Content uploaded by Donald L Baker
Author content
All content in this area was uploaded by Donald L Baker on Mar 10, 2018
Content may be subject to copyright.
1
Making Guitars with Multiple Tonal Characters
© 2018 Don Baker, Ph.D. retired
dba android originals LC
4203 S 109
th
E Ave
Tulsa OK 74146
Abstract
If a guitar, or other stringed instrument has K number of matched single-coil
electromagnetic pickups, and the magnetic poles of those pickups can be easily reversed
with respect to the ferro-magnetic strings, then it can have 2
K-1
tonally unique pole
position configurations. Taken 2 at a time, for humbucking pairs, there are K*(K-1)/2
pair combinations. If the pairs are connected in series or parallel for different tones, then
there are K*(K-1) possible unique tones for each of the 2
K-1
pole configurations. Since
for each pair combination, the pole orientations can be either opposite, for an in-phase
humbucking pair, or the same, for a contra-phase humbucking pair, for 2*K*(K-1)
possible unique tones. So each of the pole configurations will have a unique set of
K*(K-1) out of the possible 2*K*(K-1) tones.
Notice – Patent Pending
This material comes from U.S. Provisional Patent Application, filed June 20, 2017,
and from the theoretical background presented in a U.S. Non-Provisional Patent
Application, filed by this author March 9, 2018, regarding the design and embodiments of
electromagnetic pickups with reversible poles.
2
Background
The concept of humbucking pairs, using single-coil pickups, matched for equal
response to external hum signals and fields, was developed for U.S. Patent 9401134B2
(Baker, July 26, 2016). It referenced a fourth prototype guitar used four single-coil
pickups, with turns added until their responses to an external AC field was sufficiently
equal to be called humbucking. Two of the pickups had their fields reversed by applying
a stronger magnet to erase and reverse them.
That prototype connected the 4 pickups to two 5-way superswitches.through a 4PDT
switch. The superswitches are 4P5T lever switches. The pickup poles were configured
from neck to bridge as N1 (north-up), S1 (south-up), S2 & N2. The switches would have
needed to be 6PXT to produce both in-phase and contra-phase humbucking pairs, so this
setup produced only in-phase humbucking pairs and quads. On 5-way switch produced
the outputs for (N1+S2)||(S3+N2), N1+S2, N2+S3, S2+N4 and S3+N4, where “+”
indicates a series connection and “||” indicates a parallel connection. The other 5-way
switch produced outputs for N1||S2||S3||N4, N1||S2, N1||S3, S2||N4 and S3||N4.
As will be shown below, with a better switching system, the N1, S2, S3, N4 pole
configuration could have produced 4 in-phase humbucking signal pairs and 2 contra-
phase humbucking signal pairs, which pairs could also have been connected in series or
parallel for a total of 12 possibly unique tones. One uses the term “possibly unique”
because, although all of the outputs will have different tonal characters, the differences
are not equally large. Because of the interaction of string harmonics and in-phase and
contra-phase pickup pair physical separations, it is always possible that some tones could
be close enough to be barely distinguishable by ear or spectral measurement, as shown by
other experiments, not presented here
. The development of humbucking pairs continued, as demonstrated on
HumbuckingPairs.com, a sub-section of TulsaSoundGuitars.com, and based upon basic
guitar series-parallel tonal circuits (Baker, 2018).
Positional pairs from K = 2 matched single-coil pickups
Let us start with a trivial case, for K = 2 pickups. The poles north, N, and south, S,
are binary, and can thus the physical arrangements from neck to bride for K number of
pickups be considered as an ascending sequence of binary numbers, starting from
0…000, where there are K number of zeros, advancing to 0…001, and to 0…010, to
0…011, and up. Let these be replaced by N…NNN, N…NNS, N…NSN, N…NSS, and
so forth, replacing 0 with N and 1 with S. So for two pickups forming a humbucking
pair, we have the positional configurations:
Math 1. Physical pole placement of two pickups
Neck pickup N1 N1 S1 S1
Bridge pickup
N2 S2 N2 S2
Signal n1-n2
n1+s2
s1+n2
s1-s2
3
Notice the symmetry of the table in Math 1 in substituting N for S and vice versa.
For matched pickups the human ear cannot tell the difference between (n1-n2) and (s1-
s2), or between (n1+s2) and (s1+n2). In other words, tonally, (N1,S2) = (S1,N2) and
(N1,N2) = (S1,S2). So for K = 2 matched single-coil pickups, there are only 2 effectively
different pole arrangements. If the two pickups are connected in series or parallel, then
there are only 4 different signals obtained from changing the pole orientations, of which
only 2 series-parallel signals can be had for each pole configuration.
