Analysis of Harmonics and Pickup Positioning on 12-String Basses

By Philip Snyder

I recently began studying the placement of pickups on stringed instruments and how pickup placement affected the sound of those instruments. My elementary theory was that you divide the scale length of any instrument up evenly to find the primary, secondary, tertiary, etc. harmonics and place the pickups under these accordingly. If you check the math that's exactly what Leo Fender did in designing the Stratocaster back in the '50s. The neck pickup is half the distance from the 12th fret to the bridge, the middle pickup is approximately half the distance from the neck pickup to the bridge, and the bridge pickup is approximately halfway between the middle pickup and the bridge.

These subdivisions of the string produce a variety of harmonics with varying strengths. For our purposes here we will call these harmonics the Primary, Secondary, Tertiary, and Quaternary harmonics respectively.

Of course, pickup placement isn’t governed solely by harmonic locations on the strings. Tone and even aesthetics play important roles in deciding where pickups should be placed on any instrument. On basses in particular you run into situations where a pickup located too close to the bridge can sound thin and harsh, while a pickup that is set too far towards the neck can result in tone that is muddy and undefined. There is also pickup choice to factor in. A specific pickup may sound great in one location and not so wonderful in a different spot. Everything depends on everything else.

The purpose of this article is not to point out who has the “best” pickup positioning in their designs. It would difficult at best to argue that point. The purpose here is simply to educate on where these harmonic points are and how they match up to the 12-string basses that are currently available.


Measurements were taken with the end of a yardstick centered on the 12th fret

Obviously you can make this as simple or as complex as you wish. Someone who is very interested in the science of sound may really enjoy digging very deep into the physics of the relationships here, whereas I would rather put a ruler on the body and simply measure out where the harmonics are.

I have created a detailed listing of the measurements for these harmonics on three different scale lengths of 12-string basses. We will use these measurements to analyze the pickup positioning of several production 12's.


34" scale

- Primary harmonic @ 17" (center of nut and bridge)
- Secondary @ 8½" from 12
th fret (center of 12th fret and bridge)
- Tertiary @ 12¾" from 12
th fret  (center of Secondary and bridge)
- Quaternary @ 14
⅞" from 12th fret  (center of Tertiary and bridge)

Here is how a few 34" scale 12-string basses measure up:

Hamer CH-12 (Korean-made)

Neck pickup center is 1¼" off from Tertiary harmonic.
Bridge pickup center is " off from Quaternary harmonic.


Waterstone TP-2 (Korean-made)

Neck pickup center is 1" off from Secondary harmonic.
Bridge pickup center is ¾" off from Tertiary harmonic.


Chandler Royale (USA-made)


Neck pickup center is ½" off from Secondary harmonic.
Middle pickup center is " off from Tertiary harmonic.
Bridge pickup center is " off from Quaternary harmonic.


Hamer B12A (USA-made)

Neck pickup center is ½" and 1½" (split) off from Secondary harmonic.
Bridge pickup center is " off from Quaternary harmonic.


October (USA-made)

Neck pickup center is ½" off from Tertiary harmonic.
Bridge pickup center is exactly on the Quaternary harmonic.


Galveston 12 (Korean-made)

 

Neck pickup center is " off from Tertiary harmonic.
Bridge pickup center is exactly on the Quaternary harmonic.


32" scale

- Primary harmonic @ 16" (center of nut and bridge)
- Secondary @ 8" from 12
th fret (center of 12th fret and bridge)
- Tertiary @ 12" from 12
th fret (center of Secondary and bridge)
- Quaternary @ 14" from 12
th fret (center of Tertiary and bridge)

Here is how two 32" scale 12-string basses measure up:

Hamer B12M (USA-made)

Neck pickup center is 1" off from Tertiary harmonic.
Bridge pickup center is ¾" off from Quaternary harmonic.


Waterstone TP-32 (Korean-made)

Neck pickup center is ¾" off from Secondary harmonic.
Bridge pickup center is ¾" off from Tertiary harmonic.


30½" scale

- Primary harmonic @ 15¼" (center of nut and bridge)
- Secondary @ 7" from 12
th fret (center of 12th fret and bridge)
- Tertiary @ 11
" from 12th fret (center of Secondary and bridge)
- Quaternary @ 13
" from 12th fret (center of Tertiary and bridge)

Here is how a  Hamer 30½" scale 12-string bass measures up:

Hamer B12S (USA-made)

Neck pickup center is 1¾" off from Tertiary harmonic.
Bridge pickup center is ½" off from Quaternary harmonic.


Just for cross-reference purposes (and simple curiosity) I have listed the pickup positions for a Fender Jazz Bass below. Note that the neck pickup is not under any specific harmonics but the bridge pickup is.

Fender Jazz Bass specs:

Scale length: 34"
Neck pickup position: 6"
Bridge pickup position: 2¼" (under Quaternary harmonic)

There is a very good and detailed article written by J. Donald Tillman titled, "Response Effects of Guitar Pickup Position and Width" online at http://www.till.com/articles/PickupResponse/index.html#position. Not exactly what I would call light reading but certainly interesting.

Of course, once you fret the instrument all of this figuring becomes almost null and void as all of the harmonic locations adjust according to the new active string length. This is where pickup aperture comes into play.

Aperture

Electric guitar and bass pickups create a magnetic field that senses the vibrations of the strings above them. This area is called the aperture. The aperture of any given pickup is normally not much wider than the pickup itself. This diagram shows the approximate aperture of your average humbucker.

The aperture is the magnetic scope of the pickup; i.e. the area of the string that the pickup can read.  For example, the single-coil pickup that comes standard in a Fender Jazz Bass has an aperture of approximately 1". Obviously a humbucker such as the EMG-35 will have a wider aperture and a Music Man humbucker even wider than that. This wider aperture helps to compensate for the variation in harmonic change as the strings are fretted in different locations. It's not a perfect system but it does work pretty well and we are accustomed to it.

Still, having the pickups positioned correctly to begin with helps the overall tone of the instrument. As bassists we do tend to play open strings quite often. If the open strings produce harmonics over properly positioned pickups then the natural tone of the bass will be optimized. The aperture of the pickups themselves will help to take care of the variation of harmonics on a fretted string (or strings).