The conventional wisdom is that the A Clarinet sounds slightly darker than the B-flat.
First, what is the mechanical difference between the two? From a distance, the two instruments are identical. The A is only slightly longer than the B-flat. The mouthpiece is exactly the same. If both instruments are by the same maker, which is typical for professional players, the interior bore is identical. If these were brass instruments, there would be no difference in the sound whatsoever. However, woodwinds do function slightly different than brass.
The one absolute difference between the two instruments is the availability of the low concert C-sharp of the A Clarinet. This is no small issue, as this note appears throughout the literature.
Here’s where the real issue comes in, and that’s the difference between individual notes on a woodwind instrument. As a bassoonist, I will give an example on my own instrument. An F scale and an F-sharp scale sound fundamentally different. They utilize different mechanics on the instrument. One is simply closing or opening tone/finger holes, while the other is a complex series of both closing and opening tone holes at the same time. Try as a player might, an F-sharp will sound with a slightly different tone color than the F natural. And herein is the big difference between the B-flat and A Clarinets. While a competent clarinetist, or for that manner any instrumentalist, can and should be able to play in any key, certain notes and keys will sound different on different instruments.
The complex acoustics of the clarinet can make this problem larger. The lack of even harmonics in the instrument’s spectrum has a direct correlation to the different registers of the instrument. If a note lies in different registers on the different instruments, it will sound differently tone color wise.
A side by side comparison of single notes between the two instruments will result in the listener not being able to tell the difference between the two. However, music does not consist of single notes in isolation. It is the combination of notes that we desire. Ease of playability is an important part of tone color.
Let’s take for instance Mozart’s Clarinet Concerto. This is the most famous work for the A Clarinet. Could it be played on the B-flat Clarinet at the exact same pitch? With the exception of notes below the B-flat’s range, yes it could. Will it sound the same? No. The simplicity and ease of Mozart’s lines become far more difficult when played in B or E as opposed to C or F (the printed keys of the clarinet part in B-flat and A respectively). In fact, the part in B-flat just looks nasty to play and makes the piece far harder than it needs to be.
There are pieces out there where the composer expects the B-flat and A Clarinets to have different qualities. Strauss’ Elektra is king among these, as it requires a section of 2 B-flat and 2 A Clarinets that are fully independent of each other. Strauss treats these instruments in slightly different manners though the parts have great overlap.
In reading over some of the copious discussion among clarinetists about the differences between the two instruments, it seems that there is a small difference in tone. A trained clarinetist can usually hear the difference between the two. Conductors may not be able to notice the difference, and an untrained audience probably won’t even notice.
What’s the bottom line?
In music that is centered around tonality and keys, it makes sense to use both instruments, as the technique dictated has a direct correlation to the tone color produced. If the low C-sharp is required, then the A Clarinet is a must. In music without a tonal center the choice of instrument is more often than not the B-flat Clarinet as most players will feel more comfortable on what they consider their primary instrument.
Stravinsky’s “Three Pieces for Clarinet” where the player uses both the A and the B-flat Clarinets.