Patent Grant
10380986
This application is related to the use of matched single-coil electromagnetic pickups, as related in U.S. Pat. No. 9,401,134B2, filed 2014 Jul. 23, granted 2016 Jul. 26, in U.S. NP patent application Ser. No. 15/616,396, filed 2017 Jun. 7, in U.S. Provisional Patent Application No. 62/522,487, filed 2017 Jun. 20, in U.S. Provisional Patent Application No. 62/569,563, filed 2017 Oct. 8, in U.S. Provisional Patent Application No. 62/711,519, filed 2018 Jul. 28, and in U.S. NP patent application Ser. No. 15/917,389, 2018 (exact filing date subject to granting of petition) by this inventor, Donald L. Baker dba android originals LC, Tulsa Okla. USA.
Other than for confidential and/or necessary use inside the Patent and Trademark Office, this authorization is denied until the Non-provisional Patent Application is published (pending any request for delay of publication), at which time it may be taken to state:
The entirety of this application, specification, claims, abstract, drawings, tables, formulae etc., is protected by copyright: © 2018 Donald L. Baker dba android originals LLC. The (copyright or mask work) owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all (copyright or mask work) rights whatsoever.
This requests that this NPPA not be published prior to the granting of the patent.
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This invention primarily describes humbucking circuits for odd numbers of matched electro-magnetic string vibration pickups, as used in guitars and basses, also applicable to other musical instruments with ferrous strings, in which each pickup responds equally to external electromagnetic fields, otherwise known a hum; it can also apply to other types of vibration sensors, placed in other manners on other types of equipment which sensors exhibit substantially similar bipolar response to desired and detected signal and to unwanted external electric or magnetic interference.
Single-Coil Pickups
Early electromagnetic pickups, such as U.S. Pat. No. 1,915,858 (Miessner, 1933) could have any number of coils, or one coil, as in U.S. Pat. No. 2,455,575 (Fender & Kaufmann, 1948). The first modern and lasting single-coil pickup design, with a pole for each string surrounded by a single coil, seems to be U.S. Pat. No. 2,557,754 (Morrison, 1951), followed by U.S. Pat. No. 2,968,204 (Fender, 1961). This has been followed by many improvements and variations. In all those designs, starting with Morrison's, the magnetic pole presented to the strings is fixed.
Dual-Coil Humbuckers
Dual-coil humbucking pickups generally have coils of equal matched turns around magnetic pole pieces presenting opposite magnetic polarities towards the strings. Lesti, U.S. Pat. No. 2,026,841, 1936, perhaps the first humbucking pickup, had multiple poles, each with a separate coil. Lover, U.S. Pat. No. 2,896,491, 1959, had a single magnet providing the fields for two sets of poles, one for each string, with a coil around each set, the pickup design which most modern humbuckers use. These have been followed by a great many improvements and variations, including: Fender, U.S. Pat. No. 2,976,755, 1961; Stich, U.S. Pat. No. 3,916,751, 1975; Blucher, U.S. Pat. No. 4,501,185, 1985; and Knapp, U.S. Pat. No. 5,292,998, 1994;
Humbucking Pairs
Nunan, U.S. Pat. No. 4,379,421, 1983, patented a reversible pickup that could present either pole to the strings. But the patent only mentions rotating the middle pickup of three to produce two humbucking pairs with the neck and bridge pickups, using a 5-way switching system. It does not present a humbucking pair made with the neck and bridge pickups. Fender, U.S. Pat. No. 4,581,975, 1986, may be the first to use the term “humbucking pairs” (column 2, line 31), stating in column 2, line 19, “Thus, it is common for electrical musical instruments to have two, four or six pick-ups.” Yet, in the 3-coil arrangement of his patent, with the middle pickup presenting North poles to the strings and the neck and bridge pickups presenting South poles to the strings, he did not combine the signals from those pickups to form humbucking pairs. Instead, he added dummy pickups between them, underneath the pick guard (
Commonly manufacture of single-coil pickups are not necessarily matched. Different numbers of turns, different sizes of wires, and different sizes and types of poles and magnets produce differences in both the hum signal and in the relative phases of string signals. On one 3-coil Fender Stratocaster (tm), for example, the middle and neck coils were reasonably similar in construction and could be balanced. But the bridge coil was hotter, having a slightly different structure to provide a stronger signal from the smaller vibration of the strings near the bridge. Thus in one experiment, even balancing the turns as closely as possible produced a signal with phase differences to the other two pickups, due to differences in coil impedance.
A previous patent (U.S. Pat. No. 9,401,134, 2016, Baker), which supports this invention, used the concept of humbucking pairs and switching systems for four single-coil electromagnetic pickups with coils of equal turns. Baker modified standard single-coil pickups, adding turns until four single-coil pickups have a reasonably equal response to external AC fields, and shocked the magnets of two of them, with a stronger rare-earth magnet, to reverse the poles, providing two matched pickups with North poles toward the strings (N-up) and two matched pickups with South poles toward the strings (S-up). Limited to two 4P5T lever switches, that system had no out-of-phase, or contra-phase, humbucking pairs, but four humbucking pairs and one humbucking quad of parallel-connected pickups on one 5-way switch, and four series-connected pairs with a series-parallel connected quad on the other 5-way switch.
The NP patent application Ser. No. 15/616,396 (Baker, 2017), Humbucking switching arrangements and methods for stringed instrument pickups, extended this invention to humbucking quads, hexes, octets and up, as well as the special case of a humbucking triple. It makes clear that that any electronic switching system for electromagnetic sensors must know which pole is up on each pickup in order to achieve humbucking results. The NP patent application Ser. No. 15/917,389 (Baker, 2018), Single-Coil Pickup with Reversible Magnet & Pole Sensor, presented embodiments of single-coil pickups with magnets that could be removed and reversed, providing as well a signal for the state of the reversal.
For two matched pickups, the humbucker connections, either series or parallel, must be contra-phase if they have the same poles up, and in-phase of they have different poles up. For K number of matched pickups, this makes possible K*(K−1)/2 pair combinations, regardless of poles or series-parallel connections. For example, for four matched pickups A, B, C & D, the unique pair combinations are AB, AC, AD, BC, BD and CD, or 4*3/2=6. If they all have the same pole up, i.e., (N,N,N,N), then all the combinations are contra-phase, and moving any pickup to any other position has no effect. If they have one pole different, i.e., (N,S,S,S), then that pole can be moved to 4 different positions. If they have 2 poles different, i.e., (N,N,S,S), then those poles can be placed uniquely only as (N,N,S,S), (N,S,N,S) and (N,S,S,N), since reversing the poles, i.e., (S,S.N,N), (S,N,S,N) and (S,N,N,S) produce exactly the same in-phase and contra-phase humbucking pair combinations. This total 8 different pole configurations. (See also, https://www.researchgate.net/publication/323686205_Making_Guitars_with_Multiple_Tonal_Characters)
It turns out that if the pickup poles are reversible, for K number of pickups, there can be 2K-1 different pole configurations, each configuration producing K*(K−1)/2 humbucking pairs, each configuration producing K*(K−1) potentially unique humbucking tones, if both series and parallel pair connections are considered. But all the pole configuration have some common tones. There can be only 2*K*(K−1) potentially unique humbucking tones from the 2K-1 different pole configurations. For 5 pickups, this is 16 different pole configurations, with 20 potentially unique humbucking pair tones for each configuration, with a total of 40 unique humbucking pair tones for the entire set. For K>7, the number of pole configurations exceeds the number of potentially unique tones.
