Sample donated: Georgia Hamilton
Last updated: December 31, 2019
Harmonicsare a vital part in what makes music sound so pleasant. It is the epitome inwhich all music has and will continue to be created.
I am interested instudying harmonics because I have been working with music since I was aboutfour years old and to this very day, as a high school student nearing theirgraduation, I continue with it. I think of music as not only a form of beingcreative but also as a way to relieve stress or simply keep busy. Music helpskeep 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 sightread it or focus on the dynamics, I’m soon swept away by my focus and forgetabout my frustrations or whatever I was angry about.
Therefore, music hasgreatly impacted me in my life, which is why I am curious to see how math playsits role in the music world. In the theory of Left Brain vs. Right Braindominance, I had believed that I was more dominant on my right brain than on myleft 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 itwould be so hard as to figure out how it exactly plays a role in the world ofmusic because of how complex it might seem. I wanted to figure out howharmonics are intertwined with math and music because it would give me a betterchance to understand the math and Thisreport will focus on harmonics and its connection between math and music.
Investigation: Inmusic, a harmonic is a frequency that accompanies a fundamental tone at a fixedinterval, 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 ofthe harmonics to sound without sounding its fundamental frequency, it is thencalled playing a harmonic. In math, a harmonic is something that is relating toa harmonic progression. In order to understand harmonics, we must understandfrequency, which is the rate at which a vibration occurs and it is measured inhertz (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 specificfrequency, the fundamental frequency. Higher frequencies that vibrate are knownas composite frequencies because they are a result of the vibrations of fundamentalfrequencies. When the fundamental frequency and all of its compositefrequencies are perceived by a listener, they are rarely heard as separatepitches. A listener will more likely hear all of the frequencies wrapped togetherto form a composite tone. Anytime that an instrument produces a pitch, it will usually make a range ofcomposite frequencies which allows to add to the richness of the tone and willallow us to differentiate sound qualities, such as the way a violin sounds incomparison to the way a guitar sounds. Next,we move to overtones, which are any composite frequency that vibrates higherthan the fundamental frequency, even if it is or isn’t a harmonic.
Almost allof the time, overtones in an instrument will be harmonics, which makes things abit confusing because then the terms are interchangeable. However, there aresome instruments, like percussion instruments, that will not produce overtonesthat are harmonics. Mathematicsplays a large role in harmonics. For instance, in order for a compositefrequency to be considered a harmonic, its frequency must be an integermultiple of the fundamental frequency. In math, there is the harmonic series,which derives from the concept of overtones and the wavelengths of them andtheir vibrating strings.