Welcome to part 3. Let us again recap the theories we are testing:
theory 1) (mostly true) – the shape gives more inductance and DCR per turn, which makes for a lower resonant frequency with a lower Q value
theory 2) (partially true) – the additional length of wire used creates a greater capacitance, which shifts the resonant frequency
theory 3) (conditionally true or false) – a wider coil senses a wider string area, which sounds warmer/fatter
In part 1, we tested theory 1 and determined that a shorted+wider coil is a more efficient shape in terms of inductance-per-turn, and less efficient in terms of DCR-per-turn, so an equal number of turns with a shorter+wider shape will result in a frequency response has a with a lower resonant frequency, as well as a flatter frequency peak (lower Q), and a lower high-frequency cutoff: this mostly validated theory 1 as the primary mechanism behind the darker tone… but it is not the complete picture.
In part 2, we tested theory 2 and determined that a shorted+wider coil has greater winding-Capacitance, which has a slight effect on the frequency peak and high-frequency cutoff: this mostly invalidated theory #2 as the primary mechanism behind the darker tone… but it does have a slight effect.
Test #3 – string-sense area:
This theory is fairly widely-held, and for a seemingly valid reason: we know that part of what makes the average humbucker sound ‘darker and fatter’ than the average single coil is because we have 2 sets of poles, sensing two separate areas of the string, resulting in a comb-filter cancellation at regular nodes which are determined by the aperture of the poles (you can simulate this on Tillman’s famous simulator: http://www.till.com/articles/PickupResponseDemo/ which is not 100% accurate, but it can represents the general trends); and since this is the case, people assume that a wider coil will have the same effect.
Unfortunately it is not ALWAYS the case that a wider aperture = a darker sound. I will break this down into JUST the coil, and then examine it again with respect to the poles.
There are a few assumptions built into the belief that a wider coil = a fatter sound:
- Firstly, it assumes that the coil is doing a significant amount of sensing compared to the pole-pieces.
- Secondly, it also assumes that a coil sensing the string relatively evenly along a given length of string is the equivalent of integrating the signal from several poles along a given length of string.
- Thirdly, it assumes that a trend holds true when extended beyond the “normal” size parameters.
These assumptions likely arose from the obvious tonal differences between common pickups like comparing narrow single coils (like a strat or tele) and a wider single coil (like P-90), and also comparing a narrower humbucker (like a mini-humbucker) to a wider humbucker (like a standard PAF shape). Anyone who has played those pickups is well aware that theory #3 SEEMS to hold true, BUT listening to a pickup as a unified system which includes the poles, magnets, shape, metalwork, etc… and then trying to extend that logic to a the sound of a single component (like the width of the coil) is quite simply the fallacy of ‘composition/division’, and possibly a few others as well: the whole does not necessarily extend to each part, and it is QUITE possible for a pickup to be darker even if a constitute component would — all else being equal — produce a brighter sound, if that effect were swamped by the combined effects of other components. For example, we already know that our shorter+wider coil shape produces more inductance and capacitance, and that increasing the inductance in our tests effected the resonant frequency about 10 times more than increasing the capacitance by the same factor, so even if we dropped the capacitance while increasing the inductance, the coil would still sound warmer/fatter.
What I actually found in testing the coils is that the effect varies. Here are 2 tests to illustrate.
These tests were run with 5 different coil types, in several different positions along the string:
-Coil1 = very tall and very narrow, with very thin coil depth (think half of a dual-rail single-coil)
-Coil2 = somewhat tall and narrow, with thin coil depth (think tall single-coil)
-Coil3 = medium height and medium, width with slightly taller coil height:depth ratio (think 1 standard humbucker bobbin)
-Coil4 = somewhat short and wide, with square coil height:depth ratio
-Coil5 = very short and very wide, with short and wide coil depth ratio (think P-90)
Each coil was tested in 2 orientations: with the string bisecting the narrow dimension, and the string bisecting the wide section. This is the result of the tests of those coils using no core material, and round neodymium magnet. The magnet was the same distance from the strings in each test, as was the top of the coil:
-COIL1: wider sense area sounds DRASTICALLY FATTER
-COIL2: wider sense area sounds SLIGHTLY FATTER
-COIL3: wider sense area sounds DRASTICALLY THINNER
-COIL4: wider sense area sounds SLIGHTLY THINNER
-COIL5: wider sense area sounds SLIGHTLY THINNER
So in terms of JUST the coil+magnet, the trend seems to support the original theory (in terms of width of coils with the same height) for the dimensions that I used: for a taller coil, moving to a wider sense area fattens up the sound; for a shorter coil, moving to a wider coil thins out the sound. The more extreme the shape, the greater the effect (as I saw when moving from the very thin coil to a thicker coil, and the moderately thin coil to a thicker coil). I would like to study this more, but it is enough to see that the trend of wide=fat does not hold true across the board as the harmonic cancellation becomes more chaotic.
