Guitar Pickup Response Demonstration

This is a demonstration of the effects of physical parameters of guitar pickups on the frequency response of the instrument. These include position, width, and combinations of multiple pickups with various levels and polarities. This is based on the equations in the articles referenced below.

This model ignores the electrical characteristics of the pickups (inductance, capacitance, loading, etc.) as well as the instrument's body resonances. They are all important factors for the sound, but the focus here is on the physical parameters.

Instructions

You can mouse on the pickup to move it around and see the effects of the pickup position on the frequency response. The pickup table allows you to add and remove pickups, and set the position, width, level, and polarity of each independently. With multiple pickups mixed together, the response curve becomes very complex.

The main display is a classic frequency response plot. The X axis marks the frequency on a log scale running from 30 Hz to 15 KHz. The Y axis is also a log scale, dB, with 0 dB as our reference point. -10 dB is 1/10 the power. If you hover the mouse over the plot you can see the frequency and amplitude at that point displayed in the lower left.

Above the plot we have a ruler, a drawing of a vibrating string, guitar neck, bridge, and an electromagnetic guitar pickup. The ruler is calibrated in inches from the bridge going up the neck, and also ticks off selected fret locations on the bottom.

The guitar parameters are below the plot on the left. Changing them updates the plot.

The pickup position is measured from the bridge to the center of the pickup and is responsible for the main comb filter effect.

The pickup width is the aperture of the pickup, the length of the string that the pickup senses, and is responsible for the higher frequency comb filter effect. This is a first order approximation as the sensitivity gradient of a pickup is a substantial topic on its own.

The polarity checkbox lets you throw a pickup out of phase so that the lower frequencies, common to both pickups, cancel. Note how the relative levels of two pickups out of phase make a huge difference in the response.

The checkboxes on the right enable some interesting plot features.

The Fundamental Frequency Marker feature notes the range of the fundamental frequencies over the range of the neck. You can mouse on the vibrating string and see how the fundamental pitch maps onto plot frequencies.

The Show 16 Harmonics feature displays the amplitudes of the harmonics of the note being played.

There's a hidden feature: When multiple pickups are present, holding down the shift key will move all the pickups together. On an iPad, use two fingers. Left and right motion will move the pickups together left and right. Up and down motion will bring the pickups together and spread them out around their center point. This is interesting because, for the case of two pickups, you can see how the total response is a combination of two separate comb filters, one due to the average position of the pickups and the other due to the distance between them. Left/right vs. up/down motion shows these off. This effect is described in the second article of the series.

The Symmetry Riddle

The concept of frequency response here is somewhat abstract as one just plays individual notes on a guitar string and it is not a filtering function as such. But if you ripped out the frets and slide the pitch up, the levels of the fundamental and harmonics would follow this curve.

Should the curves be the same for pickups placed at, say, 1/4 the way from the bridge and 1/4 the way from the nut? No, because sliding up the neck is part of the frequency response mechansim and that loses the symmetry.

But for an open string, the discrete harmonics should be the same. To see that effect, turn off the plot and just display the first 16 harmonics, and compare those at symmetrical ends of the vibrating string.

Helpful Numbers

References

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.

Pickup Response Demonstration Applet, Donald Tillman. The 2000 vintage Java technology version of the current page. At this point it's painful and difficult to run.