As a musician I can’t hear any difference between the two notes, but I’ve heard others (sorry, no cite) say there’s a subtile difference in intonation and “feeling” between these two. (Again,on a clarinet)
Comments?
Somebody more classically trained will no doubt fill you in, but I believe that’s called enharmonic equivalence. Here is the wiki entry.
Here’s a video illustrating expressive intonation, on the violin. This involves deviating away from equal temperament, the system of twelve equal steps per octave in which sharps and flats have exact enharmonic equivalents.
One can alter the intonation on most wind instruments by changing pressure and embouchure. If you’re playing in something like F# major, you may want to intone the G# such that it’s closer to its pythagorean ratio to F# instead of the equal-tempered frequency. That will be a very slightly higher pitch than a pythagorean A-flat; in equal temperament they are enharmonically equivalent as Birdmonster points out.
I say all this knowing absolutely nothing about clarinets, BTW. Maybe there is a different fingering for use in keys with A-flat instead of G-sharp, which produces the same frequency but a slightly different timbre.
As friedo says, on wind instruments, clarinet in particular, there are often many different fingerings to achieve the same note. However, not all the fingerings produce exactly the same pitch, as they don’t all open/close exactly the same holes on the instrument.
So, different fingerings of G# might be slightly sharper or flatter than each other, and a musician might choose different fingerings based on that in some situations. These sorts of multiple fingerings usually occur in the higher registers of an instrument.
However, the absolute statement ‘Ab and G# sound different on a clarinet’ is false, or at least lacking in enough detail to make itself true. Different fingerings (or intonation changes using embochure) are at the discretion of the musician, and are tools available to almost all woodwind players.
The distinction was lost on me.
Listen carefully to the last four notes of each version (Bb - C - Bb - A), for how the B flats are flatter in the second playing.
It would have been a better demo if it was played without so much vibrato. It was very difficult for me to hear as well, and I’m usually pretty good at that stuff.
As a Clarinetist, maybe I can elucidate some part of this mystery.
I’ve been playing for almost 10 years, but I’m nothing close to a professional. Perhaps consequently, I’ve never heard any of my colleagues mention a difference between Ab and G#, although some of the reasoning for the possible difference mentioned upthread seem reasonable.
There are a total of 3 G#'s that a non-professional is likely to encounter with some regularity: the one below the staff, the one in the middle of the staff, and the one above the staff. So far as I know, there is only one “standard” fingering for each. That is to say, there may very well be other ways of achieving these frequencies, but the fingerings are ones you’d have to look up in a specialty fingering chart. In other words, most players (as far as I know) are only taught one fingering for each of these G#'s, whereas they are taught multiple fingerings for several other notes.
If you’re playing in a key like A-flat or E-flat, do you use the same fingering to achieve A-flat as you would for G#?
I am also a clarinetist. I am not a professional by any means, but when I was younger I (somewhat) mastered many of the usual clarinet repertory works. I probably would not have succeeded if I had tried to go pro, but I wasn’t bad and I played a lot.
In general, the answer to your question is yes. Where alternative fingerings exist, they are a convenience to avoid awkwardness and to enable swift and fluid play. The notes you have to play before and after the note in question dictate a possible alternate fingering.
As an aside, middle Ab/G# has some very unusual properties because the hole is so close to the mouthpiece. Its quality can vary a lot depending on the instrument, reed, and the player.
Just wanted to chime in saying that I agree with Maeglin.
I suppose the important question, for a non-string player (unlike the intended audience of that clip), is not what the difference is, but rather one performance has a different effect from the other.
Perhaps a little googling on “equal temperament” would be enlightening.
The fact that modern tempered tunings, unlike medieval tunings, equate G sharp with A flat makes this chart possible.
In some instruments (I’m not a clarinetist, so I can’t say much about that), there are alternate fingerings for the same (tempered) pitch, derived from different harmonics/overtones (another thing you might google). Some of these alternate fingerings may produce pitches slightly different from the others, but the player is going to alter that pitch slightly using other means, like lip pressure.
Inevitably, someone will say that violins play in a pure scale, not a tempered one, but I call bullshit on that one. If that were true, the clash with the rest of the orchestra, especially instruments like keyboards that cannot easily bend pitches, would be awful.
Well, on any non-fretted string instrument you can play pretty much any tuning you like. You just have to put your fingers in the right spot.
Well…Duh. Maybe I should have said, “Violinists play…” instead of “Violins…”?
Nobody’s going to say they play a ‘pure’ scale, but they can and do deviate away from equal temperament, such as in the example I gave, without the audience running for the doors.
Talking to a proffesional clarinetist he told me that he used the same fingering, however he said that if he was ascending with sharps the tone would be a tad high, but if he was descending with flat the note would be low.
He said the difference was impercetible in normal cases, but real if you had an electronic device.
Magelin
You are quiet correct. Adjustment of the embouchure is extremely important in symphony work. I’ve often played second clarinet and had to adjust my intonation to match not only the first chair clarinet player, but to other instruments also. It seemed to me that if I didn’t keep my ears open to everything I would be out of tune. I never was.
G# I would tighten my chops to barely raise the tone. A flat, depending on the piece, I would ever so slightly relax my lips. This is all depending on the music and general feeling of the piece being played.
Also, Magdelin, If you would have taken up Bass Clarinet, Contra Base Clarinet and the saxophones, (especially baritone sax) you would have probably gotten a lot of work! (they are in demand). 
Thanks All, for your responses!
I actually did play alto clarinet, bass clarinet, tenor sax, and even soprano sax for awhile. The sax was fun on the weekends, but I was pretty comitted to the clarinet until my lips practically fell off. I did play a fair amount of A clarinet by the end, which I greatly enjoyed.