Brandon Skinner and Dr. Tim Leishman, Physics and Astronomy

Introduction

The idea for this project came at a time when I was learning many new things about sound, electronics, and electromagnetic theory. In fact, it was the combination of these ideas that lead me to question the functioning of magnetic guitar pickups and to wonder if there was a more complete way to represent the sound of a vibrating string. Actually, sound is a bit of a misnomer here because with a magnetic transducer, we are measuring the physical motion of the string and not the acoustic waves it also happens to cause. With guitar pickups and other magnetic transducers, we measure the motion of the string by looking at the voltage induced in a coil of wire as a magnetized string is moved in its vicinity. The induced voltage is proportional to the change in magnetic flux from the string in accordance with Lenz’s law.

I wondered what the effect of different types of string motion would have on the voltage output, and if it would be beneficial to try and capture more about the motion of the string by using two pickups instead of just one and by mounting them orthogonally to each other. By this I hoped to be able to capture all the harmonics that the string/pickup system could produce at any instant in time.

There are many factors to consider when talking about the harmonics produced by a system like this. The string itself will vibrate with many harmonics, and the pickups will also add some harmonics depending on how the string is moving in relation to the pickup. Both of these effects are important to the overall sound of the instrument, and it is difficult to determine which effect is contributing which harmonic and how much. So the problem is not simple or trivial, and pickup design may have in reality become more of an art realized through trial and error than an academic discipline of research.

Background

2.1 Electromagnetic Pickups
Although the exact origin of the magnetic transducer is a bit unclear, it seems that the first commercial production of the technology was realized by Rickenbacker Guitars. [2] From there, Leo Fender’s classic single coil pickup designs began to appear, and magnetic pickup technology has not changed much since. In fact, many of the pickups now in production are merely faithful replications of those early “vintage” designs. There have been a few innovations in pickup technology over the years, however. The humbucker, invented by Seth Lover, is a dual-coil pickup which takes advantage of the extra coil to cancel noise signals while retaining the string’s signal. Also, “active” pickups have been developed which incorporate preamps and equalizers into the pickup itself. The basic design of these pickups still relies on the magnet/string/coil interaction in basically the same way.

The basic structure of a magnetic pickup consists of a magnet and a coil of fine wire. Different layouts and schemes are used but the basic principle is to create a magnetic field around the ferromagnetic string. The perturbations in the magnetic field due to the vibrating of the string induce a current in the coil which is conveniently placed nearby. A pickup is generally a passive device, relying on Lenz’s law to generate the electrical signal with no outside power source required.

There are many sources of non-linearity in the traditional magnetic pickup design. Many of these nonlinearities produce sounds which appeal to the listener and so are not really problematic in that sense. When studying the magnetic pickup, however, these things need to be dealt with.

2.2 Recent Research
The idea of using multiple pickups to capture vibration energy in both planes is not new. It was patented by Dennis Chobanian in 1980[?]. More recently, research was conducted at Berkeley’s CNMAT program by Adrian Freed[?]. They came up with a design for a pickup array which was mounted flush (thus more ergonomic for actual use in a guitar) but had slightly tilted magnetic pole pieces. The pole pieces were not orthogonal to each other, but they calculated the orthogonal signals by taking the sum and difference of the two pickups.

3 Research Methods

3.1 Monochord
In order to measure string vibrations we designed and built a monochord. Due to the geometry of the 2-dimensional pickup array, a single string instrument made the most sense. We also wanted to design something that could be used for many other purposes after our research was finished. For that reason we came up with a “modular” design with all bridges, pickup mounts and string tuners movable along a sliding base. This would allow one to simulate many different stringed instruments from mandolins to full scale basses, and everything in between. We also vastly over-engineered the thing in anticipation that someone might want to stretch a piano string across it requiring much stiffness in the base to deal with that kind of tension. For that reason we chose a “T” shaped cross-section and used ½” aluminum sheet for the base.

3.2 Pickup Design
For the design of the test pickups we gathered data from several sources about the type of coil wire and magnets commonly used in well-known designs. We also gathered data about the other construction materials and the number of turns of wire used in the coil and the expected impedance of the coil.

We settled on a design that basically referenced the pickups from a Fender Stratocaster guitar except that we designed it for a single string, using only one pole piece as opposed to six for a guitar. We used 42 gauge insulated copper wire and wound the pickups up to around 8750 rotations, in accordance with the Fender spec[]. The magnetic pole pieces we used measured 0.195″ diameter x 0.671″ long. We cut circular end pieces from a sheet of vulcanized black fiberboard to hold the coil around the pole piece. These end pieces were then pressed onto the pole piece using an arbor press. The pickups were then wound using a drill press, by clamping one end of the pole piece in the chuck and rotating the pickup as we fed the wire onto it. In order to count the number of turns, we set the drill to a certain rpm and then counted the minutes and seconds.

3.3 Experimental Setup
For the data gathered in this experiment, the pickups were mounted as shown below in Figure 5.

The pickups were placed about 2” from the bridge of the monochord, which is about where the ‘bridge” pickup would be placed on an electric guitar. We placed the bridges 25 ½” apart, which is a very common scale length for an electric guitar. The signals from the two pickups were fed into a computer sound card through a Behringer audio mixer, and recorded onto separate tracks using Cubase LE software. This data was cut up into manageable chunks and saved as wav files. The data was then analyzed using a MATLAB script.

Results

The results obtained show the harmonic spectrum of the signal as it varies in time. I have grouped the plots together as pairs; one showing the x-oriented pickup’s spectrum and one showing the y-oriented pickup’s spectrum for the same time period. The string was excited either by a pluck or by a pick either at mid string or at quarter string, as listed below. The ffts were calculated every 2000 samples, or roughly 45 milliseconds. A total of 40 ffts were taken from each measurement giving a total time-lapse of 1.81 seconds. Theses numbers were chosen as a compromise between the resolution of each fft measurement and the distance between each measurement in time.

Conclusions

The most striking thing about the data was the often very large difference in amplitudes between the pickups when both are seeing the same stimulus, just from different angles. Much care was taken to ensure that the pickups were matched reasonably well in output, and the spacing from the string was very carefully matched for the two pickups.

Bibliography

• Freed, A. and O. Isvan (2000), “Musical Applications of New, Multi-axis Guitar String Sensors”. Proceedings of the International Computer Music Conference, Berlin, Germany
• “Vintage Fender Guitar Pickup Spec Info”. October 10 2005. Vintage Guitars Info. [Accessed 12-21-2006]. http://www.provide.net/~cfh/pickups.html
• “The Earliest Days of the Electric Guitar”. 2006. Rickenbacker International Corporation. [Accessed 12-21-2006]. http://www.rickenbacker.com/history_early.asp
• Chobanian; Dennis A., McNaughton; R. Alan. “Transducer for sensing string vibrational movement in two mutually perpendicular planes.” US Patent 4,348,930. January 25, 1980