I just picked up a YRS-24B Baroque Soprano recorder, and am teaching myself to play C scales. First octave is no problem. On the higher octave, I can get as far as G. But when I try to play ‘A’, I’m getting a lower tone, rather than a higher one.
I suspect that you are leaving the thumb hole too far open. The term “half hole” is somewhat of a misnomer. The opening can vary in size from somewhat open to the tiniest sliver on that second octave A that you are having problems with. So experiment with the size of the thumb hole opening. All the best.
I agree, as well. As you go higher, you’ll need to narrow the gap you’re not covering with the thumb (experiment a bit to get the right thumb placement). I found it easier after I cut and filed my left thumbnail very, very short. In addition to increasing your breath pressure, you might experiment with narrowing/focusing the airstream, as well (i.e., colder/faster air as you go higher). I’ve gradually improved at hitting the notes in the second register. I can go up to a high E, currently. Still working on doing that consistently, though.