are a vital part in what makes music sound so pleasant. It is the epitome in
which all music has and will continue to be created. I am interested in
studying harmonics because I have been working with music since I was about
four years old and to this very day, as a high school student nearing their
graduation, I continue with it. I think of music as not only a form of being
creative but also as a way to relieve stress or simply keep busy. Music helps
keep me busy and allows my mind to take a break from the present. For instance,
if I’m frustrated and I pick up a piece of music to learn and begin to sight
read it or focus on the dynamics, I’m soon swept away by my focus and forget
about my frustrations or whatever I was angry about. Therefore, music has
greatly impacted me in my life, which is why I am curious to see how math plays
its role in the music world. In the theory of Left Brain vs. Right Brain
dominance, I had believed that I was more dominant on my right brain than on my
left because of my creativity, but when I heard that there was math in music,
besides the occasional counting of beats in a measure, I had wondered if it
would be so hard as to figure out how it exactly plays a role in the world of
music because of how complex it might seem. I wanted to figure out how
harmonics are intertwined with math and music because it would give me a better
chance to understand the math and
report will focus on harmonics and its connection between math and music.
music, a harmonic is a frequency that accompanies a fundamental tone at a fixed
interval, which is produced by the vibration of a string, column of air, etc.
but it does so in the exact fraction of its length. If a musician causes one of
the harmonics to sound without sounding its fundamental frequency, it is then
called playing a harmonic. In math, a harmonic is something that is relating to
a harmonic progression.
In order to understand harmonics, we must understand
frequency, which is the rate at which a vibration occurs and it is measured in
hertz (Hz), which is calculated by finding the number of vibrations per second.
When a pitch is produced, it creates a soundwave that vibrates at a specific
frequency, the fundamental frequency. Higher frequencies that vibrate are known
as composite frequencies because they are a result of the vibrations of fundamental
frequencies. When the fundamental frequency and all of its composite
frequencies are perceived by a listener, they are rarely heard as separate
pitches. A listener will more likely hear all of the frequencies wrapped together
to form a composite tone.
time that an instrument produces a pitch, it will usually make a range of
composite frequencies which allows to add to the richness of the tone and will
allow us to differentiate sound qualities, such as the way a violin sounds in
comparison to the way a guitar sounds. Next,
we move to overtones, which are any composite frequency that vibrates higher
than the fundamental frequency, even if it is or isn’t a harmonic. Almost all
of the time, overtones in an instrument will be harmonics, which makes things a
bit confusing because then the terms are interchangeable. However, there are
some instruments, like percussion instruments, that will not produce overtones
that are harmonics.
plays a large role in harmonics. For instance, in order for a composite
frequency to be considered a harmonic, its frequency must be an integer
multiple of the fundamental frequency. In math, there is the harmonic series,
which derives from the concept of overtones and the wavelengths of them and
their vibrating strings.