I agree that it sounds very similar to a Theremin but I think that a Theremin is much more difficult to master. I call the musical a Theremin unplugged or the acoustic Theremin.

As others have suggested place the handle of the saw loosely between your thighs just back from your knees a little.

The tip of the blade can be gripped with a couple of fingers under and the thumb on top and about two inches from the end. The pressure on this grip should not be overly applied as it will cause excess stress on the thumb and fingers. Simply grip it with a slight pressure in this manner. This grip is what makes the blade able to create musical tones.

I'm right handed and I hold the tip of my saw with my left hand. I bow with my right hand.

To create vibrato or that warble that many use to sustain notes while playing, I lift the heel of my right foot up off the ground a couple of inches, while the ball and toes of my right foot are kept fixed on the ground. I then bounce my foot gently. I try to use this idea with care, so as not to over do it.

One point that some of the previous posts did not mention is the use of rosin for your bow hair. I use a brand of rosin called Pops. It's meant to be used by upright bass players. It's very sticky but I find that it works well for me. I find violin rosin far too powdery. When I tried using it, I found that my bow slips instead of gripping the blade as I play.

Yes, there are saws that are made especially for playing music but you can also play regular wood cutting saw blades as well. It just becomes a challenge to find one that will offer you the best sound possibilities. If you have or run across any Sandvik brand saws you'll find them to be among the best for offering musical qualities for playing. Sandvik also makes a 30 inch long musical saw called the Stradivarius. They sell them for about $80 USD. But any of the regular Sandvik blades will give you lots of music. Even their bottom of the line saws with the plastic handles. I think that they're one of the best musical saws available. It's the Swedish steel that makes them such good candidates for music.

Once your bow has rosin on it and you are gripping the tip properly and while the blade is nearly flat or with a very slight bend you'll find that the first note that you can make clearly is located about four or five inches up from the handle. Start bowing there. Then, while maintaining the tip grip, the more you bend the main part of the blade, the higher up the blade you have to bow. This is the part that takes practice.

I started out playing simple melodies and gradually increased my level of difficulty until now I can easily play by ear along with many ballads and slow to medium paced songs. I still have some difficulty with fast paced music. I don't really think that the saw is well suited for such. After all, I am flexing razor sharp spring steel betwixt my knees as I play. The pointy parts are mere millimeters away from body parts that I hold both near and dear as I play. One slip of my clammy grip and...well, many body parts don't grow back. You know what I mean?

Have fun!