1. Ground Hog

From the recording Ground Hog

Teach Music Theory and Physics

All the tones the mouthbow makes are vibrating on the string at the same time. We just change the shape of our mouths, like we do in whistling, to amplify certain ones.
Groundhog demonstrates the tones that the string makes by itself, the tones of a bugle call.

With a little measuring, marking and plucking, the mouthbow demonstrates how the physics of vibrating strings produce the notes of the major scale.

When the mouthbow is plucked we tend to hear it as one tone, but that one string is vibrating in its whole length as well as in thirds, and quarters and halves and all other divisions to some extent .

These other vibrations are called Partials or harmonics and they are not very loud. They are sine waves that all vibrate along the length of the string at the same time. 

It's harder to find, but there is a second octave at ¼  of the string length and 4 times the number of vibrations as the whole string. I use this one to make the 4th and 6th tones of the major scale.

You can find these nodes and overtones by measuring the string length and using a little math to figure out where they should be, or you can find them by ear. You should try both!

These waves are sine waves, so if we use the 5th note of the scale for example. The string is vibrating in three pieces to make the 5th note of the scale, but four places on the string aren't moving at all....the two ends, and the 2 "nodes" of vibration, one third of  the way in.

I wrap the string around the end of the mouthbow because that puts the node right in your mouth... or right on the end of the string.... you know where it is. If you move your mouth up and down the bow as you play it, you find there are other hot spots along the wood... a good one is found exactly in the middle.

You can also play the bow with the string in your mouth... don't touch the string, just hold it between your lips with your mouth slightly open and see what happens. You should get a good loud tone this way in the center of the string...

If the string is touched lightly in the right place at one third of it length, the string will only be able to vibrate in thirds and smaller sections and not in its whole length or any of its even divisions. Everything else is "damped" out. This means you get the fifth note of the scale and also the 2nd and 7th. Being able to isolate the fifth note of the scale from the vibrations of the whole string keeps the overtones, notes 2 and 7 from clashing with the tone of the whole string.. the first note of the scale is most dissonant with 2 and 7.

I use the node for the second octave ¼ of the string length.. to generate the 4th and 6th notes of the scale. The node for the fifth 1/3 of the string length also gives 2nd and 7th notes of the major scale.
Don’t be put off by having to make a mouthbow like the fancy one in the directions.
You can use a hunting bow to demonstrate the same thing but as an individual or group project you can also make a mouthbow from a stick and fishing line… I prefer 30-40 pound test monofilament.... but have used kite string and even dental floss.
Make a bow from a yardstick... it simplifies measurements.... Measuring makes it a science project.
1. listen first then measure … pluck the string with one hand while you slowly move along the string with the index finger of your other hand .... You already know they will be about ¼, ½, 1/3 of the string length but find them first by ear, then measure
2. measure first, then pluck the string. Feel around and listen to see if the node is where its supposed to be.
3. Notice that one half the string length gives an octave at twice the number of vibrations.. and one quarter of the string length gives a second octave at twice the number of vibrations .