The neck harbours an entire octave of nodes and antinodes. Therefore the bore profile of the neck exerts great influence on intonation and sonority. After all, when a neck succeeds by means of a 'ideal' profile to exert an ideal influence on the pitch of a tone (and its partials), the instrument will be better in tune and sound more resonant as well.
As already mentioned, variations in bore diameter play quite a role in this game. To put both registers in correct relation to one another and the partials at the desired pitch, it proves to be favourable to provide the bore profile of the neck with a certain narrowing as comapred to the 'standard cone'. In some straight sopranos (Selmer Mark6, Keilwerth Toneking, Yanagisawa) this can be seen quite well with the naked eye, but at the same time it remains quite unnoticed in the flowing forms of the curved neck of the other saxophones. Measuring and drawing a bore profile brings help. On the basis of these bore profiles we can estimate which (groups of) notes will be influenced. As said: a narrowing that coincides with a displacement–antinode works as an added resistance and slackens the system: pitch falls. A widening has the opposite effect. And as is well known too: a pressure–antinode for the first partial is at the same spot as a displacement–antinode for the second. This means
certain deviation from the 'standard cone' in the profile of the neck will have opposite effects on pitch in the two registers.
Lo and behold the enormous influence on sonority and intonation that the neck exerts. The neck can really make or break an instrument.
So we have to know were these nodes and antinodes lie. For this we use the method of the 'ideal register hole'. Such holes can in practice easily establish the location of the wave. An ideal register hole is a normal tone hole that is used as a register hole. Unlike the regular very small register holes – which can serve quite a range of notes – such large holes work correctly for only one single note. And because we know the wavelength of that note and the place of the tone hole that was used as a register hole, from the two we can now safely detemine the correct position of the wave inside the instrument.
It must be admitted that this procedure is in principle about a working of the second register only. Yet it is hard to imagine that the second partial of the first register is subject to another law than the first partial of the second register. This will make this way of determining acoustical length valid for both registers.
Now here we come across a very peculiar phenomenon: when we plot the acoustical lengths so obtained for different 'ideal register holes' in a bore profile, we find that they are not in the same place. In the lower range this length more or less coincides with what we might expect on the basis of the truncation of the cone, but higher up in the range of the instrument it turnes out that we find a shift which little by little gets bigger as we go higher. In other words, acoustical length is not firmly anchored in the instrument and there is a certain compression of acoustical length towards the higher ranges.
Now, when we make scales out of these different lengths and enter them into a bore profile (I here give an example for an alto saxophone), then the compression of the acoustical length toward the top of the cone quickly becomes clear. The drawn line belongs to the main cone of the instrument and intersects the horizontal axis in the zero of SCALE A. This scale determines the theoretical length of the main cone. The other scales are based upon the working of 'ideal register holes' according to the method described. SCALE B shows the postion of the acoustical length as given by a couple of ideal register holes for tones of the right hand; SCALE C, which gives the scale for the upper register hole with the pip removed, shows an increasing shift toward the right.
In our example three profiles of different necks are plotted together in one sheet. It it clear at once that two of them (the Selmer and the Yanagisawa) are reasonably akin. These necks are interchangeable upto a certain extend, but will each give the instrument an intonation character of their own. The Martin–neck shows quite another profile, especially in the range from G through A# and it can be expected that this neck cannot be exchanged with the other two with any degree of succes. It belongs to an instrument of another type of build. In this respect, necks and their different profiles also show something of the difference between American saxophones and the French tradition.
The truncation of the cone is around the length of F3, F#3. This is true for both the alto and the tenor saxophone. Sopranos once had a truncation around the length of Eb3. This originally was the upper limit of the range of a soprano and a smaller truncation therefore was not necessary. Recently, sopranos got a little longer and their truncation is now relatively the same as for the alto and the tenor.
The bariton is a somewhat different story. The baritone shows the compression of acoustical length for the tones of the left hand, which is so evident in the smaller saxophones, to a much lesser degree. Consequently the bore profile of the baritone neck shows the characteristical narrowing to a much lesser degree. Also, the bartione has a smaller truncation which lies around the length of Ab3. Why that is so, is not directly clear but conventions about the build of the instrument and its mouthpiece make that we cannot change that overnight.
Another strange phenomenon that can be explained through the compression of the acoustical length is the gradual rise in pitch above A2 and the typical behaviour of the saxophone to sound an F3 in the well known X,2 fingering. Rather you wouldn't expect a minor sixth on A (which is the basic fingering, after all) but a fifth, which still is the number next in the series of upper partials. The compression of acoustical length makes the instrument sound a semitone higher. Note, that when you perform the same trick on, say, Eb2 or E2 with the additional opening of key 13 (Ta or side Bb) you do get a fifth (Bb2 or B2).