It is generally known that the reed, the inner form of a mouthpiece, the ligature, the way we hold our mouth and lips, the force with which we blow and a handful more of similar factors influence the sound of the saxophone. Now, how does that work in practice?


To begin with: a brighter or sharper sonority (the wording does express an appreciation and maybe has something to say about proportions, but is of no relevance here) is a sound with more partials. Especially the higher partials add to this brightness in character. As can be expected to be well known, the partials form a coherent series, which is used in practice mainly by the brass players (and by guitarists and violinists in their play with the flageolets). One after the other the series ideally is: fundamental, octave, octave + fifth, double octave, double octave + major third, double octave + fifth, double octave + (flat) minor seventh and triple octave. Above this point a great number of whole tones and semitones are included in the series which thus takes smaller steps as we get higher. These higher partials, and certainly when we get higher than the seventh, grow less and less important in the composition of the timbre. Why that is so, is explained on the page on toneholes by the 'cut–off' frequency.

Partials arise by themselves in any musical instrument and their number and intensity increases with the energy of the sound produced. That's already a first and provisional answer to one facet of the question. Now, the recipe of the composition of the series of partials is influenced by the form of the vibrating body. Clarinets for instance, surely in their first register, hardly produce any even partials. The strength of a certain partial will be different compared to the fundamental in the one instrument compared to the other, may even sound louder, the recipe will show a different composition for different pitches and different registers, &c &c. Measurements with a probe microphone even show that the composition of partials along the length of the tube of a wind instrument is not a constant one: in the mouthpiece a vibration with strong peaks predominates; in the first open tone hole we especially find the combined peaks of the fundamental and a couple of lower partials while the remainder of the higher partials travels further down the tube and sound from the lower open tone holes and from the bell. It goes without saying that the dimensions and positioning of these (open) tone holes and the lift of the keys hanging over them greatly influence the very existence of these higher partials. The character of an instrument is largely defined by it and so are the individual differences between different specimens. Change in sonority can be caused very well by (partially) closing keys very much down the tube, as is sometimes done for intonational and other musical purposes.

So, sound, as we percieve it, stems from different origins and is a mixture of those. Also the direction in which the sound radiates from the instrument is not the same for all pitches. A woodwind radiates sound largely with an angle of a thirty degrees relative to the instrument and not straight ahead out of the bell. Higher partials though are radiated under a smaller angle and do sound more straight ahead from the bell.

behaviour of the reed

The reed acts like a controllable lock to the instrument. It is not so that the vibrating reed itself generates a sound and that next this sound as a wave travels down the tube. The properties of the lock enter into a relation with the properties of the tube. It is more or less known from stroboscopic photografy of a reed functioning in an artificial embouchure in which way the reed behaves. More recently is has been possible as well to study a working real life embouchure as well. Some researchers report that the reed closes for about half its cycle; a quarter of its cycle it is competely open and the remaining two eighths are used for opening and closing again. The reed performs these hauls with a somewhat irregular and speedy movement. All in all a fairly brusque pattern of movements. Others report that the margins of the time that the reed is open vary from one eighth of the cycle to only one twentieth of the cycle, depending on dynamic conditions. Some say that under piano–conditions the reed would not close at all but retains a tiny slit at the mouthpiece tip. That would make the reed movement under such conditions much more fluent than when playing forte. Something to keep in mind.

It makes little sense to substact the differences in observations from one another. On the contrary, these differences are complementary and add to a more complex picture. Researchers agree that the embouchure controlled vibration of the reed in its turn influences the aforementioned recipe of the composition of the partials and that a greater number of partials is caused by a reed behaviour which has a relativily short time of opening – whatever that time may be exactly. And there is an agreement on the view that the reed opens shorter as we blow harder so that reed movement is more brusque when playing forte.

If we look at the graph (below) of a complex vibration of a fundamental to which its first five consecutive harmonics are added (upto the double octave + fifth) we can get an idea of what happens. Successively the constituent vibrations are coloured red, blue, green, turquoise, purple and grey. Any next higher harmonic got a little less amplitude. In reality, it will always be more complicated and more irregular as reality is always more complex and harder to understand than our representations of it.


graph by the University of New South Wales, Australia.

The graph of the addition of a fundamental and its first five harmonics shows a sawtoothed overall picture and this at once makes clear where the connection lies between the brusque reed movement and a resulting sonority. It's true that not so much the reed defines a certain timbre, but the graph does make clear that an air admittance to the instrument (a reed movement) which has strong peaks will be able to generate in the instrument a soundwave with a rich variety of partials: both these wave motions are kindred enough to mutually sustain each other. Next the form of the tube defines which partials we will actually hear.
Within limits the embouchure can exert some influence over the process. It is clear as well that when the reed motion in playing piano is such, that it delivers less strong peaks into the airflow, this will also generate a tone with fewer partials in the instrument. The other way around it follows that sound will become clearer when we blow harder. After all, blowing harder will mean that the pressure differences that are being generated in the mouthpiece will become greater (keep in mind that while blowing harder the reed will still close: the peaks will become higher, but the lows will remain as deep). At the same time this will make the reed to open over a shorter period of time. This again enhances the sharpness of the peaks in the airflow, which, in turn, enhances formation of even more higher partials. This explains the effect mentioned before why a sound that is more powerful at the same time grows richer in partials.

and further..

It can be shown that the pressure in the mouth in average is a lot higher than that in the instrument and that, contrary to the pulsating pressure in the intrument, the pressure in the bronchi and mouth is also relatively stable. Together with that the reed provides an acoustical resistance of such magnitude, that it is very unlikely that the recipe of vibrations in the musicians bronchial tubes (which probably form a kind of reverted, but srongly damped musical instrument) influence to any notable degree the recipe of partials in his instrument. In other words: unlike in singing the actual form of the musicians mouth and throat does not influence his sonority. That an instrument sounds differently with the one or the other musician is solely caused by another handling of it.

The reed can demonstrated to vibrate in a different fashion in different parts along the vamp: the tip shows a vibration pattern with more partials than the middle part of the vamp, which vibrates more to the fundamental. This corresponds to the well known areas where we can correct a reed for sonority. Thinning down a reed makes it move easier, faster, more brusquely even, thus enhancing the formation of more partials.