an opening that is smaller than the reed and beat upon the opening. Examples include most organ reeds, clarinet reeds, and saxophone reeds.

Beating double reeds are mounted on a short metal pipe so that the two reeds beat agaist each other as air is blown through the small opening between them.
Examples include oboe reeds and bassoon reeds.

Hard Reeds have a very high Q and so can oscillate only at one well defined frequency. In this case the pitch is determined solely by the reed and any resonator attached to the reed only alters the timbre. Hard reeds are made of metal and include organ reeds, accordion reeds, and mouth organ reeds. All the free reeds that I can think of are hard reeds.

Soft reeds have a low Q and can oscillate over a very wide range of frequencies. The pitch of a soft reed is determined by the resonator to which it is coupled. Soft reed are made of highly dissipative materials such as cane and are found in most beating reed instruments including clarinets, oboes, and bassoons.

Although a reed is mechanically a modified bar and thus has a set of normal modes that are totally non-harmonic, they produce sound by periodically opening and closing a passage to allow air through. The flow of air is periodic and thus posesses a truly harmonic spectrum and reed instruments are clearly pitched.

Members of the clarinet family have a single reed coupled to a cylindrical tube and thus have spectra that, at least in the lower registers, are lacking in the even harmonics and that overblow at the 12th. Thus the same fingering that leads to a C4 (middle C) overblows (with the aid of a register key) to the note G5, an octave and a 5th higher. The clarinet has large fingerholes so that the acoustic length is set quite accurately by the distance to the hole and forked fingerings are imposiible so the clarinet has an extensive key system. The instrument ends in a short slightly falred bell that aids in production of the two lowest notes.

Members of the oboe family (and the closely related bassoons) have double reeds coupled to a conical tube. The conical tube, closed at one end, has a full harmonic spectrum and overblows at the octave. Thus the same fingering that produces G4 overblows (again, with the aid of a register key) to G5. The oboe has a narrow bore and small fingerholes. The narrow bore means that the sound is weak in the lowest harmonics and the small fingerholes mean that forked fingerings are possible. The oboe makes extensive use of forked fingerings which lead to significant changes in tone color from one note to another, especially in the lower register. The oboe has a very slight bell that has a lip on it (so that the widest bore occurs just before the opening. This, combined with the narrow bore, allows the oboe spectrum to extend to very high harmonics and contributes to the thin, nasal sound of the instrument.

Members of the saxophone family have a singe, clarinet-like, reed coupled to a wide-tapered conical tube made of metal. The conical tube again gives the instrument a complete harmonic spectrum and allows the instrument to overblow at the octave. The wide bore means that the lower harmonics are strong and that the high harmonics are missing so that the sound is stronger and coarser than the oboe. The saxophone uses large finger holes and so cannot use forked fingerings but must rely on an extensive system of keywork. The wide flare of the instrument means that the fingerholes for the lowest notes must be very large, up to about 2" across in the case of the baritone sax.

Flutes

A jet of air blown across a sharp edge produces an edgetone, a clear single frequency tone, in addition to a certain amount of noise. The frequency of the tone depends on the speed of the jet of air and on the distance between the jet and the edge approximately as Eqn5.

Organ flue pipes, flutes, whistles, and recorders all operate by coupling a jet of air flowing over and edge to a resonator. In this case the frequency of oscillation is controlled by the transit time for a pressure pulse to go down the tube and back and so by the length of the tube. The air jet is forced into and out of the pipe by the resonance and the instrument sounds at a resonant frequency of the pipe, usually very much lower than the edge tone.

Drilling holes in the side of a blown pipe allows the effective length of the pipe to be shortened. A pipe with a hole in it will sound the same note as an entire pipe a little longer than the distance from the fixed end of the pipe to the hole. The sound wave continues some way past the hole. The bigger the hole is, the higher the note, the lounder the sound, and the less high frequency content the sound has.

Useful Facts

 

 

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Timestamp 3/28/24 3:52:00 PM EDT