Low/medium/high ranges for bode plot and other parameters

[timtam]

I was recently reading Wacker's 2019 article on 'outlaw' pickup parameters (his term) in Premier Guitar - inductance, resonant peak frequency, and Q factor. Some good stuff, but not all of it is the most straightforward piece of writing for that audience, especially regarding Q. And although he mentions the importance of measurement conditions, he doesn't define the loading conditions under which the parameter values/ranges he quotes were measured.
www.premierguitar.com/mod-garage-exploring-outlaw-pickup-parameters

But it did make me think ... what are "typical" low/medium/high ranges of values for the bode plot's parameters, and other parameters, recorded under standard conditions ? For the bode plot, those conditions would be the commonly-used/agreed, realistic loading of 470 pF/200 kOhm. Having the low/medium/high ranges would help in placing any new pickup under consideration in the context of its peers. And also add to the existing understanding of how particular physical features position their pickups within the range of measured values.

I couldn't think of a resource I'd seen that already describes those ranges (if there is one, what is it ?). I was going to ask the question here as to what people judged the ranges to be, but then I realized I could compute ranges myself from available data, that is, antigua's comprehensive pickup test database at:
www.echoesofmars.com/pickup_data/viewer/
I focussed on the data for resonant frequency (at 470 pF/200 kOhm loading), inductance (at 120 Hz), capacitance (at 100 kHz), and DCR; there is more data there, but no Q data.

antigua's database currently contains data for about 80 HBs, 180 strat pickups, and 80 tele pickups. There are not enough P90s, jaguar, or jazzmaster pickup types there to calculate meaningful ranges. I did not attempt to divide tele pickups into bridge and neck (I may do that later); nor was there any distinction made for any nominal placement description within the other 2 pickup categories. I also did not check the database for any "unusual" pickup designs within a pickup category that might have atypical data values. Instead, possible "outlier" values that might distort the true picture for the range of "most" data were dealt with via quartiles/'box and whisker' plots, discussed below; all 4 data types had some outliers. So please excuse any apparent statistical complexity - that was necessary to understand the distribution of values. I will try to explain it clearly for anyone interested in the minutiae. If you're not interested in that detail, just look at the values for each range - "low", "medium", and "high".

I decided on the following quartile-based definitions for "low", "medium" and "high" ranges for each of the 4 parameters. All ranges were calculated using inbuilt Excel functions.

Specifically ...

LOW range - the lower ~25% of the individual data values. From the lowest NON-outlier value to the 1st quartile value.
MEDIUM range - the middle 50% of the values. From the 1st quartile value to the 3rd quartile value ('inter-quartile range', IQR).
HIGH range: the upper ~25% of the data values. From the 3rd quartile value to the highest NON-outlier value.
Average - the median value (more robust that the mean value in the face of outliers) - the middle value of the data set, ie that divides the data set into two (50% of data values are lower, 50% higher).

The quartiles on which the ranges are based are a nice way of conveying the distribution of data in a simple, unbiased, representative way (often more so than the mean average and standard deviations). A 'box and whisker' plot is the usual way of displaying such data. For those unfamilar with such plots, the boundaries of the central "box" are the 1st and 3rd quartiles - the 25th and 75th percentiles. The box span between those quartile boundaries thus contains 50% of all values - by my definition, this is designated the "medium" range of pickup data values here. The line through the box is the median average. The ends of the 'whisker' lines show the furthest ACTUAL data values that are WITHIN limits designed to exclude outliers in such plots (lower outlier limit: Q1-1.5*IQR; upper outlier limit: Q3+1.5*IQR). All individual outlier data points that fall OUTSIDE those whisker limits are also shown. If you are particularly interested in the pickups that have those extreme high or low values, you can look up those particular displayed values in antigua's database to find those pickups. I could have added 'very high' and 'very low' categories for those outlier values, but elected not to. Since the whisker limit values are the smallest and largest actual data values that are NOT deemed outliers, "almost all" data thus lies between the whisker limit values (if normally distributed, > 99% of values would lie within those outlier limits). The max and min values can be seen on the plots too, and are tabulated below with the median and ranges.

If you see any errors, or have any other suggestions, please let me know. Would also be good to hear how these ranges correspond to peoples' perceptions of what they thought the ranges might be for pickups in general, and particular pickups specifically.

[antigua]

Your number match close with what I had in my head. I think you have to differentiate between neck and bridge for the Telecaster specifically, because unlike other guitars, it has two different pickups constructions for the two pickups, and so they tend to be very different, where as bridge and neck Strat and BH style pickups tend to be pretty close, unless it's a "high gain" set, where the bridge pickup in particular is wound to a much higher inductance than the neck pickup. 