The previous test showed the trend of wide vs narrow compared to the orientation of a coil (i.e. height and depth was the same, but rotated 90 degrees). So I ran an additional test, matching the number of turns, and keeping the resonant peak outside the typical guitar frequency range (so the response would be flat from one coil shape to another in the range that we are concerned with), and the results were similarly all over the map depending on the particulars of the shape, further illustrating that the wide=fat hypothesis does not hold true across the board. The trend was that a wider coil produced a thinner sound, unless the narrower coil was particularly narrow, or if the wide coil was particularly wide… in which case the opposite happened.
The conclusion to this test is what we might expect for coils with a relatively-even sense area across the coil: since we are sensing a great number of points along the string, depending on what harmonic nodes on the string are encompassed, we have cancellations which made produce any range of timbres: from bright to fat to thin, etc, and we cannot break the argument down to a simple ‘wide vs narrow’ debate since the traditional wisdom is false as much as it is true.
OKAY, lets move from the coils to the poles to see what else is happening here.
I placed high-permeability cores in each of the coils from test A, and re-ran the tests. What happened was that the effect was still there, but it became much less noticeable, leading me to conclude that ALTHOUGH the coil itself DOES still contribute sensing the string (that is, coupling with the string) even with pole pieces channeling the flux mainly through a higher density in the center of the coils, the effect of the core is much more pronounced, and makes a greater contribution to the overall sound (magnetically-speaking). Here is a 1 min video so that you can hear the difference:
I can only assume that the pickup’s leaky flux paths manage to still encompass the coils, which is not completely swamped by the effect of the cores. Also as expected, alnico cores’ effect fell between the air-core and steel-core results, which makes sense since their lower permeability directs the flux less-well.
Here is a short video with sound samples of one of the above coils (either Coil4 or Coil5… don’t remember which) with both air-core and steel-core, in both wide and narrow configuration. Hopefully this puts the sound into perspective:
I actually used this concept lately in a design where I was pretty happy with the output and midrange of a pickup, but wanted to add a bit of attack, so widened the aperture and fiddled with the pole pieces until I got a response that I was happy with:
Here is another example. For this test, I wound flat-response coils to prevent the resonant peak from muddling the results, and then I plotted the response of the open low string at various apertures. The distance is measured from center-to-center of the .125″ poles. I positioned the center point of each test around a point that represented the center of the pickup face:
To help show that is happening here, I categorize the most ‘important’ frequencies like this (WARNING: this is very subjective and just how I hear/describe it, but hopefully this is universal enough to get the point across):
- ~1kHz-2kHz = woodiness/honkiness/nasliness/clang:
A peak in the lower portion of this area sounds woody and thick, but can get muddy. A peak in the middle part of this area sounds honky and a bit nasal, like a way pedal. A peak in the upper part of this area can sound clanky and nasal if it is overdone. A DIP in this area can sound distant or scooped, depending on where, how much, and how wide.
- ~2kHz-3kHz = presence/smoother-highs:
A peak in the lower half of this area sounds more open, but still midrange and with a presence thrust. A peak in the upper hand of this area starts to sound more wide and bright/clicky/jangly. Cutting here will push the tone back, and sound less in-your-face at the risk of sounding a bit sterile or hi-fi if it is overdone.
- ~3kHz-4kHz = clicky-highs:
A peak in this area sounds clicky, and emphasized the sound of the pick hitting the string. As you move up toward 4kHz, the click becomes more harsh and scratchy. Cutting frequented here makes the ‘click’ sound more like a ‘tick’, and can emphasize the scratchiness of the frequencies above it if you are not careful.
- ~4kHz-5kHz = scratchy-highs:
A peak in this area emphasized the sound of the scrap of the pick on the wound strings. It also sounds very bright (approaching shrill at higher frequencies) and aggressive. A cut here can get rid of the pick noise while still preserving attack and snap if the width is not enough to cut out the frequencies in the previous range.
- ~5kHz+ air/sparkle/rattle/noise:
Once you get beyond the pick scrape zone, the sound in this area is mostly fret rattle, buzz and noise, but it does contain the upper harmonics of your signal, the ‘airy’ highs, and the ‘upper-twang’… so it’s not all bad.
