Guitar pickup theory #1: Blade vs pole pieces | alexkenis

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Guitar pickup theory #1: Blade vs pole pieces

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By alexkenis<br>/ October 22, 2015<br>/ magnetics, Making, Math<br>/ 10 comments

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...