151st ASA Meeting, Providence, RI
What Makes the Sound of the Saxophone So Distinct?
Jean-Pierre Dalmont - jean-pierre.dalmont@univlemans.fr
Popular version of paper 2aMU4
The saxophone family is a huge family of wind instruments invented by Adolf Sax in 1846. This family ranges in size from the large (contrabass) to the small (sopranino). They are all single-reed cone-shaped instruments made of metal. At first sight it could be thought that the important point is that the saxophone is a metallic instrument. In a wind instrument, the sound is not produced by the vibrations of the body like in a string instrument, but by the vibration of the air column inside the instrument. So the fact that the instrument is made of metal has very little influence on its sound quality (timbre). This is why the saxophone is a member of the woodwind instrument family instead of the brass wind family. A woodwind instrument is either a flute or a reed instrument. A reed instrument is an instrument in which the vibration of the air column is induced by a small oscillating valve made of reed wood and called the "reed." Two kinds of reeds are made: the double reed, which is used in the oboe or the bassoon, and the single reed, which is used in the clarinet or the saxophone. The fact that the saxophone has a single reed gives it some similarity to the clarinet, but recent works at the IRCAM (Paris, France) tend to show that the difference between the single reed and double reed is not so great. Indeed, some single-reed mouthpieces for bassoon can be found which make a sound very similar to that of a bassoon played with a double reed. The main characteristic of the saxophone is its conical (cone-shaped) bore. The sound of the saxophone can be explained by the physics of conical reed instruments. Surprisingly, as we have shown at the Laboratoire d'Acoustique de l'Universit du Maine (Le Mans, France), the physics of conical reed instruments is very similar to that of bowed string instruments. The physics of bowed string instruments was first investigated by Hermann von Helmholtz at the end of the 19th century. He showed that in a bowed string, two phases alternate: a long phase, during which the bow sticks to the string, and a shorter phase, during which the string slips on the bow. The ratio N of the time duration of these two phases depends on the position of the bow on the string, and it is given by the length's ratio of the portions of the string on both side of the bow. This specific behavior is usually called the Helmholtz motion. An analogous Helmholtz motion can be found in conical reed instruments. The reed alternately closes the reed channel and, similarly to the string, two phases alternate: a long phase, during which the reed channel is open, and a shorter phase, during which the reed closes the reed channel. The ratio N of the time duration of the two episodes is equal to the ratio of the length of the cone (which is truncated because of the reed) to the length of the missing part of the cone. This specific oscillation of the reed has a direct consequence on the spectrum: harmonics whose frequencies are close to N multiplied by the fundamental frequencies are weak. In other words, there is an anti-formant whose frequency is Nf1, where f1 is the fundamental frequency. This frequency does not depend on the played note and is inversely proportional to the length of the missing part of the cone. Formants are well known for characterizing the vowels: humans are able to distinguish different vowels because of the frequencies of the different formants. This is also used for distinguishing the timbre of musical instruments. So a characteristic of the saxophone is the frequency of its second formant, which is a consequence of its geometry. A remaining question is: what distinguishes oboe, bassoon, and saxophone? The reed may explain part of the difference, but the main point is probably that the frequencies of the anti-formants are different because the conicity of the oboe and the bassoon is much lower than that of the saxophone. Another difference is that the saxophone has large holes. It is known as a "Boehm-like" instrument [Theobald Boehm is the inventor of the modern flute, which is much more powerful than the Baroque flute (flauto traverso) because of its large holes]. These two characteristics (large conicity and large holes) give the saxophones a brighter sound, much more powerful than that of the bassoon and the oboe. |