Even for just humbucking pairs, never mind triples, quads, quintets and hextets, it would be a challenging problem for either electro-mechanical or digitally-controlled pickup switching systems to take full advantage of reversible pickup poles.
Electro-Mechanical Guitar Pickup Switching
The standard 5-way switch (Gagon & Cox, U.S. Pat. No. 4,545,278, 1985) on an electric guitar with 3 single-coil pickups typically provides to the output: the neck coil, the neck and middle coils in parallel, the middle coil, the middle and bridge coils in parallel, and the bridge coil. Typically, the middle pickup has the opposite pole up from the other two, making the parallel connections at least partially humbucking. But while the middle and neck coils have roughly equal numbers of turns, and the bridge coil has more turns than the other two to produce a roughly equal signal from the smaller physical vibrations of the strings nearer the bridge. The standard 3-way switch on a dual-humbucker guitar typically produces the neck, neck∥bridge and bridge pickups at the output, all of which are humbucking.
These two switches are “standards” because the vast majority of electric guitars on the market use them. There are other switching systems, such as U.S. Pat. No. 3,290,424, Fender, 1966; U.S. Pat. No. 4,305,320, Peavey, 1981; U.S. Pat. No. 5,136,918, Riboloff, 1992; U.S. Pat. No. 5,311,806, Riboloff, 1994; U.S. Pat. No. 5,763,808, Thompson, 1998; U.S. Pat. No. 6,781,050B2, Olvera, et al., 2004; US2005/0150364A1, Krozack, et al.; U.S. Pat. No. 6,998,529B2, Wnorowski, 2006; and US2009/0308233A1, Jacob. But they are either not on the market, or fill niche positions. In any case, they do not intersect or interfere with the switching systems presented here.
Microcontrollers in Guitar Pickup Switching
Ball, et al. (US2012/0024129A1; U.S. Pat. No. 9,196,235, 2015; U.S. Pat. No. 9,640,162, 2017) describe a “Microprocessor” controlling a “digitally controlled analog switching matrix”, presumably one or more solid-state cross-point switches, though that is not explicitly stated, with a wide number of pickups, preamps and controls hung onto those two boxes without much specification as to how the individual parts are connected together to function. According to the Specification, everything, pickups, controls, outputs and displays (if any), passes through the “switching matrix”. If this is comprised of just one cross-point switching chip, this presents the problem of inputs and outputs being interrupted by queries to the controls. In the Specification, the patent cites the ability to make “any combination of combinations” without describing or providing a figure any specific one, or even providing a table or scheme describing the set. It states, “On board controls are similar to or exactly the same as conventional guitar/bass controls.” But there is not enough information in the patent for someone “with ordinary skill in the art” to either construct or fully evaluate the invention.
The Ball patents make no mention or claim of any connections to produce humbucking combinations. The flow chart, as presented, could just as well be describing analog-digital controls for a radio, or record player or MPEG device. In later marketing (https://www.music-man.com/instruments/guitars/the-game-changer), the company has claimed “over 250,000 pickup combinations” without demonstration or proof, implying that it could be done with 5 coils (from 2 dual-coil humbuckers and 1 single-coil pickup).
Baker (NP patent application Ser. No. 15/616,396, 2017) systematically developed series-parallel pickup topologies from 1 to 5 coils, with 6 coils in notes not included. (See also https://www.researchgate.net/publication/323390784_On_the_Topologies_of_Guitar_Pickup_Circuits) The table labeled Math 12b in that application shows that 5 coils can produce 10717 unique circuits of sizes from 1 to 5 coils, including reversals of individual pickup terminals and moving pickups around the circuit positions. Math 12b shows that 6 coils can produce 286,866 unique circuits of from 1 to 6 coils. “Over 250,000” circuits are possible only with 3 humbuckers, or with 5 coils and a piezoelectric pickup.
Bro and Super, U.S. Pat. No. 7,276,657B2, 2007, uses a micro-controller to drive a switch matrix of electro-mechanical relay switches, in preference to solid-state switches. The specification describes 7 switch states for each of 2 dual-coil humbuckers, the coils designated as 1 and 2: 1, 2, 1+2 (meaning connected in series), 1−2 (in series, out-of-phase), 1∥2 (parallel, in-phase), 1∥1(−2) (parallel, out-of-phase), 0 (no connection, null output). In Table 1, the same switch states are applied to 2 humbuckers, designated neck and bridge. That is three 7-way switches, for a total number of combinations of 73=343.
In this arrangement, null outputs occur when a series connection is broken. This will happen once for all 3 switches set to null, and each time a series connection in the last switch is broken by a null output in the previous two switches, for a total of at 5 null outputs. Although Super has argued via unpublished e-mail that a reversed output connection is a separate tone, this inventor calls it a duplicate. This can happen when the 7-way output switch is set to parallel and out-of-phase for the second humbucker, the first humbucker 7-way switch is set to null, and the second humbucker 7-way switch is set to any output, or 6 combinations. Taking out 5 nulls and 6 duplicates that leaves 332 useful combinations.
Table 1 in Bro and Super cites 157 combinations, of which one is labeled a null output. For 4 coils, the table labeled Math 12b in Baker, NP patent application Ser. No. 15/616,396, 2017, identifies 620 different combinations of 4 coils, from 69 distinct circuit topologies containing 1, 2, 3 and 4 coils, including variations due to the reversals of coil terminals and the placement of coils in different positions in a circuit. Baker shows how an all-humbucking 20-combination electromechanical switching circuit for two humbuckers produces mean frequencies for 6 strummed strings which have 3 or 4 duplicate tones, with a tendency for mean frequencies to bunch at the warm end of the scale. The use of mean frequency in this manner has not yet been established as a measure of tone, but as a first approximation still raises the question of the practical use of so many tones so close together.
