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How do I question the engineering physics of magnetic fields in a guitar pickup?

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tl;dr don't bother. This is too abstracted and nuanced. That is okay to skip.

I like to understand the abstract scope of engineering. This is way beyond the simple surface level, with pics below to illustrate my point.

With electric guitar pickups, the complexity of field shaping and design control over the sensor seems like a place where optimising the profitable manufacturability of the final product remains the primary constraint with little deviation.

I struggle to qualify and quantify my intuitive hunch that there is a whole lot more potential to engineer something new and better within the realm of modern manufacturing. I don't know the principal questions I should ask or what might disprove my ideas from the get go.

  • Most transformers shape the magnetic field far more than guitar pickups.
  • a guitar pickup appears to be more of a two dimensional sensor that picks up the motion of a ferromagnetic string in the two primary directions of motion
  • there are more complex harmonic motions present than a pickup can register in two dimensions
  • the coil and slugs of a pickup are surrounded by a single large winding, yet the strings each have very different frequencies
  • it is now possible to make a powdered ferrite core of nearly any shape and frequency
  • the traditional pickup has little effective shaping of the magnetic field path
  • guitar pickups are not optimised to a point where they are readily used elsewhere in other sensory applications and devices as economy of scale should dictate in an open and manipulation free market... I don't think they are anyways
  • what might be the result if a 270° toroidal powdered core were designed and shaped for each string while tailoring the copper winding and ferrite for each string's mean frequency and shielding each of these
  • would a chord segment gap in a toroidal core pick up more 3d motion from the string
  • what effect would a primary and secondary winding wound in the opposite dot notation direction have on the pickup of more complex harmonics and motion
  • why does none of this matter due to the filtering of LCR and the noise floor or other aspects

Like here is the basic range of commercial products:

The typical schematic of operation:

Basic construction:

This is a typically low noise toroidal transformer that has been around for ages:

Now I need you to abstract this concept with me a little bit. Imagine if a small toroidal core was below each string and offset towards the neck or bridge so that they will fit. Nothing would stick out or surround the string. The 270° is not a radius cut like a pie. Instead it is a chord and removed segment:

There are totally random pics from DDG that are somewhat illustrative in abstract:

These are just some random powdered core ferrites that illustrate how these can be formed into any shape now:

I usually avoid anything audiophile related because it draws out pseudo science nonsense like crazy, but at the center of this question is really a desire for a deeper understanding of sensors and magnetics that have much broader applications in precise motion control and sensors for a range of equipment.

In a higher level of abstraction, I'm also really asking when and where does this subject become the realm of the illusive bearded nude virgin demigods that get enslaved to corpo NDA masters from birth. .5/s

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  • a guitar pickup appears to be more of a two dimensional sensor that picks up the motion of a ferromagnetic string in the two primary directions of motion

    It’s actually not a 2 dimensional sensor. It’s 1D, the velocity of the string induces a current in the coil (Faraday’s law)

    there are more complex harmonic motions present than a pickup can register in two dimensions

    Again not sure where 2d is coming from, but the current perfectly corresponds to the velocity of the string, which we already know is identical to the sum of the velocities created by all of the harmonics (Fourier Transformation).

    How did you reach the conclusion that some harmonics are missing from the resultant signal?

    the coil and slugs of a pickup are surrounded by a single large winding, yet the strings each have very different frequencies

    The human ear also has different sensitivity to amplitudes at different frequencies, with higher pitched sounds not needing as much energy to reach the pain threshold. The distance between each string and the pickups is also adjusted during setups, sometimes including tilting the pickups themselves depending on the type of guitar.

    Just a few thoughts I had while reading. This style of pickup really is just popular just because the’ve been popular for so long and they’re supremely reliable even with as much abuse as we put guitars through. There are others; you might enjoy reading about the physics of a piezo pickup, and the problems they often create for players haha

    • How did you reach the conclusion that some harmonics are missing from the resultant signal?

      I forget if it was Veritasium, Steve Mould or one of the other edutainment content creators that was showing how waves move through a string and form the extra major harmonics along the length. I was half baked thinking of that and how the string is not constrained to a single plane of vibrations.

      I am thinking of the motion of the string being more complex, like if I placed a coil under the string and one at 90° to the first beside the string, there should be a subtle difference between the two signals. The motion of the string may be oscillating entirely within the field of each pickup coil, but the motion with respect to the magnetic pole of the pickup will be different. If two fields are pointed at the string from opposing angles, perhaps more of this motion is defined. It might alter the sound for more subtle picking techniques like plucking, slapping, palm muting or others.

      Also there is the question of what is the optimal turns ratio and signal for each string. If each string had its own pickup and winding, it is like audio channels on a mixer, it creates versatility and nuance. It's just an idea.

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