I notice guys like Shaw or Goodman or even yourself seem to hold the clarinet facing outward, almost like you're playing a recorder, yet all the beginner clarinet method (that I'm currently following) want a player to point more towards the knee or lap. It's not a matter of tilting your head back, or you'd all be looking at the ceiling...so is it a different embouchure or mouthpieces with different beak angles? Just curious.
Thanks for the question, Mike!
The 'proper' angle at which to hold a clarinet is a much debated topic. I'm tempted to give you the short answer that Goodman, Shaw, and I are correct and everyone else is wrong. I'd be joking, of course, but unfortunately that's about the level of discussion many teachers or methods will give you, in a nutshell, though such dogma was more common a generation or two ago than it is today.
The fact is that a player's musical goals, equipment, dental structure, and other concerns all factor into the right angle to hold the clarinet. For instance, the angle Benny used changed throughout his career, especially after his years of study with Reginald Kell, when he took on a double lip embouchure and began focusing more intently upon classical performance.
Artie Shaw's embouchure was unorthodox, with a scowling muscular formation. Whether this was a legacy of his saxophone embouchure, I don't know (among the great clarinetists of the 20th century, he was one of the few who mastered saxophone before switching to clarinet, rather than the other way around). Because of this, he had a pretty unique sound concept, in many ways flipping emphasis from the chalumeau to the altissimo register.
My embouchure, compared to either of theirs, is a rather natural, simple, relaxed one. The muscles have developed well over the years, but there is far less strain to mine than Shaw's, and while I played double lip for a time (just to see what it would do for me), pretty quickly reverted to a more comfortable sing lip.
Beyond the discussion of embouchure, both Shaw and Goodman changed their equipment throughout their careers. In the 1930s and '40s both of them played on large, relatively straight bored Selmers. Shaw was also known to record and play on large bore Conns, but though he endorsed them, later admitted he preferred the Selmers for actual performance. His last recordings were made using a Buffet--but I'm not sure if it was an R13 (the revolutionary polycyclindrical model that changed clarinet culture) or a pre-R13.
Benny played Selmers on most of the famous recordings before 1950, but switched to Boosey & Hawkes for a time and then permanently to the Buffet R13.
I mention this because the angle he needed to play might have been decisively effected by the equipment change. In my own experience (and that of other pros I've talked to), large straight bores are better played while held out farther from the body--one tends to blow straight down the instrument more. If you look at pictures of clarinetists playing large bore German instruments even to this day, you might note they tend to hold the instrument out farther, but the same principle holds for vintage French made instruments (such as the Selmer Centered Tones I play). Contemporary instruments (whether they are Buffet, Selmer, Yamaha) tend to follow the basic reverse conical or polycylindrical bore that took over the market in the '50 and '60s, and tend for reasons of intonation to demand a different blowing angle.
Mouthpieces also effect things, but generally not beak shape (unless you're using something like this Morgan from the '80s.)
Most importantly, the player's dental structure and body play a decisive role. Clarinetists with overbites tend to hold the clarinet in more tightly--but students should be careful not to think that because some great player or teacher does so, they ought to as well. Your own dental structure will impact the angle more than any pedagogy.
Trail and error, experimentation with different angles and equipment: these are the best ways to find out what will work for you. Comfort, flexibility, ease of projection, ability to properly balance the instrument, and ability to properly articulate: these are the ways to determine whether an angle is correct.
Thanks again for the question, Mike, and KEEP SWINGING!