Baker, NP patent application Ser. No. 15/616,396, 2017, demonstrates, in the table labeled Math 31, that the total number of potentially distinct humbucking tones from topologically different electrical circuits of matched guitar pickups, using just simple series-parallel topologies, can be up to 2 for 2 sensors, 6 for 3, 48 for 4, 200 for 5, 3130 for 6 and 19,222 for 7 sensors, up to 394,452 for 8 sensors. Beyond 3 or 4 matched single-coil pickups, electro-mechanical switches are too expensive and impractical. One must us a cross-point matrix or switch of some kind, preferably analog-digital. Baker offered an architecture for a micro-controller system using a solid-state cross-point switch, specifying how the switch is dedicated to sensors, noting that for Mx/2 number of 2-wire sensors, an Mx by (My=Mx+2) crosspoint switch, or larger, will cover all possible interconnections, and provide a 2-wire output. But for humbucking circuits made of matched single-coil pickups, as disclosed in that NPPA, the orientation of the pickup magnetic poles to the strings must be known by the microcontroller. This requires the pickup poles to be manually assigned in the microcontroller switching or programming, or for the microcontroller to directly detect the orientation of the pickup poles. This programming problem has not yet been solved.
Baker (NP patent application Ser. No. 15/616,396, 2017) developed humbucking circuits for matched pickups only in humbucking pairs, quads, hextets, octets and one special case of a humbucking triple. The special case is important because it can be expanded to quintets, septets, nine-tets and up, including series and parallel combinations of humbucking pairs, quads and up with those circuits of odd numbers of matched pickups. This expands the range of possible matched-pickup humbucking circuits to any number of pickups, odd or even. As disclosed in the NPPAs above, there are many more possible non-humbucking series-parallel circuits than humbucking, falling as the number of pickups increase. At 6 pickups, only 1.1% of the possible series-parallel circuits are humbucking pairs, quads and hexes. So far, this inventor knows of no micro-controller algorithm to use with a cross-point switch to pick only humbucking circuits, and is precluded by medical disabilities from developing one.
Having a large, even huge, number of possible circuits and tones to pick from raises the question of how to do the picking, and how to order them from warm to bright and back. Experiments with two humbuckers suggest that tones, as measured by the mean frequency of strummed strings, are much closer together at the warm end than the bright end, and may be so close together that having a large number of possible circuits and tones becomes a matter of diminishing returns. Some method is needed to order and pick tones that are sufficiently distinct to make efficient use of available and invented switching methods, whether electro-mechanical or digitally-controlled.
This invention discloses hitherto unknown, non-obvious, beneficial and eminently simple means and methods to solve those problems. It comprises of simple circuits that are constructed and switched according to Four Simple Rules: 1) all of the pickups or sensors are connected to a common point at the pickup terminals that present the same phase of external electro-magnetic interference, or “hum”; 2) at least two pickups must be in the circuit, connected at least one from the common point to the output low terminal, and the other(s) at least one connected from the common point to the output high terminal; and 3) either the common point must be grounded, or the low terminal of the output must be grounded, but not both; and 4) the pickups or sensors must be matched, all having the same response to external hum.
Preferably, but not necessarily, some of the sensors, or pickups, will have desired signal phases that are opposite from one another, with respect to the common connection point. If the signal phases of two sensors are opposite, and one is connected to the high output terminal and the other is connected to the low output terminal, then the signal voltage difference across the output terminals is in-phase. If both sensors have the same signal phase, then the voltage difference across the output terminals is out-of-phase, or contra-phase. It turns out that any number of matched sensors can be connected to the common connection point and the output terminals in this manner, whether by electro-mechanical or digitally-controlled means, and the hum voltages will cancel. Additionally, this kind of circuit can be connected in series or parallel with any other humbucking circuit, and the output will remain humbucking. This greatly expands the number of possible humbucking circuits from pairs, quads, hexes and above, using any even or odd number of sensors.
While this invention was developed primarily for matched single-coil electromagnetic guitar pickups, it has much wider application. It can be applied to any type of sensor which follows the same rules, in any application where matched sensors can be used in this manner to reject external interference.
In the case of an electromagnetic guitar pickup, some effort has been made in the past to connect the outer windings of the coil to ground, so as to provide a kind of shield to electric field noise. But when those pickups are connected in series, this is not possible for all the pickups in the circuit, so that stratagem fails. Only one of the pickups in series can be connected to ground, it any. More often, in better quality pickups, copper or aluminum foil is wrapped about the outside of the coil and grounded. In the case of this invention, where the common connection point is grounded and output is differential, that stratagem succeeds.
Also, many patents and explanatory texts claim that the windings of coil with opposite magnetic polarities are reversed to achieve humbucking. This is not truly necessary; only the terminals of the pickup need be reversed. It makes less manufacturing sense to have two sets of coil winding machines, winding coils in opposite directions. In the case of a grounded common connection point, this invention fully justifies that economy. No terminals need be reversed, only the magnetic field, as described in NP patent application Ser. No. 15/917,389 (Baker, 2018).
Principles of Operation
The principles of operation are mostly mathematical expositions which cannot be patented. But they are necessary to discuss, as they enhance understanding of the material invention, and define the theoretical limits of the invention. Furthermore, they demonstrate that the operation of instruments such as electric guitars have not yet begun to find their limits. They can be a lot more versatile than they are now.
Circuits with Two Coils
With any two coils, (N1,N2), (N1,S1) or (S1,S2), indicating the available coils with either N-up or S-up fields, there is only one possibility, or the single combination of 2 things taken 2 at a time; one coil connects to the high output terminal and the other to the low output terminal. Let the first number represent the upper coil and the second the lower coil. Reversing those connections only changes the sign of the output signal. This inventor contends that this produces no effective difference in tone. Human ears cannot tell the differences in the phase of a signal producing a tone without some other external reference. Therefore, such changes do not count. And going forward, this will in fact reduce the number of choices when the numbers of coils connected to the high and low terminals of the output are equal. Note that when the coils have the same poles up, the switching circuit correctly produces an out-of-phase, or contra-phase, signal, such as N1−N2.
Circuits with Three Coils
Suppose that the three coils can be represented by the designations N1, S1 and N2, for 1 S-up and 2 N-up coils. They can be connected through the switching system to the output terminals as either 2 coils or 3 coils. Table 1 shows various possible circuit/switching combinations. Note that reversing the output terminals produces the duplicates in the right three columns of the table. It does not matter if the circuits are switched this way; it only matters that duplicates are not counted as separate circuits and possible tones. This might be called the Fifth Simple Rule, but it might wait until actual human trials are conducted to confirm it. Call it instead the Rule of Inverted Duplicates.
Note that in Table 1, for 2 coils, the results for 2 coils can be explained as (3 things taken 1 at a time) times the number of combinations for 2 coils, or 3*1=3. The results for 3 coils can be taken as (3 things taken 1 at a time)*(2 things taken 2 at a time), or 3*1=3. The combined results for 3 coils, taken in pairs and triples, is 6 humbucking circuits. By Math 2, for the first column of 2 coils, Vo=VN1+VS1, for the first column of 3 coils, Vo=VN1+(VS1−VN2)/2, and for the second column of 3 coil duplicates, Vo=(VN1+VN2)/2+VS1. The Rule of Inverted Duplicates also applies to reversals of all the magnetic poles.
