After hearing many professionals and students changing air direction indiscriminately and incorrectly for many years, I felt it was time for a pedagogical discussion on this topic. By indiscriminately, I mean changing air directions whenever it is convenient for the player, rather than according to what is musically correct. I hate to burst some bubbles out there, but I'd estimate that at least half of the players are using the bellows incorrectly and engaging in "cutting air."
It's a Wind Instrument
First of all, let's remember that the accordion is a wind instrument. Although most of us play the piano accordion, the mechanics of producing sound on the accordion has no relationship to how you produce sound on the piano or organ. The accordion is just as much a wind instrument as any instrument from the reed or brass family, or even the human voice, for that matter.
The basic problem I've observed is that accordionists often change bellows direction regardless of the note value they happen to be playing at the time. As a simple illustration, suppose you're a singer who's now currently singing a note that has a whole-note value in 4/4 time. Would you think of taking a breath in the middle of the note? Not likely, because you would know that doing so would abruptly terminate the note and add another note that the composer did not originally intend. That is, you would now be singing two half notes instead of one whole note.
Despite the implausibility of such a scenario for a singer, accordionists do this frequently, and not just once or twice, but continually throughout songs. Suppose you're holding a note on the pull direction and you've decided to now push. If you're still holding down a treble or bass note when you change pull to push, you've cut off the air supply to the original note value and have divided it with another note following the first of a different value. For instance, if you're holding a whole note on the pull and change to a push on the fourth beat, you have now played a dotted-half note followed by a quarter note instead of a whole note as it was originally written. Besides changing the original note value in this manner, you've also produced a hiccup by this sudden reversal of motion, which can never sound as smooth as not doing this in the first place. This process of abrupt note termination and resumption cuts the air supply, and is often just called "cutting air."
So how do you avoid the accordion hiccups? The first thing to do is not change direction while you're holding a note, and waiting to change after you've completed the full value of the note. To master directional air changes, the trick is to coordinate three things simultaneously: change to the next treble and bass notes, and change air direction at precisely the same time. The change to a new note or notes and the change of air direction must be instantaneous. If you change direction even a split second before you move to the next note(s), it will sound like a hiccup, and you've engaged in "cutting air."
This trait has undoubtedly existed since people began playing accordions. Often, teachers haven't instilled this important principle to their students, and when some of these students become teachers, this trait is further perpetuated. Once you've been playing this way for many years, it's very difficult, though not impossible, to correct. I've coached an older adult student who exhibited this trait when we first worked together. He had played this way for over 50 years, but after he became cognizant of this and learned the proper technique, he's now nearly "hiccup-free."