It's been about 2 months give or take since I've properly begun flute lessons - 3 in total so far.One thing that stands out to me is how different the embouchures are between the sax and flute.
With the sax, is more about how I deliver the air against the mouthpiece by shaping my tongue, as well as the tightness of the sides of the lips. Changing the tone from piercing to a more mellow sound is again dependent on the airflow shaped by my tongue, and with subtoning, dropping the jaw.
Comparatively, the flute focuses more on the actual lips, in controlling the stream of air being blown against the cutting edge of the headjoint. Using the lips themselves to focus the airstream seems to be key here, and the more I experiment with the lips and placement of the joint, the more resonant a sound I get. The lips going dry here is a big issue though.
As either embouchures don't seem to get in the way of each other in terms of shape, I can see improvements on both instruments without seemingly affecting either in a negative way.
In practice terms, armed with this knowledge, I can focus my effects into getting a good strong focused airflow. Being the flute is my secondary instrument, I only dabble with it a few hours a week - like maybe giving it a quick blow whilst I fry some eggs or waiting for tea to brew.
The flute also exposes me to a different side of music - classical. This was unplanned, as my main requirement was - I have flute, find teacher that is nearby. My teacher is from a pure classical (french, iirc) school, and is not at all into playing jazz. In retrospective, I think being exposed to different viewpoints would probably help expand my perspectives. I'm personally not that interested in classical music, but just a few minutes ago, playing Bach's Minuet in G just lit up my heart. A simple melody (obviously, I butchered it) - but the delivery of emotion is so strong.
Down the road, I intend to take the flute down the celtic side, which is why I got it in the first place. Celtic music just resides in another realm, and I wish I had the concentration and time to study that area of music as well. Perhaps down the road.
I leave you with a rendition of Yasunori Mitsuda's Time Scar played on Flute, accompanied by guitar. It is a piece I hope to be able to play a few years down the road.