It still works for all pickups N-up, N1, N2 and N3, as shown in Table 2, shown without the duplicates. By Math 2, the first column of 2 coil combinations has an output voltage of Vo=VN1+VN2. The first column of 3 coil combinations has an output voltage of Vo=VN1−(VN2+VN3)/2.
The Rule of Inverted Duplicates also applies to reversals of all the magnetic poles. If Table 1 had instead been constructed of 1 N-up and 2 S-up pickups, S1, N1 and S2, replacing N1, S1, and N2 at their respective positions, the signal voltages at all those positions would simply be reversed. But as NP patent application Ser. No. 15/917,389 (Baker, 2018) demonstrates, the odd pole pickup can be placed in three different physical positions, providing different tonal characters for the entire set.
Circuits with Four Coils
Suppose that we have four matched pickups designated N1, S1, N2 and S2. We can calculate the number of possible outputs for pairs and triples by taking 4 things 2 at a time and 4 things 3 at a time, multiplied by the number of possible pairs (1) and triples (3) without extra pickups. Math 3 shows this calculation.
There are 2 ways to arrange 4 coils in a humbucking quad: 1) a single coil in series with (or over) 3 coils in parallel, and 2) 2 coils in parallel, the pair in series with (or over) another 2 coils in parallel. Putting 3 coils in parallel over 1 coil would merely duplicate the first instance by the Rule of Inverted Duplicates. This will be true for any number of pickups J. If we follow the convention of putting the smaller number of pickups over the larger or equal, the number of pickups connected to the high output terminal will range from range from 1 to J/2−1 for J odd, and 1 to J/2 for J even. Table 3 shows the switched combinations for J=4, given 2 N-up pickups N1 and N2, and 2 S-up pickups, S1 and S2.
An example of 5 coils can be 2 humbuckers and a single, which a number of guitars on the market have. The number of 1-over-3 combinations can be calculated as (4 things taken 1 at a time) times (3 things taken 3 at a time), or 4*1=4. The number of 2-over2 combinations can be calculated as one-half times (4 things taken 2 at a time) times (2 things taken 2 at a time), or 6*½=3, for a total of 7 humbucking circuits from 4 pickups. Note that when all the terms are collected for the 2-over-2 circuits, Vo for the duplicates is the negative of Vo for the first three, due again to the Rule of Inverted Duplicates. This will happen whenever j=k for j-over-k circuits.
Circuits with 5 Coils
For 5 coils, one can take the previous numbers of tonal circuits calculated for 2, 3 and 4 coils and multiply them by 5 things taken 2, 3 and 4 at a time, plus the number of possibilities for combinations of 5 coils. Unique combinations of 5 coils or pickups in this switching system can be “quint” combinations of 1-over-4 and 2-over-3, without duplicate inversions. Math 4 shows these calculations:
Circuits with 6 Coils
A number of guitars on the market have three humbuckers, which can be considered 6 matched pickups for this discussion. Math 5 shows these calculations. Not the reduction of 3-over-3 hextets due to the Rule of Inverted Duplicates.
Fender (U.S. Pat. No. 3,290,424, 1966) managed to put 8 sets of poles under a pick guard, which arguably could have been 8 pickups. Whether or not it would be useful is another matter. For stringed instruments like pianos, where many more pickup coils can be used along the strings, the method of calculating the number of possible humbucking circuits can be easily expanded by the same rules. So for 2, 3, 4, 5, 6, 7, 8, 9 and 10 matched pickup coils, this switching system can produce, respectively, 1, 6, 25, 90, 301, 966, 3025, 9330 and 28,501 humbucking circuits. The natural logs of the number of HB circuits, NHB, are about: 0, 1.79, 3.22, 4.50, 5.70, 6.87, 8.01, 9.14 and 10.26. So the rise in the number of circuits is clearly an exponential function of the number of pickups.
Table 4 shows these calculations for this kind of circuit extended to K pickups taken J at a time, where K=2 to 12 and J=2 to 12. The first thing that becomes apparent is that for J pickups taken J at a time, the number of circuits is 2(J-1)−1. Math 6 shows the full equation. This determines the upper limit of switched circuits of this type.
Hybrid Humbucking Circuits
Using matched pickups, common connection point humbucking circuits can be combined in series and parallel with the kind of series-parallel humbucking circuits disclosed in NP patent application Ser. No. 15/616,396 (Baker, 2017), and the result will still be humbucking. Thus humbucking quintets can be constructed by placing humbucking pairs in series and in parallel with a humbucking triple. Humbucking septets can be formed by placing humbucking quads in series with humbucking triples, and by placing humbucking pairs in series and parallel with humbucking pairs. Humbucking nine-tets can be formed by placing humbucking sextets in series and parallel with humbucking triples, by placing humbucking quints in series and parallel with humbucking quads, and by placing humbucking septets in series and parallel with humbucking pairs.
This is less a matter of constructing new circuits than expanding the number of humbucking circuits that can be obtained by replacing unmatched pickups with matched pickups in all series-parallel circuits. In general, hybrid humbucking circuits cannot take advantage of the Four Simple Rules for the switching system disclosed here.
The Number of Possible Tones with Reversible Pickup Poles
NP patent application Ser. No. 15/917,389 (Baker, 2018) shows that for J number of matched pickups with reversible poles, there are 2J-1 possible pole configurations: 2 configurations for 2 pickups, 4 for 3 pickups, 8 for 4 pickups, 16 for 5 pickups, and so forth. Suppose the one has matched pickups with reversible poles in positions A, B, C, D, . . . , where A is N-up and A′ is S-up. Each position picks up fundamentals and harmonics of vibration that are at least slightly different in tonal content. How many different circuit-pole combinations have possibly different tones? For 2 pickups, there is only 1 circuit with 2 possibilities, A+B′ and A−B, where A, B and B′ also stand in for the signal voltages.
For 3 pickups, there are 4 pole position configurations: (A,B,C), (A′,B,C), (A,B′,C) and (A,B,C′). Table 5 shows the results. The first pickup in the pole position sequence is assumed to be connected between the common connection point and the high output terminal. For humbucking pairs, there are only 6 possible tonal differences, because of duplicates, like A-B, and the Rule of Inverted Duplicates, i.e., −A′−B=A+B′. To look at it another way, there are only unique three pairs, and A±B allows for 2 choices, or 3*2=6. For any pole configuration, there are 3 switched pairs, each of which produces a set of 3 potentially unique tones out of 6. The lower half of Table 5 shows how a 1-over-2 humbucking triple produces 3 possible triples with 12 possible tones. The possibilities go as A±(B±C)/2, or 22=4 sign choices, and 3 circuit choices for 3*4=12 unique circuits with potentially unique tones. We must say “possible tones”, or “potentially unique tones”, because the following experiment with two humbuckers demonstrates that some tonal results can be very close together. So for 3 pickups, we have 18 potentially unique tones, from 4 different pole configurations, each of which has 6 switched circuits with a set of 6 of those 18 potentially unique tones.
