Yesterday, June 7, 2017, I filed my second patent with the U.S. Patent and Trademark Office. It covers the math and circuit topologies necessary to determine how many potentially unique tones can be obtained with up to 8 pickups, and the switching controls necessary to obtain those connections with simplified controls to allows tones to be chosen without the musician ever knowing which pickups are used in what configurations. In other words, you’ll get a whole lot more choices and won’t need a map. It also distinguishes those tones which can be expected to be humbucking, either by combining dual-coil humbuckers, or matched single-coil pickups. The configurations can also be applied to other string vibration sensors, such as piezoelectric, optical, proximity, hall-effect, and magnetostrictive sensors, with 2- and 4-terminal outputs.
This will present some of the results of the math studies, showing the numbers of potentially different tones, both humbucking and not. The column on the right hand side of each Table shows the number of total configuration for combinations up to the sized of the number of pickups. In some of these tables, the number of possible tones has been reduced by the circuit configurations which circuit theory suggests are duplicates of others.
Table 1: Numbers of possibly unique tones for K (left column) pickups connected together J (top row) at a time, humbucking or not
| J | 1 | 2 | 3 | 4 | 5 | KT |
| K | ||||||
| 1 | 1 | 1 | ||||
| 2 | 2 | 4 | 6 | |||
| 3 | 3 | 12 | 32 | 47 | ||
| 4 | 4 | 24 | 128 | 464 | 620 | |
| 5 | 5 | 40 | 320 | 2320 | 8352 | 11,037 |
| 6 | 6 | 60 | 640 | 6960 | 50,112 | 57,778 |
| 7 | 7 | 84 | 1120 | 16,240 | 175,392 | 192,843 |
| 8 | 8 | 112 | 1792 | 32,480 | 467,712 | 504,104 |
Table 2: Numbers of possibly unique tones for KK (left column) dual-coil humbucking pickups connected together JJ (top row) at a time.
| JJ | 1 | 2 | 3 | 4 | KKT |
| KK | |||||
| 1 | 2 | 2 | |||
| 2 | 4 | 16 | 20 | ||
| 3 | 6 | 48 | 256 | 310 | |
| 4 | 8 | 96 | 1024 | 7424 | 8552 |
Table 3: Numbers of possibly unique tones for K matched single-coil pickups connected together in humbucking pairs, quads, hexes and octets.
| K | Pairs | Quads | Hexes | Octets | Sums |
| 2 | 2 | 2 | |||
| 3 | 6 | 6 | |||
| 4 | 12 | 33 | 45 | ||
| 5 | 20 | 165 | 185 | ||
| 6 | 30 | 495 | 568 | 1093 | |
| 7 | 42 | 1155 | 3976 | 5173 | |
| 8 | 56 | 2310 | 15,904 | 203,118 | 221,388 |
Notice that to get anywhere near “over 250,000” tones, as one guitar company claims, it takes at least 7 single-coil pickups in Table 1. And about 3% or less of those (Table 2) can be expected to be humbucking, and then only if the 7 pickups are matched respond equally to external AC fields. The rest of the combinations will pick up hum.
Furthermore, the useful space between the neck and bridge of a standard guitar is about 5.75 inches. This is about the size of 4.8 mini-humbuckers or 8 semi-standard single-coil pickups that are slightly redesigned to fit. At this spacing, the electromagnetic field of each pickup interferes with its neighbors. Coils which are close enough together are called “coupled” or “transformers”; transformers especially if they share a magnetic core, as many if not all humbuckers do. One might expect that this smears any tonal differences.
Dual-coil humbuckers have two coils that are not only magnetically entangled, but are separated by about the half-wavelength of vibration of the 32nd harmonic of the fundamental of a 25.5” base length string. So the two coils see essentially the same signal for most frequencies of interest, and combinations of single coils from different humbuckers should not be expected to have significantly different tones from similar connections of their humbuckers. So two humbuckers and a single-coil pickup would count more like 3 pickups, and a number of the possible connections shown in Table 1 would not be humbucking.
This is theory. Practice will be different, but cannot be expected to produce one to three orders of magnitude more tones than this. Unique switch combinations are not the same as unique tones. Distinct tones have to be proven with actual measurements of their spectral distributions, or at least the detection of beat frequencies. Guitar makers would be well-advised to be prepared to back up their claims.