Am I observing subharmonics using this method on guitar?

Question

Are we hearing a subharmonic? Friends and I hear a note that is lower than my lowest unfretted string on my standard acoustic guitar with standard tuning when I use the following very simple, easy method, pictured here:

As seen in the picture, a guitar pick is placed on top of the bass E string and under the next string (A string) in a manner similar to the way folks usually store a pick near the top of the fingerboard. I wedge the pick in between the E and A strings so that the edge of the pick rests on the fingerboard and the A string pushes down on the pick. The pick pushes down on the E string in this manner. (If the guitar action is too high to get the wedge affect, a piece of light cardboard can be placed under the edge of the pick that contacts the fingerboard, in order to shim it.) Then the E string is gently stroked or plucked with my finger. We hear a very low note that is much lower than the E unfretted string would make.

The resultant note is constant frequency, with unremarkable amplitude falloff in a fraction of a second or so. It does not warble or "beat", as far as we can tell. It sounds an octave or so lower than the bass E string.

I am wondering and investigating if it is the brain filling in the "missing fundamental," which is a known phenomenon of human hearing. I cannot find an example of a mechanical system that will produce subharmonics.

Answer 1

The actual tone you hear is lower, because the pick adds mass to the strings. When wedged as shown in the picture, the pick and two strings vibrate together. The frequency is determined by the tension and mass of the strings, the mass of the pick and additional rotational inertia because the pick rotates around its contact point with the fretboard.

On my electric guitar I get almost exact octave drop with a one millimeter Ultex pick, lighter picks produce smaller changes.

Regarding the point about half node presented in the other answer, I believe the pick stays connected to the fretboard and strings all the time. If you pluck the string hard enough that the pick loses contact with one of the parts, you get a buzzing sound not unlike fret buzz and the pick does not stay in place.

Edit: I had a guitar and audio interface at hand, so I had to see what really happens. It turned out that the base frequency drops from E2 to D#2, but with that special pick the first harmonic is much reduced, which makes the usually weak base frequency more audible. This was with the pick at 16th fret, with the pick at 12th fret the pick stops the base frequency and 1st harmonic is stronger.

Answer 2

Based on the answers to my question about subharmonics, I think yes, this is a subharmonic. As ojs's answer suggests, you are creating a compound vibrating system out of the two strings and the pick. (Do be scared, so far this is just fancy words describing everything that's already been said)

Think about the whipping around of a string or rope or hose that you've played with in childhood. Now slow down the movie. Sometimes parts of the string are moving up while other parts are moving down and always with some amount of spin around the axis.

The pick wedged against the string creates an artificial node in the string's vibration, but also in a way it's making only half a node because the string can lift off the pick a tiny amount since there is no obstruction in that direction.

The pick absorbs some energy from the pressure and impact of the first string and sets about vibrating, too.

Some of the vibration from the pick is sympathetically transferred to the second string, giving rise to a resonant vibration.

The two (or three) different parts vibrating can easily give rise to the intermodulation effect where difference pitches (aka Tartini tones) are observed.

But I think, sadly the real conundrum for most guitar players will be: "If my pick is wedged in like that, how on earth am I gonna pick the string?" :)