This is a highly-modified Fender Squier Bullet ™ with two Allparts.com (p/n PU-6430-010) Hofner-style mini humbuckers (HB) with Alnico V magnets in Brazilian Cherry mounts. The blue polygon on the right side of the white pick guard obscures the patent pending switching and tone control system, which offers 20 different combinations of the two HB. Measurements of parallel coil resonance indicate that the inductance of the HB coils varies with frequency, on the order of about 1.2 Henry per individual coil (standard deviation of about 0.29), with a coil capacitance of about 0.11 nF, and a coil resistance (the least important parameter) of about 3000 ohms.

## Method of Measurement

There are 20 different switch combinations in this Patent Pending dual-HB system. The FFT analysis software, SpecAn_3v97c.exe (About image below), provided FFT spectral analysis with the following setup parameters:

Amplitude scale = 135 dB, zero-weighted

Frequency scale = Logarithmic

Visualization = Spectrograph with Average

Sample rate = 44.1 kHz

FFT size = 4096 samples

FFT window = Hann raised cosine (“Hanning”)

The guitar was connected to the front panel microphone input of a Dell Optiplex 755, running Windows 7. After starting the software, all six guitar strings were strummed six times using a rubber eraser for a capo, in the order of fret 0 to fret 5. This provided a fuller band of frequencies (fewer peaks and valleys in response) for the FFT software to analyze than just strumming the six strings without fretting them. A brief experiment in strumming frets 0 to 5, then frets 5 to 0, then up to 5 and down to 0, demonstrated mean frequencies (explained below) for one switch setting of 783.1 Hz, 775.1 Hz and 802.5 Hz. So the measurement error is taken to be on the order of about plus or minus 20 Hz.

The SpecAn software can export the averaged spectral plot of dB output versus frequency to the Window Clipboard, where it is pasted into Wordpad, then saved as a text file with a *.csv file extention. This was then imported into Excel 2002 SP3. SpecAn data comes in two columns, Freq (Hz) and Ave dBFS (which runs from clipping levels down 135 dB). Typically, the Ave dBFS data is averaged over more than 250 windows of 4096 digital samples of guitar output, with a frequency resolution of about 11 Hz.

The spreadsheet converts dBFS to linear voltage (Lin V) by the formula 10^{dB/20}. Dividing the column by its sum produces the probability density function of frequency, Pv(f). The sum of the Pv column in the spreadsheet always equals 1. The cumulative sum of frequency, f, times Pv equals the mean frequency of the output, Mean-f. The spreadsheet also calculates the square root of the 2^{nd} moment of frequency and the cube root of the 3^{rd} moment of frequency, but those are not presented here.

## Results

The plot below shows the mean frequency of each switch setting, ordered by increasing frequency, going from 801 Hz to 2052 Hz, a range of about 1.36 octaves, or about 16 frets.

Since the frequencies of the strings run for standard tuning from 82.4 Hz for the fundamental of the 6-string to 659.2 Hz on the 12^{th} fret of the 1-string, these numbers all seem a bit high. Other than the fact that guitar strings have a lot of harmonics, I have no explanation.

Note that before the 500k audio-taper volume pot was added, the measured mean frequencies ran from about 407 Hz to 704 Hz. In the cases of those measurements, the strings were strummed five times per switch setting without fretting the strings. The changes are puzzling, but consistently different.

It is possible that SpecAn has a systematic measurement or calculation flaw, which I cannot verify, not having written the software. However, the Fast Fourier Transform (FFT) is linear, and any linear error can be calibrated out. For the purposes of this discussion, we will take the results as being relative.

One can see, for example, that there are several switch positions that are effectively equivalent. The first two, show 801 and 808 Hz; next up we see 907 and 907 Hz. The 4^{th} and 3^{rd} from the top are 1571 and 1572 Hz. That means that only 17 of the 20 switch combinations are potentially different.

The gray circles and triangles show the equivalent 3-way switch results. 3-way switches on dual-humbucker guitars typically produce outputs of the bridge HB, the neck HB and the two in parallel. The circles show the mean frequencies for the individual HB coils connected in series. The triangles show the HB individual coils connected in parallel. The order of mean frequencies in both cases is: neck HB, neck & bridge combined, and bridge HB.

If the neck and bridge HBs had equivalent outputs, we should expect the combo to have the lowest mean frequency. These do not. Note that the neck and bridge HBs in this case are the same model and that the bridge HB has only 70% of the output of the neck HB, likely due to the reduced movement of the strings. In this case, the HB vertical adjustment screws were too short to move the neck HB far enough from the strings to equalize the outputs. On many dual-HB guitars, the bridge HB compensates with more turns on its coils, and produces a higher output than the neck HB. Live and learn.

## Conclusions

Taking the measurements in this case as relative, it is possible to obtain a much wider and more finely divided range of tonal output from a dual humbucker guitar than with the standard 3-way switch. Designs (not presented here), using the same approaches for a triple humbucker guitar switching system suggest a tonal range that is more finely divided, if not extended, by a factor of 10 or more.

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