How Sensitive is a pickup to horizontal vs vertical string vibration?

[Mike Sulzer]

The asymmetry of the guitar pickup signal is best viewed on an oscilloscope to observe that one of the poles of the signal , either above or below zero is about 20% to 25% higher in amplitude than the other pole. This occurs for one very simple reason; vertical string motion generates more output than horizontal string motion.

The guitar signal is inherently asymmetrical because the string vibration has even harmonics. The non-linearity should also make a contribution, but it is not so easy to figure out how much.

[Mike Sulzer]

The variation of the permanent B field, Vertical and Horizontal

In this post, we analyze the variation of the permanent magnetic field from a steel core with an alnico magnet on the bottom. We use FEMM in its axial-symmetric mode, so the core is a cylinder, as is the magnet. This is not necessarily realistic, but the extreme nature of the results suggests that is unnecessary to look at other cases. We assume that the string is located 0.1 inch above the pole piece and is centered, and examine the field variation along two contours:
1. along the axis of the core, from the top up through the string location.
2. Horizontally across the top of the pole through the string location.
These two contours are not a complete description of the variation, but they do show a typical comparison between the variation in the two directions.

The figure is here:http://www.naic.edu/~sulzer/BVarFromStringEq3D.png. The vertical variation is roughly linear about the string equilibrium position. We assume a motion of .01 inches in each direction. The horizontal variation is not linear at all. By symmetry, there is no variation at all in the center, and the field falls of very slowly in both directions. I estimate that the variation is about 25 times less in the horizontal than vertical direction for the assumed motion, as indicated on the figure. This means that the horizontal variation of the magnetization contributes very little.

Also consider that the horizontal variation falls off in both directions. Suppose the string starts off on one side, moves to the other and back again. This is once complete cycle of variation. During this cycle, the field variation increases and then decrease in moving to the other side, and then does it again coming back. This is two cycles. Thus, horizontal motion is frequency doubling. If horizontal variation were dominant, the pickup would be a frequency doubler.

[bbsailor]

The guitar signal is inherently asymmetrical because the string vibration has even harmonics. The non-linearity should also make a contribution, but it is not so easy to figure out how much.

Mike,

I always like definitions in any of my discussions. Please define what you mean by the asymmetry being caused by "the string vibration has even harmonics".

Thanks

Joseph Rogowski

[Mike Sulzer]

Mike,

I always like definitions in any of my discussions. Please define what you mean by the asymmetry being caused by "the string vibration has even harmonics".

Thanks

Joseph Rogowski

The function describing the position of the string as a function of time can be resolved into multiple sinusoidal components that are harmonically related. The lowest frequency is the fundamental; in general there are both even (2x, 4x...) and odd harmonics (3x, 5x...). The evens combined with the fundamental can make a signal that has greater deviation in one direction than the other.

[bbsailor]

String Motion Direction Experiment

Since the string is vibrating in both planes, how do you know that the vertical motion generates a stronger signal than the horizontal motion? Do you have a way to excite a string in one plane at a time and compare signal strength?

Diablo,

You need access to an oscilloscope to try this experiment.

1. Connect the pickup output directly to the scope.

2. Plunk the string by pinching it between your fingers and pulling it sideways (horizontal), then release and look immediately at the oscilloscope signal. Pay attention to the amplitude peaks of the first few cycles.

3. Do the same thing but this time pinch the string and pull up on the string in the vertical plane and release so the string snaps toward the pickup.

Look at the peak signal on the oscilloscope and you will notice that the immediate response is stronger in the first few vertical cycles in step 3 than with the horizontal cycles done in step 2 above.

There is no practical way to isolate vertical and horizontal string motion without interfering with the string's natural vibration, but this simple experiment should give you a feel for the string motion directions that contributes mostly to the output.

I hope this answers your question?

Joseph Rogowski

[Mike Sulzer]

Diablo,

There is no practical way to isolate vertical and horizontal string motion without interfering with the string's natural vibration, but this simple experiment should give you a feel for the string motion directions that contributes mostly to the output.

