1. A method for interconnecting the signal outputs of K number of electrical sensors, also known as pickups, especially vibration sensors for the vibrating parts of musical instruments, in circuit topologies of J number of said sensors at a time, such that duplicate topologies with electrically equivalent circuits and vibrational outputs, also known as tonal outputs, also known as output timbres, are eliminated from consideration, comprising the steps of:a. designating categories of electrical circuit topology, as category (1), (2), . . . (J), such that category (M) is comprised of M of said pickups connected together, where 1?M?J, such that,

a.i. beginning with 1 of said pickups, designated as said category (1) with 1 member, constructing said category (2) with 2 members,

a.i.1. connecting 1 of said pickups in series with another 1 of said pickups, for one member of said category (2), and

a.i.2. 1 of said pickups in parallel with another 1 of said pickups for the other member of said category (2), and

a.ii. constructing said categories of (M) for M>2 by the same process of connecting lower-orders of said categories in series and parallel, such that, for (M)=(3), all the members of said category (1) in series and in parallel separately with all the members of said category (2), and such that, for (M)=(4), all the members of said category (1) in series and parallel separately with all the members of said category (3), plus all the members of said category (2) in series and parallel with all the members of said category (2), such that said category (M) is constructed by connecting said category (1) in series and parallel to all the members of category (M-1), and by connecting the members of said category (2) in series and parallel with all the members of category (M-2), and continuing until all the members of category (N) are connected in series and parallel with all the members of category (M?N), wherein N is an integer less than or equal to M/2, such that, (M)=(5) be constructed from (1)&(4) and (2)&(3), and such that (M)=(6) be constructed from (1)&(5), (2)&(4) and (3)&(3), and up, excluding duplicates of any previously constructed topologies for said (M)>(3), such that this method shall be extendable to higher complexities, and

a.iii. wherein each said topology of said category (M) may be deconstructed into t number of topologies of sub-categories, (Mi)=(M1), (M2), . . . , (Mt), such that M=M1+M2+ . . . +Mt, with 1?Mi?M, such that the members of each said sub-category (Mi), i=1, . . . , t, comprise of Mi number of sensors connected all in series, or all in parallel, between two nodes with no circuit branches in between, also called a basic topology, such that the order of placement in the circuit of said basic sub-category (Mi) of said individual members of said sensors, without reversing phase or connections relative to the other said sensors, makes no difference to the timbre or tonal quality of the output of either said sub-category or said category (M), such that a set of allowable topologies of said category (4) can be constructed of members with sub-categories (2+1+1), (3+1), (2+2) and (4), and such that the set of allowable member topologies of category (5) may be constructed of members, or versions, with sub-categories (2+1+1+1), (3+1+1), (2+2+1), (4+1), (3+2), and (5), such that the number of allowable unique circuits of that subcategory is limited to the product of versions, or members, times the combinations of sensors allowed by the basic topologies in each sub-category, so that such distinctions can be used to determine how many possibly unique tonal outputs can be obtained from each of said J=M sensors, constructing combinations of sensors rearranged in all circuit positions, subject to the limits of combinatorial math, such that this method shall be extendable to higher complexities,

a.iv. wherein the limit of the number of unique circuits from which K sensors can be constructed J at a time is less than or equal to the product of [K sensors taken J at a time] times the number of allowable sensor terminal reversals, NSGN, times the sum of [the products of the number of said versions of each sub-category of circuit topology times the allowable number of combinations of J sensors in each sub-category, as determined by said basic topologies],

b. constructing combinations of phase by switching in reverse said terminals of selected said sensors in each distinct topology, so that their phase relative to the remaining said sensors is inverted, producing a change in tone at the output, such that for a topology of said J number of said sensors there can be no more than 2J-1 different said combinations of said phase reversals of said sensors that produce potentially unique tonal outputs, constructed by taking one set of connections of said J sensors to be all in-phase, and selectively reversing said connections of said sensors until 2J-1 unique phases result,

b.i. in one method by successively reversing said terminals of all the said J sensors, for said J?2, in an ordered sequence of said combinations of said terminal reversals, by sets of (J said sensors taken i at a time), for i=0 to (J-1)/2 if said J is odd, and by said sets of (J sensors taken i at a time), for i=0 to (J-2)/2+1, and said J is even, limited to ((J-1) taken (J-2)/2 at a time) members in the last said set, such that

b.i.1. in the zero said set of said sensor terminal reversals, no said sensor is reversed, for said reversal combination set of one said member, and

b.i.2. in the first said set of said sensor terminal reversals, if said J?2, only one said sensor at a time is reversed, to the number of said J sensors taken 1 at a time, unless said J=2, then said single sensor reversal occurs only once, and if said J=3, then said single sensor reversals occur only 3 times, and

b.i.3. in the second said set of said sensor terminal reversals, if said J?4, 2 of said sensors at a time are reversed, uniquely, such that no pattern of said reversals is repeated, and said reversal continue to said J sensors taken 2 at a time, unless said J=4, then said sensor reversals of 2 each occur only 3 times, and if said J=5, then sensor reversals of 2 each occur only 10 times, and

b.i.4. so on, increasing the number of times said J sensors are reversed at a time,

b.i.5. until if said J is odd, then said pattern of said sensor reversal combinations is continued to said J sensors taken (J-1)/2 times, such that there are never more than 2J-1 of said reversals of any number of said J sensors taken any number at a time, and

b.i.6. if J is even, then said pattern of said sensor reversal combinations is continued to said (J sensors taken (J-2)/2), plus said J sensors taken ((J-2)/2+1 times), to the limit of said members of (J-1 sensors taken (J-2)/2 times), such that there are never more than 2J-1 of said reversals of any number of said J sensors taken any number at a time.