There's a couple big problems with the "PAF style" HB data in my data set, but not so much with others, and that's the mix and matching of pickups with two and four conductor wire, which yield difference capacitances per a given length, and because it's not easy to detach the wire from the humbucker, I never do, so the capacitance always varies somewhat based on that. In general it's around 70pF, which is higher than the capacitance of the pickup itself, so it comes out to 120pF, 70pF will be the hookup wire, 50pF is the actual pickup, and the reason it's so low is because it's wired in series, and if you wire it in parallel the capacitance becomes remarkably higher. I should have documented the type of lead wire but I didn't, although I could probably do that by just looking at the pictures. It's almost always four conductor unless it's a vintage replica, such as Seth Lover set. 

The other big PAF style HB problem is some have covers, some don't, and that also affects the Q. Worse still, different covers impact the Q factor to different degrees, even aside from whether they're nickel silver or brass material. The thickness and exact makeup of the alloy layering in the metals cause the Q to be a little higher or lower than you mighty expect. For example, I'm noticing gold plated covers tend to associated with higher eddy currents than chrome plated, on average. Ideally I'd always remove the cover, or measure with and without, but that's not just a hassle, but if someone looks at the solder spots and sees that the cover of a pickup has been removed at some point, that also reduces it's resale value to some extent. 

The good news is that the capacitance and the Q factor are relatively stable for a given type of pickup made with the same materials, where as the inductance is heavily dependent on how many wraps of wire were put on the bobbin, which of course can vary widely, so if you know the inductance of a pickup, you can lay that against average Q and capacitances for that class of pickup, and create a practical and usable bode plot, and it's easy to gather the inductance of a pickup with an LCR meter such as the DE-5000. Also a lot of pickup makers, such as TV Jones have provided inductance values on their website which agree with what I measured with my own LCR meters. 

[timtam]

I got around to separating the tele neck and bridge pickups in the data from the echosofmars database - the new table and the quartile-based 'box and whisker' plots are below. Only the tele data has been changed. The separate tele pickup plots do show some interesting relationships not only between those two tele pickup types, but also the comparisons with HBs and strat pickups; for example, the typically-higher resonant frequencies of tele neck pickups compared to tele bridge pickups.

To reiterate from my rather long post above for those who may not have read it, the top and bottom boundaries of the plot 'boxes' represent 50% of all the values, with the top boundary being the 75% value (3rd quartile) and the bottom boundary being the 25% value (1st quartile) - this range is designated the 'MEDIUM' range of values - more definitions below. The line through the box is the median average value (2nd quartile). The data extent between the top/bottom 'whiskers' in the plots includes around 99% of the values (if the data were normally distributed). The labelled values outside the whiskers are 'outlier' values. This style of plot gives a more accurate representation of the data than simple means and standard deviations, which can be distorted by outliers.

In the table ...
LOW range - the lower ~25% of the individual data values. From the lowest whisker (NON-outlier) value to the 1st quartile value (bottom of box).
MEDIUM range - the middle 50% of the values. From the 1st quartile value to the 3rd quartile value ('inter-quartile range', IQR).
HIGH range: the upper ~25% of the data values. From the 3rd quartile value to the highest whisker (NON-outlier) value.

Apologies for the table being a JPG (which makes it hard for anyone to cut and paste the numbers if they wants to use them). I tried everything I could to paste as a formatted text table direct from Excel, but the board didn't like it (it allows you to create a table here, but it appears that the data then has to be manually entered).

As antigua clarified above, the capacitance values especially in HBs can be dominated by the hookup wire capacitance in some cases (esp 4-conductor), which helps explain the outlier values. The capacitance data is also based on fewer pickups (N now shown for each measure).

antigua do you have Q data on (m)any of these pickups ? If not is there a reasonable way to estimate/calculate it from the other data ? Could you estimate Q from your bode plots ?

[antigua]

It's interesting to see what was intuitive confirmed with a graphical representation. The spreads of the loaded resonant frequencies are all similar in size, even though the more basic measurements are all over the place, showing that guitarists  seem to have a certain tolerance range for brightness or darkness in a given type of pickup.

AFAIK nobody (maybe Manfred Zollner did and I haven't seen it) has determined exactly why lower resonant peaks are favored with PAF's (and/or P-90's) as compared with Fender Strat or Tele single coils. In general, when a PAF has a loaded resonant peak closer to 4kHz, it's perceived as too thin sounding.  There's some degree of difference in timbre with two coils instead of one, and it could be that the preference for lower frequencies with PAFs is because the lower frequency compliments that timbre somehow. It could also be as simple as there being an expectation that when you see a larger pickup, that it should produce a darker, louder sound, and vice versa. The fact that P-90s are single coils also, and tend to be preferred with a lower resonant peak like a PAF, also suggests that expectation is at play. It could be a combination of both expectation and timbre. It's interesting that guitarists are happy to put PAFs in Fenders, but almost never put Fender single coils into guitars that traditionally featured a P-90 or a PAF. To really get to the bottom of that would require capturing audio of the different pickups and carefully comparing the FFT analysis to see how they differ, but that's rather difficult to do, much harder than making bode plots.