Truncation length plays a role in instrument behaviour. The German acoustician and instrument maker Otto Steinkopf makes quite clear assertions on the subject. I used my baritone as a laboratory and made three different necks with different lengths.
The second one, to start with, is a standard modern baritone neck. This neck remained unchanged and for comparison purposes only. The first neck is longer and the third one is shorter; the bore profiles of all three necks in principle are the same.
The first neck serves two purposes: one is to reduce truncation, and the other is to provide a place for a third register hole, which facilitates top tones.
The third neck serves quite another purpose. I found that baritones in general have a smaller relative truncation than the other saxophones. According to Steinkopf, a larger truncation makes your instrument more open and thus favours a bigger tone and the lower range. The aim of this neck is to explore this possbility.
First purpose: the profile of the first neck is the same as that of the standard neck, except that it is 2 centimetres longer. I did not change the profile, because I did't have to (yet intonation stabilized in the higher ranges) and I only wanted to compare a difference in (truncated) length. It confirmed Steinkopf's claims: the centre of gravity of the tone, so to speak, moves upward and the higher partials are enhanced. (You can easily check this by adding a simple piece of plastic tubing onto the existing neck inside the mouthpiece's shank. Take care that its inner dimensions are correct. Most probably, you will find that any sharpness of the higher range is reduced agreeably, but you will also find a shift in sonority.)
Second purpose: the added register vent makes the baritone to easily play a minor sixth higher on the same fingerings that are normally used for your written A2 up to F3 and obtain F3 up to Db4. An extra mechanism is needed to operate the key. A picture of my baritone shows the way in which it is done. It is of course the instrument makers solution to a problem. Most people will have to rely on the musicians solution and practice and practice...
As stated, the aim of this neck is to obtain as open an entrance to the instrument as possible. The limits are posed by intonation and stabilty. The standard neck has an opening (in my case) of 13.1 millimeter and is a 13% wider than the longest neck. This already makes an appreciable difference. Equipped with the standard neck the instrument produces with the same ease a bigger tone and feels more open and more dynamic than with the first neck. The lower range is somewhat more 'airy' and slightly less briljant. This again conforms Steinkopf's assertions. Wouldn't it be possible to open up the entrance once more with a similar step? The neck would have to get shorter and wider still. Probably the mouthpiece would need to be adapted, too...
This third neck was not an immediate success. I had to work toward a correct bore profile in at least three successive steps. At first a profile was chosen that was simply a shorter version of the second neck, neither wider nor narrower. Truncation was almost 40% bigger in volume than with the standard neck. In this state the neck indeed needed a special mouthpiece, but it proved not to be a success. The tone lacked any power. Moreover, in the upper end of the second register the instrument was unstable. It was dismissed.
Finally I settled on a compromize which is about 1½ centimetre shorter than the standard neck and has an entrance width a 23% wider. This gave an appreciable difference with the second neck: there is more 'air' to the tone and a certain preference for the lower range. Also the instrument seems to be more dynamic. Instability now has gone. It all confirms Otto Steinkopf's assertions that a greater truncation favours the lower range and is helpful in greater dynamics. Don't expect too much though. Within the limits of what is musically viable, the difference is a nuance, but quite an interesting one.