From a listening test, I would categorize the sound of each sample from the above graph as:
green = punchy and fat with a nice snap and no scratchiness
blue = still punchy and fat, but more aggressive, a stronger attack, and more pick scrape
orange = not as aggressive/edgy, less nasaly and more throaty, with a lot of pick and finger noise
purple = wide, throaty, scooped, and a bit hi-fi with scratchy highs… it had sort of like a baritone-guitar sound
Since we determined that A)the shape DOES have an effect, but that the effect does NOT always hold consistently as a relationship of width, and that B) the poles dominate the sound and sense-area in relation to the raw coils, then we should take a look at how the distance between two POLES — on the same coil, long the length of the same string — effects the sound. It became very obvious (after I made about 30 frequency graphs) that it would be easier to explain this via the medium of audio/video, so here is a 15-min video detailing the results of test D (NOTE: the aperture measurements in the video are from center-to-center of the poles i.e. they do not represent the magnetic window, just the physical layout). Also, note that this is for a single coil, so it does not take into account any cancellation from the interaction of the two coils in a humbucker:
Bear in mind that this example uses multiple-poles, in the same coil, along the length of the string, but the effect is also true of the shape and size of a coil with a single pole-piece. Here is an example of a single 1/8” pole piece vs a single 1/4” pole piece in a single-coil pickup.
Here is a video that I made which shows the evolution of the response curve as we change the aperture (warning, it is a bit long):
Here is a slew of graphs from the above tests to illustrate the effects visually.
Here is a graph of our mini(tall+narrow) vs (short+wide) without pole pieces. You can see that while there IS some cancellation of the treble harmonics in the wider coil — which would indicate a warmer sound — but there is also cancellation in the lower frequencies and not in the upper-mids, so the sound will be thinner and more nasal-y (think of a kinda lo-fi telephone type sound) moving from the tall+narrow to the short+wide without pole pieces in this instance:
Here is exactly half a strat coil, with an alnico pole piece in the middle. You can see that the longer orientation is still brighter than the narrower orientation:
Here is Coil4 from the test. You can see that there is little difference:
Here is coil2 from the test, with a tensioned string being excited at it’s resonant frequency. You can see that there is a decent amount of higher frequency cancellation, but not too drastic (ignore the 60Hz spike, that is just noise):
Conclusion of TEST #3 – string-sense area:
The theory that ‘a wider coil senses a wider string area, which sounds warmer/fatter’ is only true within a certain window (for example, between zero and roughly standard-humbucker width), but outside that window (i.e. moving to a wider humbucker aperture and beyond): the effect begins to reverse, and the frequency nulls also shift around depending on frequency, amplitude, and wavelength of the harmonics being sensed along the string, which can also cause cancellation in various frequencies (for example: if we cancel lows or mids more than highs) in addition to effecting the highs.
This complicates the matter since we can end up with not just the wider=warmer result or vice-verse, but also wider can = scooped (if we cancel mids, but not highs and lows), or wider can = thinner (if we cancel lows and/or lower-mids), or any other spectrum of timbres, depending on the particulars of the coil, string, scale-length, position, etc. Coil winding height also seems to effect the degree of the effect, as well as the length of the magnetic path, and core material.
OVERALL CONCLUSION ACROSS ALL 3 BLOG EXPERIMENTS:
If there is one thing we have established, it is that the timbre of a pickup is a complex and inter-related relationship between components, parameters, and geometry: some have greater effect and some have lesser effect, but there are many many factors to bear in mind, as well as a thousand thousand variations to experiment with and try out yourself. In terms of potential contribution to the difference in tone between a tall+narrow coil and a short+wide coil, the experiments put inductance on top, and DCR and winding-capacitance on the bottom. Winding capacitance is also the least relevant in relation to external factors.
Coil-only sense window area has a bit of effect (especially if you are using an air-coil or alnico pieces), and aperture CAN have a great effect (especially if you are using multiple steel pole pieces), but bear in mind, that the pole aperture in the video uses multiple-poles in the same coil along the length of the string. This pertains more to humbuckers, and although it DOES exist in single-coils, more commonly we will be considering, in that case, the aperture of the actual pole piece face, which is a lesser effect: although potentially greater effect than winding-capacitance if considering the difference between… say… a .112” hex-screw pole and a quarter-pound-like .25” slug, or between a thin 1/16” pickup blade and a fat 1/4” blade (just as a few examples), and also how the shape and size of the pole head spreads the magnetic flux before it hits the string… which will obviously have less effect than going from a 1/8” aperture to a 1.25” aperture in a humbucker, but it will still be noticeable.
Here is a graph of a single coil with thin vs wide pole pieces:
If I may be so bold as to toss some conjecture out there… the experiments in pole aperture may also help explain a part of why pickups like, for example, side-by-side dual rail single coils and hum-cancelling P-90 designs can match the electrical parameters and sweep response curve of the originals so closely, and yet miss the mark in terms of tone.
But regardless, I’ll pump as much free info out there as I can to try to stimulate some lateral thinking. This is a wonderful area where science and music hold hands, and it brings me much joy to play around in it. Hopefully some of the information here will spark that desire in other people, as well as clarify some dubious old-timey beliefs. And as always, don’t take my word for any of this… try it out yourself! Also, it is quite possible that I have overlooked some other aspect, or used sub-optimal testing methodology, so as always: test it yourself.