In his first patent of 1846 Sax claims that his instruments are build according to a 'cône parabolique', a parabolic cone bore. It is uncertain what he precisely meant by that, because he himself gives neither details nor indication.

In his first patent Sax presents his new instruments, which, other than stringed instruments, will be able to stand firm in open air, yet at the same time will produce an agreeable sound. In the patent there is only one paragraph which describes the instrument in which he poses (in full):

Struck by the various inconveniences, I have been searching for a means to amend these by creating an instrument which, by the very character of its voice, approaches the stringed instruments, but which possesses much more power and intensity than these. This instrument is the saxophone. More than any other [instrument] the saxophone is susceptible to modify its tone in order to give it the mentioned qualities and to conserve a perfect evenness over its entire range: I made them out of copper and in the shape of a parabolic cone. For embouchure, the saxophone has a mouthpiece with a single reed, the interior of which is expressly bell-shaped and that contracts toward the part where it adapts to the body of the instrument.

The parabolic cone became subject of many speculations. Measuring the original instruments is the regal road to possibly clarify what was meant. As for the mouthpieces, two originals by Sax – one for soprano and one for alto – are documented in the page on mouthpieces, in the MEASUREments section.

bore profiles

Measurements were done on four Adolphe Sax instruments from the pre-1866 period out of the collection of historical instruments of Leo van Oostrom. At the time of the measurements all instruments were in good condition and free of damage. It appeared that they all were more or less out of round, though. Diameters were, whenever possible, taken in more than one direction and averaged. In the baritone circumference was taken and recalculated to a diameter. From top to bottom and in relative size:

  • soprano saxophone 19575 in Bb from 1859
  • alto saxophone 24495 in Eb from 1861
  • tenor saxophone 15676 in Bb from 1856
  • baritone saxophone 22500 in Eb from 1860

The four instruments are 'stacked' in a graph, each time placing the zero of the vertical scale a step upward and were drawn on a percentage scale. 100% length and width were each time taken at the centre of tone hole no. 6 (third finger right hand). The advantage of such a scale is that it becomes easy to compare the cone shapes of instruments which differ greatly in size; the disadvantage is that it appears as if instruments all four have the same conicity, which is not true. The broken lines give the theoretical instrument cones.

profiles of four instruments by Adolphe Sax sr. toon profielen


We try to define the parabolic cone bore on the basis of these measurements. When we take Sax's soprano as an example, it appears that the parabolic cone is one which over its entire length has a long curvature toward the outside or, to be more exact, it is composed of three successive cones, each next cone with a smaller conicity, which together constitute this long curvature. It thereby clearly sets itself apart from the straight cone. For the alto too this holds true, though a bit less clear-cut, but then it becomes more troublesome. Not only the extend to which the cone bulges out lessens when instruments get bigger, but there are more and more details that do not obey this curvature. The wide bell, for instance, and in the tenor we find a form at the entrance of the neck that is quite contrary to the parabolic cone. Sax by all means did what he deemed necessary in order to make his instruments work and he did not in the first place slavishly obey his own definition. Maybe as far as pertaining to patent law, there might have been an advantage as well.

Apart from that, it is understandable that Sax mentions mouthpiece proportions and the cone shape in one and the same paragraph, as both aspects of his design are related to intonation. When you simply attach a bass clarinet's mouthpiece on to an ophicleid (as the story goes) the result will be that the instrument plays annoyingly sharp in the upper half of the second register. Although the oboe and the bassoon in principle face the same problems, they are much narrower and being equipped with a double reed, the player can more or less successfully handle the problems with his embouchure (and still, proportions of the piece of tubing onto which the reed is attached are extremely delicate). Not so in the wider saxophone. Sax must have found out that a constriction of the bore in the upper end of the cone together with a wide mouthpiece cavity solved his problem sufficiently to turn his invention into an playable musical instrument. Both aspects were at the time new developments in the field of instrument making an as such open to patent.

For the rest, it must be stressed that the term 'parabolic' is not to be understood in the strict mathematical sense of the word. It seems to have been fashionable in the 19th century to make use of this kind of terminology to express oneself, as we nowadays like to refer to computers for coming to grip with all kinds of aspects of the world, or like in the middle ages religion provided a vocabulary. Rather this 'parabolic' is understood in the same way as in linguistics we speak of parables in the sense of similarity, or of 'hyperboles', a figure of speech of exaggeration. Sax meant a shape which at the same time widens yet it widens at an (irregularly) diminishing rate and called it 'parabolic'.


Anyway, and this cannot be stressed enough, all these subtleties in bore shape are hardly visible to the naked eye and so it is no great wonder that people have been mislead by Sax's mysterious description. Especially Jaap Kool spread a notion about what he thought the parabolic cone would be. Kool based his idea on a rather naive observation on an instrument made by Sax's son, but he nonetheless did not hesitate to come to far-reaching conclusions and in this manner rather vitiated the truth. Also, he seemed not to have been acquainted with Sax's statements in his 1866 patent (about which more is to follow on the next page..) and he therefore missed a crucial understanding. Nonetheless, Kool's views have been influential, if only because there was no other range of thought available.