We can see that for 4 pickups, with four 1-over-3 circuits and three 2-over-2 circuits, changing the pole configurations can only change the signal phases as A±(B±C±D)/3 and (A±B)/2±(C±D)/2, or 23=8 signal sign configurations. That means 7*8=56 potentially unique tones, plus those for 4 pickups taken 2 and 3 at a time. In general, if we have K number of pickups, with 2K-1 number of pole configurations, we can have signal phase changes at different positions that go as A±B±C± . . . ±K or 2K-1 possible phase changes for each possible circuit, regardless of where the parentheses and divisors go to fit the solution in Math 2. We cannot count ±A±B±C± . . . ±K, or 2K possible phase changes, because of the Rule of Inverted Duplicates.
For humbucking pairs with 4 pickups, we have [4 pickups taken 2 at a time]=6 pair combinations, times [2(2−1)−1]=1 circuits, times 2(2−1)=2 phase changes, or 6*2=12 potentially unique tones. For humbucking triples with 4 pickups, we have [4 pickups taken 3 at a time]=4 triple combinations, times [2(3−1)−1]=3 circuits, times 2(3−1)=4 phase changes, or 4*3*4=48 potentially unique tones. This gives a total of 12+48+56=116 potentially unique tones, from 8 different pole configurations, each of which has a set of 25 switched circuits, each of which has a set of 25 of those 116 potentially unique tones.
Math 7 shows the total number of tones for K number of matched and reversible pole single-coil pickups, for circuits of J=1 to K. The first term in the summation is the number of circuits of K pickups taken J at a time; the second term is the number of common-point switched circuits for J pickups; and the third term is the number of pickup sign changes obtained by changing poles in J pickup positions. Table 6 shows the results of this equation in the Totals column on the right. The first header row is J; the second is the number of the number of pole configurations and pickup signal sign changes for J pickups; and the third is the number of unique circuits for J pickups in a common connection point switching circuit. The Totals column represents the total number of potentially unique tones possible for K pickups in circuits of size J=2 to K.
Table 7 is self-explanatory. All the other columns tend to rise exponentially with K. There are always fewer tones per circuits than there are pole configurations. All tones are potentially unique until proven so. No more than about 9 standard-size single-coil pickups can fit in between the neck and bridge of a standard length six-string electric guitar. But there will be diminishing returns with the increasing number of pickups, since having coils close together reduces the differences in harmonic differences they see from a vibrating string. Plus their magnetic fields tend to interfere, and they also become weak transformers when side-by-side. Five or six may be the practical limit. Ten matched pickups is likely practical only on un-fretted instruments of much larger scale, such as pianos. Or, if the principles can be applied to piezo-electric and other vibration pickups, to instruments such as drums and horns. In any case, these limits extend far beyond standard 3-way and 5-way switches.
An Experiment with Two Mini-Humbuckers
Math 8 shows the equations used to process this FFT data in a spreadsheet. There are 2048 magnitude values in the dBFS scale for frequency bins from 0 to 3998 Hz, with a resolution of about 1.95 Hz. These are converted to linear values, linVn(fn), which are summed to obtain the relative signal amplitude. Dividing each magnitude by the total provides a probability density function, Pv(fn), which sums to 1. Multiplying and summing over the product of all the bin frequencies and the density function values gives the mean frequency in Hz. The second and third moments of the FFT spectrum are the bin frequency minus the mean, raised to the second and third powers, times the density function. For the purpose of simply maintaining smaller and more comparative numbers to consider the second and third roots of the second and third moments have units of Hz.
Table 9 shows the results of this experiment for the 25 HB circuits from the 4 coils in
Table 10 shows the same results, ordered by the 1st moment, which is the mean frequency of the spectral analysis, with a range from 632.9 to 1201.1 Hz.
This suggests that there may be only 17 distinct tones available, a result consistent with a two-humbucker experiment in NP patent application Ser. No. 15/616,396 (Baker, 2017) using a 20-circuit switch. Note also that the relative signal strengths run from 0.23 to 2.83, a factor of 12.3, or about 22 dB. This data will be used to demonstrate a method for ordering tones and choosing switching connections accordingly, with variable gains to equalize signal strengths.
Embodiments of Electro-Mechanical Switching Systems
For 3 unmatched single-coil pickups, there are 47 different series-parallel circuits. For 3 matched single-coil pickups, there are 6 different humbucking series-parallel pairs, plus 3 humbucking triples for a total of 9 different humbucking circuits. For 4 unmatched single-coil pickups, there are 620 different series-parallel circuits. For 2 humbuckers with 4 matched coils, there are 20 series-parallel arrangements, considering only the internal humbucker series-parallel connections and the external humbucker to humbucker series-parallel connections. For 4 matched single-coil pickups, there are 48 combinations of humbucking pairs and quads, with 12 humbucking triples and 4 humbucking circuits with one pickup over three, for a total of 64 different humbucking circuits. The humbucking circuits with 2 over 2 pickups duplicate humbucking quads already constructed.
The simplicity of the circuits disclosed here, using the Four Simple Rules, reduces the number of humbucking circuits from 9 to 6 for 3 matched pickups, and from 64 to 25 humbucking circuits for 4 matched single-coil pickups. This, in exchange for simplified switching that can be ordered according to the warmth (or at least the mean frequency) of humbucking tones. This switching system can be achieved with a number of different embodiments, from those using available mechanical switches, to those with both mechanical switches and active amplifiers, to those with microprocessor-controlled switching and gains. As the following examples show, there are a wide number of possible embodiments, not limited to just those depicted here.
In
If each of the matched coils have inductance, LC, then the first three throws have circuit with a lumped inductance of 2*LC, and the last three have a lumped inductance of 3*LC/2. Tone capacitors CT1 and CT2 can be used to maintain the equal effect of the tone pot, PT, on tone. Since resonance frequency is a function of the product of inductance and capacitance, the products, 2*LC*CT1 and 3*LC*CT2/2 must be equal to achieve similar tone results, implying that CT1=3*CT2/4. Both the tone circuit and the volume pot, PV, lie across the output of the switching circuit. The wiper of the volume pot is connected to the output, Vo.
This is not the only possible selection of matched coils. They could all be either all S-up or all N-up. In which case, all the outputs would be humbucking but out-of-phase, or contra-phase. Without amplification and signal equalization, the output signals would be much weaker, but much brighter. A selection of matched coils that has only one S-up, as shown here, and a selection that has only one N-up will produce the same tones if the opposite poles from each set occupy the same positions under the strings. In other words, N-S-N is the same as S-N-S. In the case of N-S-N, the physical positioning of the S-up pole under the strings will also determine tone, with different sets of tones from S-N-N and N-N-S.