Joseph,

Please consider this alternate explanation for your observation:
1. The pickup responds significantly to vertical motion only.
2. When you pluck mostly in the horizontal plane, you at first see little, but as the plane of vibration rotates, you pickup more vertical component.

[Diablo]

Joseph,

Please consider this alternate explanation for your observation:
1. The pickup responds significantly to vertical motion only.
2. When you pluck mostly in the horizontal plane, you at first see little, but as the plane of vibration rotates, you pickup more vertical component.

Why should the plane of vibration rotate from horizontal to vertical? How does a string know where vertical is?

[Mike Sulzer]

Why should the plane of vibration rotate from horizontal to vertical? How does a string know where vertical is?

The motion of the string is generally something like elliptical. If you start the string in one plane, you could think of the evolution as a rotation and a spreading into both modes.

The string is not terminated in a symmetrical manner. I have not studied the physics of mode change in any detail.

[bbsailor]

Joseph,

Please consider this alternate explanation for your observation:
1. The pickup responds significantly to vertical motion only.
2. When you pluck mostly in the horizontal plane, you at first see little, but as the plane of vibration rotates, you pickup more vertical component.

Mike,

I agree. However, that is why I said "first few vertical cycles" to account for that elliptical normal rotation. The first few cycles tend to be dominated by the direction that the string was struck. This can be seen more easily on the low E string.

Joseph Rogowski

[Mike Sulzer]

Mike,

I agree. However, that is why I said "first few vertical cycles" to account for that elliptical normal rotation. The first few cycles tend to be dominated by the direction that the string was struck. This can be seen more easily on the low E string.

Joseph Rogowski

I am sorry I misunderstood what you said; I should have understood the first time.

Mike

[Mike Sulzer]

The Change in Flux from the Moving string, Constant Magnetization

The diameter of the string is smaller than the distance to the pole piece; small magnetic sources look much like dipoles independent of the details of how they are magnetized. Thus, one could say that this exercise is unnecessary: a dipole has a pattern broad in angle that falls of rapidly with distance. Therefore it is obvious that the variation in the change in field throughout the pole piece will be much greater from vertical than horizontal motion. But it is interesting to do the analysis and see that FEMM can only do the job very approximately.

If one were to use FEMM in its axial symmetric mode, the string would be represented by a small disk or washer. This is not very realistic. In the 2D mode, we have a rectangle (the pole piece) with a small magnetized circle (the string) over it. This corresponds to an end on view of a slice across a very long string with a pole piece under the whole length. When the string moves, the field through the pole piece changes, in a sort of semi-realistic way.

We can use FEMM to measure the flux (the field integrated along a contour). The contours run horizontal at various distances from the pole piece. The vertical component of the field is used in the integral since it is the component perpendicular to the windings. The results are shown in this figure: http://www.naic.edu/~sulzer/fluxChangeUpRt.png. The distance moved is 0.01 inch to the right or up. The horizontal motion has much less effect than the vertical motion.

So both effects (change in magnetization due to string motion, and the change in flux with constant magnetization) emphasize vertical motion. Also in both cases, horizontal motion is frequency doubling. It cannot produce the sound one hears, which corresponds to the fundamental and harmonics produced at the expected (not doubled) frequencies. Obviously there is a small amount of signal produced by the horizontal motion; as long as it is small the doubling has a small (but perhaps significant) effect on the sound. But even in the observation that Joseph described, the initial effect is not from horizontal motion alone.

[David Schwab]

I agree. However, that is why I said "first few vertical cycles" to account for that elliptical normal rotation. The first few cycles tend to be dominated by the direction that the string was struck. This can be seen more easily on the low E string.

There is also the "ping" from the initial attack which travels up the string and back again.

It's common when doing digital samples of acoustic instruments to loop the steady state waveform after the note attack settles down.

[bbsailor]

There is also the "ping" from the initial attack which travels up the string and back again.

