This is a Java applet I wrote to demonstrate some of the effects of the physical parameters of guitar pickups on the frequency response of the instrument, including position, width, and combinations of multiple pickups, with various levels and polarities. The applet is based on the equations derrived in my articles below.
The applet does not show the effects of the pickup's electrical parameters (inductance, capacitance, loading, etc.) or instrument's body resonances, which are certainly at least as important.
The Applet should appear above. It is intended to run on most browsers.
(Recent changes: Fix UI quirks, preset guitars feature, draw harmonics of the string frequency, hold shift to move all pickups at once.)
On top is a diagram showing a vibrating guitar string, a 24-fret fingerboard with inlays, a nut on the left, a bridge on the right, and a pickup. Two rulers above the string display the distance from the bridge in inches and the fret number.
In the center is the resulting plot of the frequency spectrum. The horizontal axis is a 20 Hz to 20,000 Hz log frequency scale and the vertical axis is a +10dB to -40dB amplitude scale. The horizontal red bar shows the pitch range of the fretted notes along the neck from the open string to highest fret. The gold vertical lines mark the frequency of the currently fretted note along with the harmonics up to the 8th.
On the lower left are fields for setting the number of frets, the string's open tuned frequency (in Hz) and the scale length (in inches). There is also a button for adding a pickup.
On the lower right is a table of pickup parameters, one entry for each pickup. The Applet starts with a single pickup.
Below the applet is a menu and button to preset the display to one of a selection of popular guitars.
Experiment, have fun.
Click on a pickup and drag it to move the pickup to a new position. The actual position, in inches from the bridge, is displayed below the pickup. The response curve is updated as you move the pickup around.
Click on the string to fret various notes and the gold vertical line displays frequency of the current note on the response plot.
Entering a new value for the number of frets will adjust the fingerboard display as well as the red pitch range bar. Legal values are from 0 to 60 frets.
Entering a new value for the open string frequency will also update the response curve, effectively sliding the curve left or or right. Legal values are from 20 Hz to 10 KHz.
Entering a new value for the scale length will rescale the diagram so that the string endpoints (the nut and the bridge) are displayed in the same locations, but the positions and sizes of the rest of the diagram scale to accommodate the new scale length. Legal values are from 10.0 to 100.0 inches.
Clicking the Add pickup button will create a new pickup and update the response plot will show the response of a mix of all the pickups together. Pickups are numbered from 1, and new pickups are colored randomly to help differentiate between them.
The table at the bottom has a set of controls for each pickup; the pickup position (in inches from the bridge), the pickup magnetic aperture width (in inches), the pickup level (in dB) both as a value and as a slider control, the polarity of the pickup, and a button to remove that pickup.
The low-end response disappears as the pickup gets closer to the bridge. This particular model keeps the string vibrating behind the bridge, at the opposite polarity, so it's entirely possible to position the pickup behind the bridge. I just didn't bother limiting the string vibration.
For a single pickup the response is the product of two "comb filters responses". A comb filter response contains a series of notches a constant number of Hz apart and "looks like a comb". One of the combs is due to the position of the pickup, the distance the pickup is from the bridge while the other is due to the width of the pickup. And both will scale with the pitch of the open string.
A few readers have pointed out that the frequency response curves for a single pickup ought to be identical when the pickup is placed at symetrical locations about the center of the string. Ie., the curve for a pickup 4.0 inches from the bridge ought to be the same as the curve for a pickup 4.0 inches from the nut. Yet the curves are very different.
The frequency response plots are built by shortening the vibrating string length towards the bridge, effectively fretting notes up the neck. This corresponds to the formant filtering model (start with a flat response and filter it) that we are accustomed to hearing in acoustic instruments. But fretting the string imediately loses the symmetry of the pickup locations.
The curves of symmetrically placed pickups are the same, however, at the specific frequencies of the open string and it's harmonics.
The most extreme case of this can be seen by comparing the response of a pickup placed right on the bridge to a pickup placed right on the nut. And sure enough, the frequency response of a pickup placed on the nut has nulls at all harmonics of the open string.
For those interested, the source code is here:
Here are some reference numbers to use.
Scale lengths: Rickenbacker 325 (Lennon) 20.75 inches Fender Jaguar, Gibson Byrdland 24.00 Most Rickenbacker guitars 24.75 Most Gibson guitars (Les Paul, SG, etc) 24.75 Most Fender guitars (Stratocaster, Telecaster, etc.) 25.50 Short Scale basses (Fender Musicmaster, Gibson EB) 30.00 Rickenbacker basses 33.25 Fender Jazz, Precision basses 34.00 Bass open string frequencies: low B (5, 6-string basses) 30.87 Hz low E 41.20 A 55.00 D 73.42 G 98.00 C (6-string basses) 130.1 Guitar frequencies: low E 82.41 Hz A 110.0 D 146.8 G 196.0 B 246.9 high E 329.6
I've written this applet in JDK1.0 to be able to run it on the out-of-date Java VM that comes with Macintosh Netscape. The applet should be compatable with all major browsers on all major platforms -- if it isn't, tell me. I understand that the WebTV browser cannot handle applets at all.
Response Effects of Guitar Pickup Position and Width, Donald Tillman. An analysis of the freqency response characterstic of pickups due to their physical location and width.
Response Effects of Guitar Pickup Mixing, Donald Tillman. An analysis of the effects of mixing the signals from two and three pickups.