If the pickup magnetic poles are reversed to change the tonal character of the guitar, each pole change will affect both the frequency and order of tones. The order of tones for the switch wiring for one set of poles likely will not hold for another. So there must be some way to change the wiring of the switching along with changing the poles to at least keep an order of tone monotonic from warm to bright. U.S. Pat. No. 9,401,134 (Baker, 2016) disclosed such a device in
The other three times 6 throws, connect through a line of cross-point interconnects (17) to the high output terminal, Vo+, and through another line of interconnects to the low output terminal, Vo−. The vertical circuit lines over the interconnects are on one side of the board and the horizontal lines on the other, so that they do not connect, except through the interconnects. The interconnects can be either non-plated-through holes for soldered through jumpers, or standard computer board jumpers, or some other type that fulfills the function. The white dots show no connection, and the black dots show interconnections. The interconnections shown produce output voltages of Vo=VN2+VS1, Vo=VN1−VN2, Vo=(VN1+VN2)/2+VS1, and Vo=VN1+(VS1−VN2)/2, for throws 1, 2, 5 and 6, respectively. Any combination and order of humbucking pairs and triples, including duplicates, is possible.
At the output, only one of jumpers J1 and J2 may be connected. If J1 is connected, then the lower terminal of Vo− is grounded, and the output is single-ended, as are most electric guitar circuits. If J2 is connected, then the common pickup connection point is grounded and the output, Vo, is differential. A differential output requires either that a differential amplifier convert it to single-ended, or that the output jack of the electric guitar is stereo, and feeds through 2-conductor shielded cable to a guitar amp with a differential input. A single-ended output has the advantage of using circuits and connections already common to electric guitars. A differential output has the advantage of suppressing common-mode electrical noise from external sources, possibly such as fluorescent lights, which put out much higher frequencies of noise than 60 Hz motors.
In this case, for a selection of poles from neck to bridge of N1, S1, N2 and S2, all 4 poles of the switch are taken by the terminals of the coils that are not connected at the common connection point (1). Compact 6P6T switches, capable of fitting neatly under a pick guard, are considerably less common, as well as much more expensive.
Note that for the pair in throw 3, N1+S2, the lumped inductance of the circuit is 2*Lc, where Lc is the inductance of the coil of any matched pickup. For a humbucking triple, the lump inductance is 3*Lc/2, for a humbucking quad of 1-over-3, the inductance is 4*Lc/3, and for a humbucking quad of 2-over-2, the inductance is Lc. There are no poles left on the switch to make adjustments to the tone capacitor, so a tone circuit, T1, T2, T3 and T4 has been placed across each pickup. This might be comprised of a tone capacitor and a small multi-turn pot, accessible through a hole in the pick guard. Or it could be four separate capacitors connected to the switch end of each pickup, with a single 4-gang tone pot connected to each capacitor and the common connection point.
Note also that the plug board in
Since we have no experimental data for a 3-coil guitar, let the relative signal amplitudes before amplification in Table 11 stand in for the sake of argument and example. We conveniently choose the maximum relative signal strength of 3.161 as the first gain, and we wish to adjust the other gains to bring all the other signals up to that level at the output, Vo. Dividing that relative amplitude by all the others, give the relative gain, Gi#, for each signal that we need to approach. But if we pick a feedback resistor, RF=47 k, and a minimum gain resistor RG1=2200 k, or 2.2M, then the first gain will be 1.024 instead of 1. We have to multiply this number times all the gains to get the real gains, then calculate RGi. Math 9 and Table 11 show these calculations.
Only a few of the RGi values are close to standard resistor values. Given that and the differences between human perception and electronic measurements, it would be better to use small, square multi-turn potentiometers for the other RGi. And if any of the pickup poles are to be reversed, it would be better to use a connection plug board, like that in
Since only 4 poles of the 6 pole switch are needed to switch the pickup terminals to the switch output, ΔVs, the other 2 are available to switch the gain resistors, RGi, and the tone capacitors, CTi. The gain resistors are again calculated according to the principles of Math 10 and Table 11, according to the measured relative signal amplitudes of ΔVs for all 6 throws. Since the resonant or low-pass frequency of an inductor and capacitor goes according to the product of LC, Math 11 shows the relationships between the values of CTi, for which only 3 actual capacitors are needed, since there are only 3 lumped values of switched circuit inductance.
The tone circuit can be any useful form, such as Tone Circuit 1 or Tone Circuit 2. The switch output, ΔVs, feeds into the differential amplifier comprised of U1a, U1b, 2 feedback resistors, RF, and the switched gain resistor, RGi, has a differential output, ΔVo. Considering that the four coils can be connected into 25 different circuits with this switching system, and with 116 potentially unique tones, using the plug board of
Embodiments of Analog-Digital Switching Systems
The possibility results of Tables 4, 6, 7 and 10, of so many more configurations and tones than electro-mechanical switches can control, justify the use of digitally-controlled analog switches. Micro-power micro-controllers (uC) offer display, user interfaces, control and longer battery life, but few if any have the arithmetic processing units with the necessary trigonometric functions to calculate Fast Fourier transforms, which might be used to order tones. It will likely be necessary to add math processing units (MPUs). With such capability, and not yet fully determined algorithm for determining timbre and tone from strummed strings, it should be possible to offer the musician a user interface with a simple one-switch to one-swipe control to shift progressively from bright to warm tones and back without the musician ever needed to know which pickups are used in what configurations. In this disclosure, the mean frequency of six strummed strings is used as an example of the order of tone, which will likely be superseded by other measures. Nevertheless, the system architecture that will allow such measures and control will remain relatively constant for a while.
Suppose that we have J number of N-up pickup coils and K number of S-up pickup coils, and we have chosen to use the common connection point switching system, where one terminal of each coil, regardless of magnetic pole direction (or electric pole for other sensors), are connected to a single point according to the same phase of external hum. In this switching system, there are 3 choices, or 3 states, for the other terminals of each coil to be connected by the switching circuit: 1) connected to the low output terminal of the switching system; 2) connected to the high output terminal of the switching system; or 3) not connected to either terminal. There is also the choice of how the ground is connected in the switching system, according to Rule 3. It is connected either to the low output terminal, or to the pickup common connection point. It is also possible to break the Rule, and ground both the common pickup connection and the low output terminal, so as to isolate the output of just one coil connected to the high output, for tuning and measurement purposes.
For this we need digitally-controlled solid-state analog signal switches to reach the full potential of a switching system with more than 3 or 4 coils.
The 1P3T switch in
While it is possible to use a digitally controlled analog cross-point switch, they can come as large DIP chips, with more than a score of pins, or require supply voltages in excess of 5V, or have contact resistances of tens of ohms. A cross-point switch typically addresses only one contact at a time, requiring addressing and data strobing for each separate connection. For a 6×8 cross-point switch (should one exist), used with four coils, a set of gain resistors and a set of tone capacitors, there are 6*8=48 different cross-connections that have to be set individually by addressing.
The switches in
With 4 coils, there are as may as 25 possible circuits requiring as many as 25 gain resistors to equalize the signal voltages. Or, alternatively and more efficiently, since a micro-controller is now available, digital pots can be used to set gain.
