Something different… again: GUITAR PICKUPS!
I decided to take a break from my research to put up a quick blog and clear my head a bit. I wanted to investigate the 3-axis response of blade pole pieces vs a bar pole piece to test a hypothesis that I had about one of the contributing factors to the difference in sound between blade style pickups and pole piece style pickups.
The reason for this test is that I had theorized that the transversal string-movement response (across the pickup face) was lower for a blade style pickup as a result of the orientation of the lines of magnetic flux, and as a result, the horizontal movement of the string contributes less to the overall output signal, which is significant for a few reasons that I will explain.
I will not rehash material that is well-covered elsewhere, but I WILL touch on the parameters that are directly relevant to this discussion to give some background and context (If you are familiar with guitar pickup theory, standing waves, and psychoacoustics you can just skip to the experiment at the end).
FIRST: string movement
Guitar strings vibrate in an elliptical pattern which rotates slowly (precessing), so this can be mapped into vertical and horizontal components (it actually has x, y AND z components, but that is not relevant to this discussion). The wave is not a perfect sine however. There are standing waves along the string that increase in order (lambda(n) = (2/n)*lambda) in correlation to input energy (how hard you pluck) and have decreasing amplitude in relation to the original wavelength because of the higher energy requirement. This harmonic series is integrated (much like additive synthesis) to create a complex wave that is then translated into the string movement that disturbs the magnetic flux and is then transformed into AC by the pickup. Complex eh? Oh it gets much worse because that brings us to the next point:
SECOND: pickup as an integrator or x and y string movement
Magnetic guitar pickups function as variable reluctance sensors: the strings are oscillators which are loosely-coupled to the pickup coil(s) through the field of the permanent magnet, and as the string moves through that field, it varies the amount of magnetic flux through the coil(s), which produces voltage via induction.
In terms of string movement through the field, vertical movement of the string produces a change in flux through the pickup that is a simple exponential decay curve since it can only move in relation to one side of the magnet, while horizontal movement across a pickup’s pole piece produces a change in flux that increases exponentially as it approaches the center, and then decays exponentially as it passes through it and continues to the other side. This rectifies the waveform, essentially doubling the fundamental frequency.
Since this frequency is higher, it is perceived as ‘brighter’ or ‘more treble-y’, so the waveform through the pickup is the integration of the vertical signal and the rectified horizontal signal, and since this an asymmetric signal in a non-linear system, we produce both even and odd harmonics, whereas the horizontal movement produce only harmonics starting at the 2nd AND does not reproduce the fundamental frequency. Furthermore, the proportion of vertical to horizontal flux change the overall harmonic content: more horizontal movement suppresses both the odd-order harmonic content, and adaptively raises the overall harmonic content in relation to the fundamental.
So that can be boiled down to (as far as the pickup was concerned):
-Vertical component produces the fundamental as well as odd and even harmonics
-Horizontal component produces harmonics, starting at the 2nd harmonic
-A higher ratio of horizontal component suppresses odd-order harmonics and raises the overall harmonic content in relation to the fundamental
OKAY… since the science is out of the way, we can get into psychoacoustics since that relates to the experiment.
THIRD: psychoacoustics and the harmonic series
(Disclaimer: psychoacoustics are tied into one’s psychology and physiology, so it is inherently subjective… BUT… the subject is well-trodden, and spans centuries, so consensus is a good indicator with such a large data set)
Even-order harmonics (2nd, 4th, etc) are musically-related to the fundamental in that their frequencies are (close to) consonant intervals, with the lower order harmonics being more consonant than higher order. They make the sound “fatter” in the they add in a pleasant way (basically they form a nice chord, which sounds fatter than playing a single note).
ODD-order harmonics, however, begin consonant at lower orders (but not as consonant as low even-order), and then tend toward dissonance at higher orders.
The consonant (pleasant) intervals are PP(octave), P5th, P4th, 3rd, 6th. Dissonant (unpleasant) intervals are 2nd, 7th, b5th and any frequency that does not fall directly on any interval (like a microtonal interval). See the chart below (* = consonant):
*2nd = PP
*3rd = P5th
*4th = PP
*5th = m3rd
*6th = P5th
7th = (not quite) M6th
*8th = PP
9th = M2nd
*10th = M3rd
11th = flat 5th
*12th = P5th
13th = (not quite) m6
14th = (not quite) M7th
15th = (not quite) M7th
*16th = PP
So you can see that a combination of just about any lower-order harmonics will sound fatter and more pleasant, whereas all higher order odd harmonics are dissonant and most higher order even-order harmonics are consonant.
FOURTH: how this relates to the pickup
So let’s make the following assumptions in general:
-more low-order harmonics = fuller (and a bit brighter)
-more high-order harmonics = brighter (and a bit fuller)
-more even harmonics = fuller and more smooth and pleasant
-more odd harmonics = fuller and a bit more sharp and punchy
So you MIGHT think ‘oooooh! so I want low-order even harmonics and it’ll be nice and fat and bright’… not quite. That sentiment needs to be tempered by the taking things to the extreme:
-too many even and low-order harmonics can sound muddled or spongy
-too many odd and high-order harmonics can sound piercing and icy
So there has to be a balance between the two… and that is where the magic happens. Also bear in mind that the ratio of vertical-to-horizontal components as well as the number of harmonics varies with both attack, decay, picking speed/force, and as the elliptical path of the string vibration rotates during sustain. (other variables that can effect the strings’ vibration and overtone coloration include: string thickness/mass/material, scale length, and other outside factors like the actual guitar construction, hardware, string height, pickup height, wood choice, etc, etc…)
FIFTH: FINALLY THE ACTUAL EXPERIMENT!!