Positional pairs from K = 3 matched single-coil pickups
Math 2. Physical pole placement of 3 pickups; “+” means in-phase signals, “-“ means
contra-phase signals
Neck
pickup N1 N1 N1 N1 S1 S1 S1 S1
Middle
pickup N2 N2 S2 S2 N2 N2 S2 S2
Bridge
pickup N3 S3 N3 S3 N3 S3 N3 S3
Signals
(n1-n2)
(n1-n3)
(n2-n3)
(n1-n2)
(n1+s3)
(n2+s3)
(n1+s2)
(n1-n3)
(s2+n3)
(n1+s2)
(n1+s3)
(s2-s3)
---- ---- ---- ----
Phases
-
-
-
-
+
+
+
-
+
+
+
-
Again, the positional order of north poles, N1, N2 & N3, produces the same tones as
the positional order of south poles, S1, S2 & S3. So the second (right) set of 4 columns
in Math 2 merely duplicates the tones in the first (left) set of 4 columns. If changing all
the poles of one order merely produces the magnetic mirror image of an order already
created, then it can only produce duplicate tones and must be discarded. The same is true
of pairs, such as (N2,S3) and (S2,N3). Note that starting with all contra-phase tones on
the left, all the additional tones due to changing poles are in-phase. All the signals that
are underlined are duplicates in tone of signals already generated to the left.
With positional pole combinations for K = 3, one can choose either all contra-phase
outputs, or two in-phase outputs and one contra-phase output, regardless of whether or
not the pair is connected in series or parallel. By trying different pole combinations, one
can see that it is not possible to choose a setup with two contra-phase and one in-phase
output. Nor is it possible to set up a pole position combination that produces all in-phase
outputs.
K = 3 things taken 2 at a time produces K*(K-1)/2 = 3*2/2 = 3 different pair
combinations, as shown in the Signals and Phases rows of Math 2. Each of these pairs
can be connected in series or parallel, producing K*(K-1) = 3*2 = 6 tones per pole
configuration. Each of the pole pairs can be either in-phase or contra-phase, depending
on the poles up, producing a total of K*(K-1) = 3*2 = 6 different in-phase and contra-
4
phase pairs, as shown by the Signals row signals in Math 2 without underlines.
Combining series-parallel and pole configuration choices give 2*K*(K-1) = 2*3*2 = 12
different possible tones from all choices.
Positional pairs from K = 4 matched single-coil pickups
Math 3. Physical pole placement of 4 pickups
Neck
pickup N1 N1 N1 N1 N1 N1 N1 N1
Upper
Middle N2 N2 N2 N2 S2 S2 S2 S2
Lower
Middle N3 N3 S3 S3 N3 N3 S3 S3
Bridge
pickup N4 S4 N4 S4 N4 S4 N4 S4
Signals
(n1-n2)
(n1-n3)
(n1-n4)
(n2-n3)
(n2-n4)
(n3-n4)
(n1-n2)
(n1-n3)
(n1+s4)
(n2-n3)
(n2+s4)
(n3+s4)
(n1-n2)
(n1+s3)
(n1-n4)
(n2+s3)
(n2-n4)
(s3+n4)
(n1-n2)
(n1+s3)
(n1+s4)
(n2+s3)
(n2+s4)
(s3-s4)
(n1+s2)
(n1-n3)
(n1-n4)
(s2+n3)
(s2+n4)
(n3-n4)
(n1+s2)
(n1-n3)
(n1+s4)
(s2+n3)
(s2-s4)
(n3+s4)
(n1+s2)
(n1+s3)
(n1-n4)
(s2-s3)
(s2+n4)
(s3+n4)
(n1+s2)
(n1+s3)
(n1+s4)
(s2-s3)
(s2-s4)
(s3-s4)
Phases
-
-
-
-
-
-
-
-
+
-
+
+
-
+
-
+
-
+
-
+
+
+
+
-
+
-
-
+
+
-
+
-
+
+
-
+
+
+
-
-
+
+
+
+
+
-
-
-
In Math 3, there is simply not enough room on the page, nor need, to show the next 8
columns which have magnetic symmetry to the first 8 columns. K = 4 things taken 2 at a
time produces K*(K-1)/2 = 4*3/2 = 6 different pair combinations, as shown in the
Signals and Phases rows of Math 3. Each of these pairs can be connected in series or
parallel, producing K*(K-1) = 4*3 = 12 tones per pole configuration. Each of the pole
pairs can be either in-phase or contra-phase, depending on the poles up, producing a total
of K*(K-1) = 4*3 = 12 different in-phase and contra-phase pairs, as shown by the Signals
row signals in Math 3 without underlines. Combining series-parallel and pole
configuration choices give 2*K*(K-1) = 2*4*3 = 24 different possible tones from all
choices.
We see that in the 8 different pole positional combinations, 6 unique contra-phase
signals and 6 unique in-phase signals are produced for a total of 12. Note in the columns
that it is possible only to have either 6 contra-phase signals, or 3 contra-phase and 3 in-
phase, or 2 contra-phase and 4 in-phase signals.