Calculations elsewhere, using the resistance granularity of digital pots, indicate that using digital pots to set gain in
The outputs of the coils are switched by the respective 1P3T digital-analog switches, SW1 to SWj, and SWj+1 to SWj+k. The intermediate switches are not shown. The 1P3T switches, as in
The two 1P2T switches, SWa and SWb, perform other functions. For S=0, SWa connects the ground to the pickup common connections, making the switching output, Vs+, suitable for connection to a differential amplifier in the Analog Circuits section (
For S=0 (a separate control line from SWa), SWb shorts itself out and has no function, but for S=1, it connects Vs− to the pickup common connection point (1), allowing the output of a single pickup coil, or a set of parallel pickup coils, connected to Vs+ to be fed to the Analog Circuits section. This will be useful for measuring or tuning single coils. The Analog Circuits section is taken to contain all the analog signal circuits.
The micro-controller, uC, is shown with two-way digital connections to the User Controls and Display (adequately defined in NP patent application Ser. No. 15/616,396); one-way control connections to 1P3T switches SW1 to SWj+k; one-way control connections to SWa and SWb; one-way connections from the switching system output, Vs, to an internal analog-to-digital converter (A/D); two-way sense and control connections with the Analog Circuits section, and a Math Processor Unit (MPU). The MPU section can be either internal to the uC, if available, or an add-on co-processor. Either way must be capable of at least 32-bit floating point operations on complex variables, having sufficient trig and other math functions to accomplish Fast Fourier Transforms (FFTs).
Using start-stop signals from the Analog Section or the User Controls and Display, the FFT section performs complex FFTs on such inputs as the six strummed strings, as described in “An experiment with 2 mini-humbuckers”. The FFT section takes A/D information from the audio signal, Vs, to generate the complex FFTs needed for Math 8. The complex FFTs generated should have a resolution of at least 1 Hz, and a frequency range of at least 0 to 4 kHz, preferably to 10 kHz, and adjustable in bandwidth. It will be necessary to switch the pickups during the A/D signal collection to obtain nearly simultaneous sequential measurements either of all the coils separately, and/or all the coils in humbucking pairs, corrected for time delays according to Math 13, to produce effectively simultaneous complex FFT spectra for the calculations in Math 8.
x(t−t0)⇔X(f)*e−j2πft
A digital-to-analog converter (D/A), which can be either internal in the uC, or an external circuit, feeds the audio from inverse-FFT transformations of measured signal spectra into the Analog Circuits section to help the user recall pickup circuit tones and to make better decisions on any user-defined tone switching sequences. From this information, the switched coil combinations can be ordered by mean output frequency from bright to warm or warm to bright, as a first approximation of the order of tones. Or set by user preference. The tones in signal output from the switching system can be equalized in volume, according to Math 12ab, and Math 9 or Math 11, in the Analog Circuits section by variable gains set by the uC. Then the user can use the User Controls and Display to shift monotonically from tone to tone without having to specify the particular switched coil combination that produces it.
If for some reason a uC will not be used, the switching circuit in
The single bit of each ripple output can be connected to multiple switch control lines (S, S0 and S1 in
Method of Choosing the Spacing and Switching Order of Tones
The object of the exercise is to offer a much wider range of tones, and to allow the musician to use one control to shift progressively from bright to warm and back, without ever needing to know which pickups are used in what circuit. For that, one needs a way to order the tones.
There is no guarantee at this time that using the mean frequency of the signal from one or more strummed strings, with either open fretting or some chord, will correspond exactly to brightness or warmness of tone, as commonly perceived by a musician's ears. For example, R. M. French (2009, Engineering the Guitar, Theory and Practice, Springer, N.Y.) noted in a section on psychoacoustics, pp 190-193, that louder tones mask nearby tones. And on pp 29-36, in a section on human perception of sound, he notes that the sensitivity of human hearing to tones peaks at 1000 to 2000 Hz. This method of ordering tones needs a simple one-number measure of tone that has not yet been developed and proven. But the mean frequency of six strummed strings is a start, used here as an example until better methods come along.
The mean-frequency numbers used here for illustrating the method come from Math 8 and Table 10, from the dual-humbucker experiment previously disclosed, which also helps to illustrate the method. Ideally, the frequency resolution should be 1 Hz, with a range of from 0 Hz to a top end of at least 4 kHz, but preferably the full range of human hearing, which extends to 20 kHz or more. Preferably, enough sample windows should be taken to cover from the very beginning of a strummed or plucked note or chord through the full sustain of the sound. But it may turn out that other sampling techniques have certain advantages not discussed here.
One should expect that, like the dual-humbucker experiment, some tones will be too close together to count, and the separation of tones with switched pickups circuits will vary considerably, likely with most of the tones bunched together at the warm end. So, for four pickups with 25 different circuits, there may be only half that number of useful tones. And for 25 different circuits and a six throw switch, only half of those can be used. For pickups with reversible poles, four pickups have 8 different pole configurations, sharing 25-member sets of 116 potentially unique tones. (The ratio of the numbers poles times circuits to the numbers of tones is always greater than or equal to one.)
Digitally-controlled analog switching may have a much wider range of choice than mechanical switches, but the problem of bunched tones still exists. Note that in Table 10, the range of mean frequency from 632.9 Hz at the low end to 1201.1 Hz at the high end, for one pole configuration, is barely an octave. Without actual measurements, it is not yet possible to know what other pole configurations will produce. Nor is it yet possible to account for the variations introduced by moving pickups themselves about in space, as disclosed in U.S. Pat. No. 9,401,134B2 (Baker, 2016), offering 5 degrees of freedom, vertically and along the strings at each end of a pickup, as well as across the strings.
This method assumes that whatever the measure of tone, it should be divided along bright to warm, or warm to bright, according to virtual frets. In most Western music, adjacent notes differ by a multiplier or divisor of 21/12, counting 0 to 12 frets from an open note to its octave note. Other musical traditions can have three times as many notes in an octave. This division of frequencies comes from the way that the human ear is constructed and responds to sound. So it is natural to assume that the most effective and efficient way to chose the separation of tones chosen and ordered from those available is by a constant frequency multiplier from one tone to the next higher tone.
The method disclosed here is fairly simple: (1) chose a measure of tone (mean frequency of six strummed strings from FFT analysis in these examples); (2) cause the musical instrument to emit tones in some standard fashion (strum six strings several times in these examples); (3a) take digital acoustic samples of the signal outputs from each pickup simultaneously (not quite possible in these examples), or alternatively, (3b) take digital acoustic samples from each switched pickup circuit; (4) digitally process the acoustic samples to obtain complex number frequency spectra for each pickup or each pickup circuit (only magnitudes of frequency bins were possible for these examples, leaving out phase information); (5) apply the measure of tone to the individual frequency spectra (Math 8 and Table 10 in these examples); (6) pick the range of tones (from mean frequencies in Table 10 in these examples); (7) pick the number of tones to be switched (for example, six tones for a 6 throw switch); (8) calculate the virtual fret steps between switched tones; (9) choose the closest available tones to those steps; and (10) wire or program the mechanical and digital-analog switch to select the circuits that produce those tones.