It's common when doing digital samples of acoustic instruments to loop the steady state waveform after the note attack settles down.

David,

Bass players have made an art form out of controlling the string attack to create unique rhythmic and harmonic effects. The ear seems most sensitive to the character of the initial string attack.

Unfortunately, it is not easy to separate the ellipitical, cross section motion of a string to examine which motion creates the greatest output. Even a pure horizontal string motion, at it's limits, produces some vector change in distance between the string and the pole piece. But, the more pure vertical motion produces most of the measurable output.

Once a picked string settled down, it tends to loose its higher harmonics first due to these higher harmonics having less energy, and then it produces a sustained tone that remains rather constant until it fades out. When looping the acoustic tones, as you mentioned, loop points are chosen that represent that rather constant/steady harmonic sustain vibration period.

Here is an onservation about playing techniques related to string attack. Guitarist and bass player right hand (strumming or picking) techniques seem to produce a more player-identifiable-sound than the left hand note playing techniques. This seems to suggest a conscious (???) or unconscious (???) way to control string attack in a musically pleasing way. Any comments about this observation?

Joseph Rogowski

[David Schwab]

I agree that the attack portion of a plucked string is what gives the overall character of the sound. The steady state portion of the wave has a lot less harmonic information. This is why simply sticking a piece of foam under (or palm muting) the string creates a different tone.

A really neat playing technique I've done is to palm mute a picked note on guitar, and immediately remove your palm. You get the palmed pluck tone, and the regular sustain of the string. It almost sounds synthetic. On bass I find the direction you pluck the string has a bearing on the tone. Plucking the string sideways sounds a lot different from pulling it from the top. I've come up with a technique where I pluck the string with a sort of "rolling" motion across the top, near or over the fingerboard, and it has an acoustic bass sort of tone. So the angle you pluck the string seems to make a difference. This is probably done more on bass since many players use their fingers instead of a pick, and the strings are spaced farther apart.

I do agree with Mike's observation about the up/down motion being the main tone in a pickup. If for no other reason, the coil/core/magnet is arranged perpendicular to the top surface of the guitar. I'd wager if you put the pickup on its side facing the string (parallel to the top) you'd get more side-to-side motion picked up. I've always noticed pickups are more sensitive to metal objects (like screw drivers) moved toward them, then waved side-to-side over them, which makes sense

But I've also noticed that different shaped fields, not just in aperture width, but also in height, affect the tone. Just going from round rods to a blade changes the tone. Even if more rods are used so that they touch each other across the face of the pickup. If you have a tall field coming from the magnet, you will have more nearly vertical lines of flux which the sideways motion of the string will pass through. You see this with rod magnets. Humbuckers have a lower field that returns to the other pole quickly. With the flat topped Bartolini "shelf" you have a field with more lines parallel to the face of the pickup.. thus sensing less sideways motions.

Lace have also used "flux guides" as it were to manipulate the shape of the field. There was also the Melvin Lace (Adder) products where you stuck the combed metal thing on top of the pickup.

Call it "poetry" but these designs produce a different tone. Having used a '76 Bartolini Hi-A pickup for many years, which is based on his original patented design, I can attest that it doesn't sound like a regular humbucker.

This particular pickup only has two coils, arranged in a "normal" humbucker configuration, and one coil is wound about 1,000 turns less. So it's an easy pickup to copy, except for the planar pole tips (since I can't see what's inside the thing). My experiments with redirecting the field out the top of the coils shows that you can alter the overall tone of the pickup quite a bit. This is true of humbuckers and single coils. True, it may have a lot to do with widening the string sensing aperture, but it sounds different than simply increasing the distance between the two humbucker coils, or using larger diameter poles.

Incidentally one low tech (and fun) way to see the field over the pickup in 3D is to place the pickup in a zip lock plastic bag, and then sprinkle iron/steel filings on top. It has physical limitations in height of course, but it's nonetheless enlightening. I've been wanting to try it out with ferrofluid.