OKAY! Enough of the music-math, lets build some things. For this experiment I took two single pickup coils: one with a mild steel blade pole piece and the other with individual mild steel slugs. I used the same magnet for both (I swapped it between the two). The output of the pickups was roughly equivalent (around -16dBfs RMS) despite their radically different construction and specs, with the higher-turn-count pole-style coil being about 3.7dB hotter (which is a 1.5x Voltage Ratio).
Hum-bucker sized 2.75” x 0.5” x 0.6875”
resistance = 7.75Kohms
dual mini coil hum bucking single coil sized 2.5” x 0.5” x 0.34”
Gauss on the blade coil measured about 25% higher than the pole piece coil at 1cm above.
So obviously I had to find a way to provide consistent string movement in only one plane, so I had to whip something up that was A) mechanized and B) had linear movement. My initial thoughts were to modify a fan with some kind of linear guide, but that was a mess. My second thought was to pluck the string with an automated armature and guide the string movement, but that was a failure. Ultimately, I needed a high speed linear actuator servo… which is not exactly in my budget since I am a broke-ass musician, and then it hit me: speakers!
I am a pack-rat, so I pulled out a pair of old desktop speakers that had blown tweeters, and I pulled out the woofers. I measured the cone excursion at a little less than 1/4” at 60Hz, which was sufficient to simulate string movement. For simulating the string movement, I needed something that was ferrous, and stiff enough that it would not bend or produce any unwanted harmonics, so I chose a 1/8” mild steel rod from the local hardware store. The speaker cones were very stiff, so I decided that they would work for structural support, so secure the rod to the speakers, I hot-glued a mount right to the cones that consisted of a bottle cap with a bolt threaded through it and a metal collar to form an eyelet. The collar had a threaded hole in the side, which I used both to mount it to the screw and to secure the rod. I wrapped some electrical tape around the contraption just for peace of mind so that the rod would not rattle it’s way out.
The speakers were 60 watts each, but I put a 20w resistor in series with them to protect them from excess power regardless. For the initial tests, I just ran the speakers from a huge 120v:12v, 4Amp AC transformer right off the wall to produce a 60Hz vibration. In the future I will power it from a simple chip amp so that I can sweep the frequency.
Here is a pic of one of the contraptions, which worked well, although it produces more of a triangle wave than a sine, but one step at t time, and it is good enough for relative comparisons of output level:
So as you can see, my initial thoughts were correct, which is logical since there is no change in position-dependent flux density along the surface of the rail pole piece: For the blade style pickup, the horizontal response was down 20dB from the vertical response, and some of that is likely due to slight vertical oscillations in the bar’s horizontal movement (I have to figure out how to damp that). Here are the results in numerical values:
Pole Vert -16.37dB RMS
Pole Horiz -18.8dB RMS
Blade Vert -16dB RMS
Blade Horiz -36dB RMS
One particular note is that there is a magnetic field null between the pole pieces, so the response was down about 1/2 on that model between the poles, but the horizontal voltage amplitude was equal to or higher than the vertical voltage amplitude on the extreme outer pole pieces. Also, just for curiosity’s sake, I flipped the blade coil about 70 degrees and positioned the pickup edge under the oscillation rod and saw a 3dB improvement in output, suggesting that (as expected) a narrower pole piece produces a more focused flux field and improves coupling (which is true and calculable if you look into solenoid documents) as well as producing a higher change in flux differential (and this a higher voltage amplitude), but that is at the expense of off-axis sensitivity (i.e. signal drop-off when bending a string away from the center axis).
Consequently, this behavior has been manipulated by companies for decades to tune pickups between a blade style and a pole style. Bartolini employed a pole piece ‘fan’ on some models of pickup to tune the ratio of vertical-to-horizontal string sensitivity. Other examples are the Seymour Duncan Invader and Quarter Pound . (Bear in mind though: this post only covers string movement and not materials and geometry… which I will likely cover in the future.)
(UPDATE: I am improving the design of the oscillating gizmo by using a single speaker and a hinged rod to give it more horizontal stability, as well as more control over the amplitude of the movement (I was having some annoying problems with strong magnets distorting the path of the rod or even sticking to it). So hopefully that will allow for more accurate and controllable readings for future experiments).
(Update 2: here is a video that I made for a different post, but it is appropriate here so that you can hear clips of the isolated vertical and horizontal movement, and see the associated waveforms. You can easily hear the higher-pitched/more-trebly timbre/pitch of the horizontal movement, and the bass-ier, lower timbre/pitch of the Vertical movement):
<Update: 3/12/16 corrected error about pickup manufacturer- thanks Wolfe>