Flattening the second octave

[MervynD]

Mostly Off Topic:
Paddler, you said you're dealing with severe Dupuytren's contracture. I have it in both hands, affecting two fingers on each, had needle treatment followed by surgery with complications on the left around 10 years ago (I'm 69 now). After recovering I rearranged the songs I play on guitar to avoid little-finger stretches.
A year ago I picked up my wooden flute again and found my daily guitar practice had stretched my fingers enough to reach all six holes with a little warming up. I then bought a used 6-key Lehart flute, which I play alone with great pleasure, mostly airs, improvisation, and slowed-down dance tunes. The flute tips and discussion on this forum have been a great help as I work on my embouchure and fingering technique.
My little fingers can't reach keys, so I only use C, short F, and Bb keys with a rare R1 stretch for a G#. Eventually, I expect R3 will worsen and further limit what I can do but my voice is now much better so, one way or another, there's a way to keep playing music. Feel free to message me if you have questions about Dupuytren's.

[skap]

We're talking about the bottom lip, right? That's the only lip that's "covering" the hole, if by "covering" you mean actually obscuring it. And if I move it forward so it's covering 1/4 of the hole, everything flattens (particularly the first octave) and it has a really breathy, quiet sound with a rather bad tone. I can only get it to sound good if my bottom lip is barely covering the hole at all.

I think this "covering" should be seen as a "lid on a hinge" covering the hole (where the lid is the lips), not a lid that slides along the hole. So it's difficult to assign a value to it (be it in fractions or mm). The edge of the embouchure hole should align with the edge of the lower lip to start with, this is the "hinge" (see this video for exemple: https://www.youtube.com/watch?v=Te_22KWgkWI). So when you say you are barely covering the hole at all, you probably got it right. From there you should be able to flatten the notes by changing the angle between the lips and the embouchure hole (consequently you will blow more into the hole than across), but your lip should not slide on the flute, there is only a rolling movement, and it is not huge.

[chrismontez]

Sometimes people blow harder as they play the 2nd octave, which sharpens the notes. The blowing pressure should remain the same as in the lower octave, but your embouchure needs to become smaller to increase the speed of the air. Air speed needs to get faster as you go higher but you don't blow harder.