Leonardo Lospennato is the author of a 250 page book focused entirely on electric guitar design. Checkout his great book and work at lospennatoguitars.com. This article is a short excerpt that will help with a common uncertainness when designing an electric guitar or bass.
Excerpt from the book "Electric Guitar & Bass Design" by Leonardo Lospennato
July 13, 2010
Where do I place the pickups? In a place that allows each pickup to better fulfill its mission.
Plucked strings vibrate in a complex way, a superposition of several vibration modes activated simultaneously. In the next figure, the sinusoidal curves represent the first eight vibration modes:
The biggest curve represents the fundamental mode, and each subsequent overtone has less amplitude and higher frequency than the previous one - ad infinitum. The four vertical grey bars mark the location of the pickups' magnets, and show how each pickup "reads" the different vibrations.
Changing the placement of the pickups changes the way each vibration mode is perceived by the pickup. In the example, the gray bars (i.e., the magnets) do not meet any nodes, that is, the points at which the curves values are zero.
It is often said that if a pickup (or more properly, its magnets) were placed under the node at the 24th fret, three of the principal eight modes would simply not be perceived by the pickup, because three overtone curves have a zero value at that particular point. Such a situation is not unusual on guitars (or some basses) with 20, 21, or 22 frets: the neck pickup often ends up placed under that point, one fourth the distance from the bridge.
But the graphic above only shows the nodes created by the vibration of the open strings. Each fretted string gets its vibrating length shortened, so a new configuration of nodes emerges; the cancellations occur in different places for each fret!
Additionally, magnetic pickups have wide "apertures": they sense a pretty big length of the string, not the string at just one point (humbuckers: doubly so). So even when they are located right under a node they still read string vibration around that node, too.
That makes it impossible, from a practical standpoint, to avoid all nodes for all frets. In short, trying to avoid (or meet) any tonal node is a non-issue. Yes, the sound may vary with millimetrical pickup position changes - but there is simply no "mathematical", "correct" way to place pickups, because the resulting, slightly different sounds are not objectively good or bad, they are simply different.
What is the practical way to place pickups, then?
Bridge pickup: in electric guitars the bridge pickup is placed a few millimeters away from the bridge. The nearer the bridge, the more "trebly" the tone will be, with lower output level (due to the shorter amplitude of the string vibration at that point). Changes in pickup placement near the bridge are far more noticeable than those near the neck position.
In basses, it is better to place the bridge pickup not so close to the bridge: we need it where those fat strings are vibrating enough. Depending on the scale and personal preferences, the distance from pickup to bridge could be 1" (25.4 mm) or more. Check the measurements of basses of the same scale as yours whose sound pleases you. Placing the pickups in an analogous way will likely produce an analogous dynamic response (not necessarily a similar tonal response, though, unless you use the same pickups).
Neck pickup: in guitars, place the pickup close to the end of the fretboard. In general, the closer to the fretboard the better, since the sound will be mellower and louder. If the truss rod adjustment is at the body end of the neck, space will have to be provided between the end of the neck and the neck pickup for the truss rod adjustment to be made.
In basses, leave some space between the end of the fretboard and the neck pickup to provide room for slap style playing if the instrument will be used in this fashion.
Some luthiers don't place the pickup perpendicular to the strings, but at a slight angle. The magnets of the treble strings get closer to the bridge, and the magnets that "read" the bass strings become gradually more separated from the bridge. This is done to increase the tonal range response of the instrument, since the treble strings will sound more "twangy", more brittle, and the bass strings will sound more "bassy" (see figure):
Does it work? Yes, the response of the pickup should be audibly different.
Is it better? That depends on the sound you are looking for. Again, there is no mathematical recipe. Is all about testing different angles, and checking the results.
Slanting is not recommended for humbuckers, though. The magnets will not end up in line with the strings. Slanting single coils in too big an angle will cause the same situation. Using pickups with magnetic rods instead of individual magnets for each string will eliminate the problem.
© Leonardo Lospennato, Berlin, Germany
http://www.lospennato.com