Curiously, she doesn't mention two things that I've always thought as essential to good spins:
1) Spotting - Let the head be the last thing to go and the first thing back. Sometimes spotting alone can increase the number of turns one can complete in a short period of time. Secondly, much less force is required in torque through use of the arms, shoulders and hips when spotting is employed. Also, spotting makes the turn appear much faster to the observer.
2) Stopping - the ability to stop a turn at a predictable time shows good balance and makes the turn appear much faster to the observer. Settling into the hip helps in this regard. Try to think of settling about a half turn ahead of the actual stopping point. More drastically and for added effect, one can extend the arm to the side. For example, if you are spinning to the left, bring your right arm from the center of the body to the outside for a nice effect.
3) I know I said two, but I thought of one more point. On solo turns, try bringing both arms tightly into the body after the second spin, and chances are you'll be able to add one more turn than you were able to do previously.
4) Stance - this makes 4...I'm on a roll. On the step preceding the turn, make sure the feet remain close together. Nothing ruins a good spin like a wide stance.
Edie is a wonderful dancer and I am in no way trying to claim some level of higher knowledge. I just thought these things were worthy of addition and/or discussion.
You made my day. I have been going in circles for over a half century trying to get those turns right. I've tried turning inside on my right foot and on my left, I've tried turning outside on my left and my right, and I've tried turning bare foot, and even on skis, and even tried turning on my knees, but I always ended up on my derriere if you please, but now that I have your advice that I can't refuse, I know my 50 year search for the way to turn is definitely not on my knees. Excuse me Mentor, I have to close now because I have to sneeze.
Have you ever done any excercises where you bend one leg at you straighten the other? This excercise helps with hip motion in Latin-American dancing. Other things that are happening: As you straighten your right leg and bend your left knee, the right hip settles back, right side of the rib cage lengthens and the left side shortens. The result: a forward poise that favors the left side.
If you spin to the right and settle into the right hip, you are bringing your poise forward and left. This opposing actions helps to provide and crisp stop.
Now for the othere reason: it's much easier to explain.
As you settle, you are pushing your heel toward the ground, helping you to stop.