Clarinet Acoustics (Greg Barrett) - NIU - School of Music

Clarinet Acoustics

The three main parts of the clarinet

An understanding of the acousticalphysics of the clarinet is aided by mentally disassembling it into threeparts: the reed, the bore and the side holes.  Vibrations in the columnof air in the bore (standing pressure waves) are set up by air blown intothe clarinet through the reed and mouthpiece.  It is the vibratingcolumn of air that produces the clarinet's sound.  The frequency atwhich the air vibrates is determined mainly by the bore dimensions whichcan be changed by different open and closed combinations of the side holes.

A stopped cylindrical pipe

The clarinet is the onlymodern wind instrument that functions acoustically like a stopped cylindricalpipe.  This means that the wavelength corresponding to a given frequencyis (with minor corrections) four times the length of the instrument frommouthpiece to the first open hole.  This contrasts with the fluteand oboe in which the wavelength formed is only twice the length of thecorresponding length of tubing.  Knowing that wavelengths double inlength for every octave lower in frequency and that the wavelength formedin the clarinet is four times the length of tube used versus only two timesthe length of tube used in the flute or oboe explains why though all threewoodwinds are similar in length the clarinet can play almost a full octavelower than the flute or oboe.

The tone quality of the clarinet

The clarinet is furtherdistinguished from other wind instruments by the relatively low intensityof the even numbered partials (this is more prominent in modern Germansystem clarinets than modern French system clarinets) in the compositesound of a given note.  This is most pronounced in the chalumeau register. In higher registers both odd and even partials are more equally present. Therefore the clarinet loses its distinctive tone quality the higher inpitch it plays.

How the clarinet sound is produced

To produce the resonatingair column in the clarinet, energy is admitted to the clarinet from theplayer's higher-pressured mouth cavity.  The reed and lip unit actslike a valve admitting energy at the right time into the resonating aircolumn whose resonant frequency is determined by the open and closed holeson the clarinet.  In very soft playing the tip of the reed moves almostsinusoidally without contacting the tip of the mouthpiece at all and inloud playing the reed moves far enough to completely close the end of theclarinet tube during part of each cycle of vibration.  In this typeof coupled system energy must be fed into the resonating tube at the righttime during each cycle for the vibration in the tube to continue. This only works if the frequency of vibration of the reed/lip system ishigher than the frequency of resonance inside the clarinet.  Thereforeeven if the correct fingering is used for an upper register note it willnot sound unless the vibrating frequency of the reed is high enough. This is accomplished primarily by controlling the length of the reed thatis actually vibrating.  Through embouchure control the player canadjust where on the lay of the mouthpiece the reed makes contact and hencethe reed's vibrating length.  If the reed is too soft it may not bepossible to find a position on the reed relative to the lay of the mouthpiecethat will allow production of high altissimo or altissimo notes. The strength of the reed also affects how quickly the reed restores itsshape upon deflection by the air stream.

Compensating for the interaction of the reed and the holes

There is a discrepancy between the lengthof the resonating air column in the clarinet for a given frequency andthe value that is one quarter of the corresponding free-air wavelengthat room temperature.  The factors that account for this differenceare: that the air in the clarinet is moist and is warmed above room temperature,the bore of the clarinet is marked by irregularities of tone holes andabsorbent pads, and the mouthpiece is not completely closed and cylindrical. Clarinet makers have individually by trial and error made alterations of a fewthousandths of an inch in the cross section of the bore at different placesto compensate for unwanted effects produced by the complex behavior ofthe reed and holes.

More factors affecting the sound

With any fundamental frequency, thethird and fifth harmonics of the many generated by the reed are also stronglypresent resonances which help to define the clarinet's tone color. The ability of the clarinet to play in upper registers is dependent onthe presence of these harmonics.  When the very small register holeis opened it is very difficult to make the air column resonate at the frequencyassociated with the tube to this length.  The register hole does notvent the tube well enough.  In this situation the next possible primaryresonance to form in the clarinet is for the second resonance (third harmonicor the interval of a 12th higher) which is present for the length of tubeestablished ignoring the register hole.

Another factor greatly affecting thetone color of the clarinet is that there is a large drop off in the energyof resonances above the cut-off frequency of ca. 1500 cycles per secondin the modern clarinet.  This value is determined by the array ofopen holes (or the design of the bell when all the holes are closed) thatradiate the sound for a given note.  Early clarinets with a very differentarray of tone holes will therefore have different cut-off frequencies anddifferent sound characteristics.

Harmonics affect the tone

The exact relationship between resonancesof different harmonics affects both tone and intonation.  If the secondresonance is not an exact 12th above the fundamental, a duller sound willresult because the relevant partial in the reed motion will not adequatelyexcite this harmonic.  There will not be as much "ring" in the sound. The intonation between 12ths will also be out of tune if the second resonanceis not an exact 12th above the fundamental.

Another factor affecting the perceivedtone of the clarinet is that for a given note the lower frequencies ofthe composite pitch are emitted relatively weakly from the first one ortwo open holes omnidirectionally while the higher components are radiatedfrom all the open holes but in a highly directional manner.