5
Examples with Four Matched Pickups
Fig. 1
Fig. 1 shows and arrangement of four matched single-coil pickups, designated N1,
N2, N3 & N4, mounted between the neck and bridge in a guitar like that presented in US
9401134 B2 (Baker, 2016). Note that they all have moveable mounts, and are situated on
rails with an extended fret scale, with the pickups sitting on extended frets 24, 29, 36 and
48 near the bridge. All have north poles up, and thus must be connected together in
contra-phase pairs to be humbucking, producing K*(K-1)/2 = 4*3/2 = 6 different contra-
phase combinations, designated (N1,N2), (N1,N3), (N1,N4), (N2,N3), (N2,N4), &
(N3,N4). Designating the signals from the respective pickups as n1, n2, n3 & n4, the
corresponding pair outputs would be (plus or minus) (n1-n2), (n1-n3), (n1-n4), (n2-n3),
(n2-n4) & (n3-n4). Series and parallel connection of each pair would double the number
of possible tones to 12.
6
Fig. 2
Fig. 2 shows changing the pole at the second position to south up, designated as S2,
leaving the designations N1, N3 & N4 unchanged. Note that this configuration produces
3 contra-phase humbucking pairs and 3 in-phase humbucking pairs. Also note that the
pairs (N1,N3), (N1,N4) and (N3,N4) will produce the same signals as they do in Fig. 1.
So only 3 new signal combinations, and thus possibly unique tones, have been added to
the total. Using s2 to indicated the signal from pickup S2, those signals are (n1+s2),
(s2+n3) & (s2+n4). Note that the “+” symbol in these expressions refers to addition in
the context of signals, not a series connection.
7
Fig. 3
Fig. 3 shows the pickup in the 3
rd
position changed from north up to south up,
designated as S3, with signal s3. This produces 2 contra-phase humbucking pair outputs,
(n1-n4) and (s2-s3), and four in-phase humbucking pair outputs, (n1+s2), (n2+s3),
(s2+n4) & (s3+n4). Note that the human ear has no reference to distinguish a signal in
Fig. 1, (n2-n3), from a signal in Fig. 3, (s2-s3). Also, the signals (n1-n4), (n1+s2), and
(s2+n4) are also duplicated from Figs. 1 & 2. So this configuration adds only 2 new
signals to the total, (n1+s3) and (s3+n4). So among these three Figures, which are not
exhaustive, there are 6 unique tonal combinations of pairs.
Comments and Conclusions
So for each pole configuration, K number of pickups can produce 2
K-1
pole
configurations, as shown in Math 4. Each pole configuration has K*(K-1) unique
humbucking pair tones, including series and parallel connections of the pickups in the
pairs. The total number of unique humbucking pair tones one can achieve with both pole
8
configurations and series-parallel pair connections is 2*K*(K-1). Obviously, a musician
has a great many more tonal choices if he or she can change the poles of matched single-
coil pickups at will. But this can only be achieved if the pickup switching system has and
uses information on which pickup has which pole up.
Math 4. Number of pole configurations, tones per configuration & total tones for K
pickups
K = 2 3 4 5 6 7 8
2
K-1
= 2 4 8 16 32 64 128
K*(K-1) = 2 6 12 20 30 42 56
2*K*(K-1) = 4 12 24 40 60 84 112
So a guitar with 3, 4 or 5 matched single-coil pickups can have 4, 8 or 16 different
tonal characters, or personalities, if the poles of the pickups can be easily reversed. But
not all of the personalities will be useful for all musicians. A limit of about 8 or 9 single-
coil pickups can fit between the neck and bridge of an electric guitar with the common
nut-to-bridge base length of about 25.5 inches (648 cm). As the pickup get closer
together with increasing K, the distinctions between tones will diminish. There may even
be electromagnetic coupling between very close pickups, which will tend to reduce tonal
differences. Furthermore, the contra-phase signals from pickup pairs that are close
together tend to be thin and weak. A pole configuration with all contra-phase tones may
be somewhat less useful that those with a mix of in-phase and contra-phase tones.
So on a standard-sized electric guitar, the practical limit for the number of matched
single-coil pickups may be in the range of 4 to 6. On the other hand, a piano would have
no such limitations, since at least half of an entire string could have pickups placed along
it. Nevertheless, having 3 or 4 useful tonal personalities for a 3-coil electric guitar would
make the instrument much more versatile and customizable.
References
Baker, D.L., 2016, US9401134
Baker, D.L., 2018, On the topologies of guitar pickup circuits, DOI
10.13140/RG.2.2.18044.85123,
https://www.researchgate.net/publication/323390784_On_the_Topologies_of_Guitar_
Pickup_Circuits
HumbuckingPairs.com
TulsaSoundGuitars.com