Results
It is obvious that a scale cannot be produced on a saxophone using a small speaker. The reason of course is that the reed interacts with the vibrations of the air column inside the saxophone whose length determines the speed and therefore the frequency of the reed's vibrations on each note. The small speaker on the other hand cannot interact with the aircolumn inside the tube and can only play the frequency that is sent to it by its electronic source.
CONVERSATIONS WITH SANTY
THE FIRST MEETING BETWEEN A STUDENT AND SANTY
This is a theramin. See the picture. It happened to be the only electronic instrument at that time [ in the 1930’s]. And this young college prof had one and like I told you, he said, he complemented me on my saxophone playing, but not very favorably. He said that you are not getting the right sound. Come over to my lab. I’ll see if I can help you. And he asked me if I had a mouthpiece that I didn’t care about. [We] cut this part of it off and just used the shank and [then we] built a little box with a speaker in it. And this thing had a control [rod to raise and lower the notes]. ...The closer ... [your hand] got to this rod, the higher the pitch. I saw one [recently] and it really made a comedy of it on television and I was very surprised that there was one still in existence. And this guy was doing like this and making a real wild vibrato out of it. And the sound it made, it sounded like a musical saw . You ever hear a musical saw? [It] sounded like a musical saw.
Anyway he built this speaker and attached it to the saxophone. And turned this thing on and it proved beyond a question of a doubt that you don’t have to have air go into that saxophone. The band directors say fill it up. Blow it full of air. I have heard that a thousand times. Well it’s not a vacuum. It’s already full of air. The object is to set the column of air in motion that’s already in the instrument. So when we set this thing on 880 vibrations a second you could play the upper register and lower register [with a] nice sound all over the horn and nobody blowing it. The only human element was me fingering ... When you got it below 880 [vibrations/second] , the lower register played in tune, but the octave key wouldn’t work. ... You get it above 880 [vibrations/second], the upper register played fine and you released the octave key and it stayed in [tune] in the upper register. Only when it would work in both registers [is] when you got it on 880 [vibrations/second] ... right on that note.
Student: And that control panel pictured, what happens there is that you are setting it at 880 ?
Santy: Yes.
Student: You are bypassing that little rod ... you are playing just one tone; is it a low register A?
Santy: Yes, you’re right. Now then what happens is that when you put a finger down to play a G instantly and automatically the vibrations in the saxophone adjust themselves to the vibrations of the reed.
Fact and Fallacy About Mouthpiece Pitch
The following is an excerpt from a pamphlet put out by the Runyon Company entitled "Conversations With Santy
To test the theory that a saxophone can actually be played with a small speaker playing A = 880 the pictured apparatus was constructed to try to replicate the results described in Santy's famous story. The tone was generated from a computer using a feature of the Cool Edit 2000 program and the results were recorded using the same software. The linked sound file tells the story.
- The first tone heard is the earphone "speaker alone".
- The second tone heard is the speaker attached to the neck which amplifies the sound somewhat.
- The third tone is with the neck attached to the saxophone which amplifies the sound even more.
- The last sounds on the recording are created by fingering a scale opening and closing the saxophone's keys.

Conclusion
Playing with the most effective mouthpiece pitch on woodwinds is indeed a valid performance concept and an incredibly useful teaching tool for which woodwind players have the great Santy Runyon to thank since he was the first to come up with the idea. It will probably remain part of the folk lore about this wonderful old gentleman as to where and why the tale of the "saxophone playing theramin came into being. It may have been to get his idea of mouthpiece pitch across to those skeptics of his day. It is highly unlikely that we will ever know for sure or that it even matters.
* no quality mouthpieces were harmed in the making of this device