The Three Main Parts of the Clarinet
Clarinet acoustics are determined by the reed and mouthpiece, the bore and the tone holes. Vibrations in the column of air in the bore are created by air blown into the clarinet through the reed and mouthpiece. The vibrating column of air in the bore produces the clarinet's sound. The frequency at which the air vibrates is determined mainly by the bore dimensions, which are changed by combinations of open and closed side holes.
A Stopped Cylindrical Pipe
The clarinet is the only modern wind instrument that functions acoustically like a stopped cylindrical pipe. The wavelength corresponding to a given frequency is approximately four times the length of the instrument from mouthpiece to the first open hole. With the flute and oboe, the wavelength is only twice the length of the corresponding length of tube. Wavelengths double for every octave lower in frequency so the wavelength formed in the clarinet is four times the length of tube used versus only two times the length of tube used in the flute or oboe. This is why, though all three woodwinds are similar in length, the clarinet can play almost a full octave lower.
The Tone Quality of the Clarinet
The clarinet is further distinguished from other wind instruments by the relatively low intensity of the even numbered partials in the composite sound of a given note, especially in the chalumeau register. This is more prominent in modern German system clarinets than modern French system clarinets. In higher registers both odd and even partials are more equally present, so the clarinet loses its distinctive tone quality.
How The Clarinet Sound is Produced
To produce the resonating air column in the clarinet, energy is admitted to the clarinet from the player's higher-pressured mouth cavity. The reed and lip act like a valve admitting energy into the resonating air column. In very soft playing the tip of the reed moves almost sinusoidally without contacting the tip of the mouthpiece at all and in loud playing the reed moves far enough to completely close the end of the clarinet tube during each cycle of vibration.
Energy must be fed into the resonating tube at the right time during each cycle for the vibration in the tube to continue. This works only if the frequency of vibration of the reed and lip is higher than the frequency of resonance inside the clarinet. Even if the correct fingering is used for an upper register note it will not sound unless the vibrating frequency of the reed is high enough. This is accomplished primarily by controlling the length of the reed that is actually vibrating. Through embouchure control the player can adjust where on the mouthpiece the reed makes contact and hence the reed's vibrating length. If the reed is too soft it may not be possible to find a position on the reed that will allow production of high altissimo or altissimo notes. The strength of the reed also affects how quickly the reed restores its shape upon deflection by the air stream.
Compensating for the Interaction of the Reed and the Holes
There is a discrepancy between the length of the resonating air column for a given frequency and the value that is one quarter of the corresponding free-air wavelength at room temperature. The discrepancy is caused by the moist warm air in the clarinet above room temperature, the irregularities in bore of the clarinet caused by tone holes and pads and the mouthpiece is not completely closed and cylindrical. Clarinet makers have made alterations of a few thousandths of an inch in the cross section of the bore at different places to compensate for unwanted effects produced by the complex interaction of the reed and tone holes.
More Factors Affecting the Sound
The third and fifth harmonics are strong resonances and define the clarinet's tone color. The upper registers are dependent on the presence of these harmonics. When the very small register hole is open it is very difficult to make the air column resonate at the frequency associated with the tube length. The register hole does not vent the tube well enough. The next possible primary resonance is the second resonance (third harmonic or the interval of a 12th higher) which is present for the length of tube established ignoring the register hole.
Another factor affecting the tone color of the clarinet is the large drop-off in the energy of resonances above ca. 1500 cycles per second. This value is determined by the array of open holes (or the design of the bell when all the holes are closed) that radiate the sound for a given note. Early clarinets with a very different array of tone holes had different cut-off frequencies and different sound characteristics.
Harmonics Affect the Tone
The exact relationship between resonances of different harmonics affects both tone and intonation. If the second resonance is not an exact 12th above the fundamental, a duller sound will result because the relevant partial in the reed motion will not adequately produce this harmonic. The intonation between 12ths will be out of tune if the second resonance is not an exact 12th above the fundamental.
Lower harmonics affect the perceived tone of the clarinet is the lower notes. They are emitted relatively weakly from the first one or two open holes omni-directionally while the higher components are radiated from all the open holes but in a highly directional manner.