Since human hearing is very subjective, there's an alternative extension to the method that orders the tones according to the musician's preference. Anytime after step 4, when the samples have been taken and FFT transforms have been stored, the inverse-FFT transform can convert the spectra back into a string of sounds. The sound that comes out will be the average of all the sample windows taken over the entire original length of the notes. So the strike and decay of the sound may be averaged together.
It's the Optometrist approach, and requires either the use of a micro-controller with a digital-to-analog converter to produce the sounds and ask the musician for decisions, or presentation by a person customizing the guitar. The inverse-FFT characteristic sound of each of two switched circuits plays back to the musician, and the software asks, “Which sound is warmer? Tone A? Or Tone B?” Or, the guitar customizer simply plays the tones on the guitar and asks the same questions. Then the musician picks, and the use of an efficient sorting algorithm, such as a shell sort, determines the order of the tones for switching. Then the entire set is played back in order for confirmation and adjustment.
The following examples include equations and tables to help illustrate the method.
Suppose that the only switch available is a 6P6T mechanical switch, and we wish to use the entire frequency range in Table 10 from 632.9 to 1201.1 Hz. Math 14 shows a simple way to calculate the ratio between frequency steps, r, where the lowest frequency, 632.9 Hz, is multiplied by r five times to get the highest frequency and all the steps in between for a 6-throw switch.
It is usually not possible to use the measured mean frequencies to hit those marks exactly. So one takes the choices that seem best. The first frequency, 632.9 Hz, has a pickup combination, S1overN1N2S2, a quad circuit. The closest ones to 719.4 Hz are 712.6 at 0.74 relative amplitude and 713.5 at 2.05 amplitude. The best choice is 713.5 Hz, from combination N1overS2. The 3rd frequency, 817.8 Hz, is 24.9 Hz up from 792.9 and 9.8 Hz down from 827.0 Hz. If signal strength is important, then the lower frequency would be better, but the relative amplitude of the highest frequency output, 1201.1 Hz only has a relative amplitude of 0.23, so S2overN1S1N2 at 827.0 Hz it is. The closest and only choices for 929.6 and 1056.6 Hz are N1overS1N2 at 933.1 Hz and N1S1over N2S2 at 1006.8 Hz, leaving N1overN2S2 at 1201.1 Hz. Table 14 shows the chosen order brightest to warmest tones, according to the mean frequencies of 6 strummed strings.
Compare this to Table 15, representing a 3-way switch giving the bridge HB, the neck and bridge HB in parallel, and the neck HB.
The representation for the middle of the 3-way switch may not be entirely correct, because in this circuit, the center taps of the HB are connected to each other, whereas they are not with a standard 3-way switch. Note also that the relative amplitudes for choices on the 3-way switch are relatively equal to each other, and much larger than those for this switching system using a 6-way switch, by as much as 12.3 times. This means that the output of the 6P6T switching system will have to be electronically amplified, and the gains switched as well to equalize the volumes of the signals. This was addressed in the section on embodiments.
Suppose it should be determined that a better measure of tones comes from giving a weight of 1 to the mean frequency, ½ to the square root of the 2nd moment, and ⅓ to the 3rd root of the 3rd moment in Table 3. The normalized fractions would be 6/11 of the mean frequency, 3/11 of the root 2nd moment and 2/11 of the root 3rd moment, as shown ordered by Weighted moments in Table 16.
Suppose that the same 6-throw switch will be used, with 756.2 Hz the lowest tone, 1206.7 Hz the highest tone, and 4 in between, all separated by the same frequency multiplier. Math 15 shows the calculations.
For 830.3 Hz, 821.8 is 8.5 Hz below and 848.7 is 18.4 above, leaving 821.8 Hz the closest. For 911.6 Hz, 911.7 is closest. For 1001.0 Hz 993.8 Hz is closest, leaving 1076.5 for 1099.0 and 1206.7 Hz. Table 7 shows the results of these choices. Because of the dearth of choices at the high end, only the choices for throws 4 and 6 have changed from Table 4.
Suppose that we wish to remove the near-duplicate tones by specifying that the difference in virtual fret step between tones be 0.5 fret or greater, or a frequency multiplier of 21/24, from Table 10. Obviously, not all of those slots will be filled, and some closer choice may be sacrificed for another with a larger signal. Table 18 shows the first-cut list, choosing 12 out of 25 circuits, with approximate fret steps between mean-frequency choices ranging from 0.5 to 3.1. The first column starts with the first choice, 632.9 Hz, with the value for the half-fret step up in the second column. The next value in the first column is taken from that, either 0.5 fret or more, and so on, except that 933.1 Hz is chosen instead of 934.1 Hz because it is so close. The signal for 792.9 Hz was chosen over 792.8 Hz because it had a stronger signal. The 3rd column shows the relative number of frets from 632.9 Hz; the 4th shows the relative measured amplitude of the signal derived from 6 strummed strings; and the 5th shows the coil connections, with the “+” output shown over the “−” output. The 6th column shows the amplifier gain for each switching combination required to equalize all the signals to the amplitude of the strongest signal, 792.9 Hz for S2 over N1N2. They range from 1.0 to 11.47
Table 19 shows the same method used for Table 18, using weighted moments in Table 6, i.e., [6*(mean−freq)/11+3*(root−2nd)/11+2*(root−3rd)/11] (Hz). In this table, 967.2 Hz with a 0.4 fret step is used because there was nothing else closer, and it allowed 12 tones instead of just 11. This gives a range of fret steps between weighted moments of 0.4 to 2.0. Under the criterion of 0.5 fret step or more, it could be discarded, leaving 11 tones, and a range of fret steps of 0.5 to 2.0. The range of gains required to equalize amplitudes goes from 1.0 to 12.32.
This application claims the precedence in elements of U.S. Provisional Patent Application No. 62/711,519, filed 2018 Jul. 28, U.S. Non-Provisional patent application Ser. No. 15/917,389, filed 2018 Jul. 14, U.S. Provisional Patent Application No. 62/569,563, filed 2017 Oct. 8, U.S. Non-Provisional patent application Ser. No. 15/616,396, filed 2017 Jun. 7, and U.S. Pat. No. 9,401,134B2, filed 2014 Jul. 23, granted 2016 Jul. 26, by this inventor, Donald L. Baker dba android originals LC, Tulsa Okla. USA
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| 62711519 | Jul 2018 | US | |
| 62569563 | Oct 2017 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 15917389 | Jul 2018 | US |
| Child | 16139027 | US | |
| Parent | 15616396 | Jun 2017 | US |
| Child | 15917389 | US | |
| Parent | 14338373 | Jul 2014 | US |
| Child | 15616396 | US |
