Different harmonics available on the guitar. We can

Different pitches are achieved on
the guitar in several ways. One of which is the scale length, which is broken
at 21, 22 or 24 places by frets. Each of these frets is located in a
mathematically calculated place, so that the correct pitch can be achieved. The
formula used for this isThis recursive formula shows that,
for a typical guitar of scale length, distance between the nut and brige,
25.5″, the first fret is at 1.431″, the second at 2.782″, the third at 4.057″
and so on. The value of 18 used to be used, referred to as the “rule of 18” but
by further refinement this has been narrowed down to 17.817 5, known
as the equal temperament constant.

In the same way as for other stringed
instruments, it is simple to work out the lowest harmonics available on the
guitar. We can do this by considering a standing wave on the guitar. As it is a
closed string, we must have a minimum at each end, so the largest wavelength
available for the string is twice the length of the string, with the second
being the length of the string and so on, following the formulaThe key thing that differentiates
the electric guitar from an acoustic guitar is the magnetic pickup. A pickup is
created by coiling a metal with a high intrinsic magnetic moment around 6 permanent
magnets roughly 5 to 10 thousand times, creating a dynamo.

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The magnets in the pickups cause
the portion of the strings above them to become magnetised and thus to produce
a magnetic field. Therefore, when the string vibrates after being plucked, the
string vibrates with a certain frequency and therefore so does the magnetic
field generated by it. This changes the flux through the coils of the pickup,
so the rate of change of the flux is non zero. The induced potential difference
is caused by the electromotive force, described by:When the string vibrates above the
pickup, it generates a potential difference which, when the guitar is plugged
in and makes a complete circuit, creates a voltage and current flows to the
amplifier, allowing for amplification of the note. The pickup is either one
coil, or two coils wired in series but placed in opposite polarities, known as
a humbucker. This humbucker design was created by Gibson and the patent was
applied for on June 22nd, 1955 6. The design was
necessary as single coil pickups are very effective at picking up frequencies
of 50 Hertz 7, frequencies produced by mains wiring, leading to a
distinctive and irritating hum. As the level of electronic gain is increased, a
layer of natural compressions is added which increases the volume of this hum
and leads to feedback loops when playing at high volumes. The design of the
humbucker pickups deals with this by having each coil pick up the same amount
of string vibration and background hum, meaning the voltages are added together
but the ratio of noise to signal is the same. However, as one coil is reversed
relative to the other, the signal produced by the vibrating string is unchanged,
but the hum produced by interference from radio sources and AC current nearby
is reversed between the coils, which cancels out the hum in the output of the
pickup as a whole. In practise, due to small differences between the two coils,
not all hum is cancelled although the majority is.

Using humbuckers, however, changes
the “tone” of the guitar. It does this for several reasons. One of these is
that, by utilising two coils, the total number of turns is more, and a greater
potential difference is generated by the vibrating string. This results in the output
having a higher amplitude, which, when amplified by a valve amplifier, changes
the tone. For example, the natural compression by the valves is increased by the
greater strength of the input signal, resulting in a slightly more artificial
sound. This natural compression in valve amplifiers also results in a more
pronounced bass end of the tone due to the bass elements of the sound being
relatively lower in presence, meaning the sound will cut through a mix with
greater difficulty and therefore will have a harder time being perceived by the
audience. The compression has a third factor to it as well; due to the signal
compressions resulting in asymmetric clipping of the generated wave, distortion
is generated by the amplifier. This change in sound is desirable for certain
genres such as rock and metal where humbucker equipped guitars are
predominantly used but for other genres such as funk, this sound is not.
Therefore, most players in this genre will use low output single coil equipped
guitars to achieve the correct sound.After this, the signal travels through
the circuit of the guitar, often through two potentiometers, one which controls
volume and the other which controls tone. These work by reducing the voltage of
the signal travelling through and therefore reducing the amplitude of the
signal. For the volume control this reduces the volume. For the tone control,
the processes are slightly more complicated. With this potentiometer, a
capacitor is wired between terminal of the potentiometer and the ground, and as
the voltage is changed by the potentiometer, the capacitor acts as a high
frequency drain on the signal, by the formulaIn conclusion, the physics of the
electric guitar are fascinating and allow it to produce a far wider variety of
sounds than most other physical instruments, rather than the technological, for
example by the ability to bend strings and apply vibrato to change the pitch of
a note subtly outside of the chromatic 12 interval Western scale structure. In
addition to this, the pickups of the guitar, by converting the mechanical wave
to an electrical signal by electromagnetic inductance, allow a guitar to be
amplified and have analogue processing applied to the signal, resulting in a
plethora of tones varying both in gain level as well as tonal structure and
balance. This is one of the reasons the guitar is one of the most played
instruments on the planet.