![]() ![]() So the ratio 3:2 gives us what’s called a perfect fifth or the note G, the ratio He theorized that every consonant note between C and its octave could be arrived at by multiplying and dividing 2 and 3. The mathematician Pythagoras also created a tuning system based on ratios. The next is called an octave which is also C, with a 2:1 frequency. Unison intervals are when the ratios are 1:1 known as the note called C. ![]() If we take the ratio of the frequencies, we get the interval. Pleasant sounding notes are caused by consonant sound, or paired frequencies that are different. So, the more cycles the wave makes per second the higher the frequency, meaning the high the pitch. The frequency is measured in seconds, the frequency is thus measured as Sounds waves are periodic, and the opposite or inverse of the period is the frequency. On the other hand, sometimes the waves that we hear are sweet, and pleasing. We see the strings vibrate or oscillate, while sometimes those sounds are harsh and just seem like noise. We hear the frequency of sound from a string that’s strummed. Because frequency is pertains to math, as it can be calculated using an equation, it’s easy to see how math is applied to music and vice versa. Frequency, diatonic and chromatic scales and tunings have used math. To apply this to a guitar, the body of the guitar is designed to vibrate and thus are not actually rigid, meaning the calculations will have a small percentage error.Īll of western music theory has been tied to mathematics for thousands of years. ![]() Volume of the cavity, L is the length of the tube and the x a variable. Is the frequency, c is the speed of sound, S is the surface area of the opening, V is the Different bottles emit sounds of different frequencies due to the sound, the area of the opening, the volume of the cavity and the length of the tube. A classic example of a Helmholtz resonator is a glass bottle when you blow on the top of the bottle, a noise with a certain frequency comes out. The body of a guitar acts very similar to what is called a Helmholtz resonator, which is a cavity with a tube feeding into it. Every instrument creates a sound, and the way the sound is measured always has to do with math. Music is measured by frequency which relates it to math. Math and music have always been connected. They date back to before 1,000 BC as archeologists discovered a clay tablet with a chordophone like instrument. Chordophones can be lutes, guitars, bass guitars and so one. The chordophone is an instrument with a wood body with a long neck and strings. Its predecessors are the gittern, vihuela, the Renaissance guitar, and the baroque guitar. The guitar is a type of chordophone, usually made out of wood with strings originally made from gut, but more commonly today nylon, and steel. The guitar has a rich heritage which isn’t known by many. What math is used to build a guitar? What math is used to engineer sounds? Did the ancient guitar luthiers know about the math? These are some of the questions I’d like to explore. This is what I would like to explore and explain. But, when the subject of guitars is brought up no one ever talks about or explains the math behind it all. The guitar can be acoustic, with a hollow body and no amplification or electric, with a solid body and amplification through an amplifier. The guitar is a string instrument that usually consist of 4 to 18 strings, most commonly known by only having six. At that moment I sprung into conversation and told my dad that I would like to learn the guitar and he responded “ok, let’s get you a guitar.” The guitar has become a big part of our society, an icon of rock music, and a way for people to express themselves. My brother responded that he did not want to. He asked my brother if he would like to learn the guitar. One day, when I was about twelve years old, I overheard my father talking to my oldest brother. ![]()
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