Excerpts from Provisional Patent Application Filed for Humbucking Quads
So KK number of humbuckers can have:
KK = 2, 3, 4, 5 humbucking pairs
2*KK = 4, 6, 8, 10 humbucking pair tones
KK = 1, 3, 6, 10 humbucking quads
16*KK*(KK-1)/2 =16, 48, 96, 160 humbucking quad tones
Total Tones = 20, 54, 104, 170
The number of single coil quads from K single coils can be expressed by:
Nqk = Summation of j = 4 to K: (K-1)*(K-2)*(K-3)/2, K > 3
And the number of quad tones is: 16*Nqk. This means that:
K = 2, 3, 4, 5, 6, 7, 8 singles
K*(K-1)/2 = 1, 3, 6, 10, 15, 21, 28 humbucking pairs
K*(K-1) = 2, 6, 12, 20, 30, 42, 56 humbucking pair tones
Nqk = 0, 0, 3, 15, 75, 135, 240 humbucking quads
16*Nqk = 0, 0, 48, 240, 1200, 2160, 3840 humbucking quad tones
Total Tones = 2, 6, 60, 260, 1230, 2202, 3896