May 2014

The Physics Behind the Violin.

Here is a paper I wrote for physics as extra credit. I didn't include absolutely everything I could, but still I hope you enjoy!

The Physics Behind the Violin.
The violin remains to be the most loved, most antique, and most appreciated musical instrument. Officially originating in northern Italy in the early 16th century, the violin created a simple connection with the human voice due to the nature of both instruments’ tone. As well as being used as the dominant instrument within any orchestra, it became a good solo instrument too, for this reason, and continues to be used in music today, especially in film—both with the context of a romantic setting, producing warm vibrato, or a dramatic battle scene, whirling away with a rapid succession of notes. As many aspects there are within the violin—in regards to not only performance, but also tone color, compositional techniques, or even within the art of crafting the physical object itself in types of wood or strings—an aspect that remains to fascinate and amaze is the science behind how this amazing piece of wood manages to create such a beautiful sound when played.
Stringed instruments go all the way back to 9th century Ancient Greece. In that time, music was not so much an art form as it was mathematical . Consider the A string on the violin (the next-thinnest one). Let us assume that the string is x meters long. When the string is bowed or plucked, the sound of an A4 is heard, also known as Concert A. The string has a fundamental frequency of 440 cycles per second, but the sound also contains frequencies of 880, 1320, 1760, and so on, because the note contains many harmonics (or ‘tones’) that vibrate around the hall. This can be graphed into a sine wave (see Figure 1.) Each curve on the wave represents the number of cycles—or the frequency of oscillation. 440 Hz translates to the sine wave cycling through 440 times in one second. In Ancient Greece, Pythagoras contemplated the math behind these strings. If the string is x meters long, and one were to lightly touch one’s finger exactly halfway along the string and bow or pluck, the area in which the string has to vibrate is now 1/2 x meters along the string. This will raise the pitch by an octave, which is called a harmonic. By placing fingers down on each string, the violinist is able to change the pitch this way, due to the string having less and less room to vibrate.

Figure 1.
However, the violin is an incredibly complex instrument—the object itself contains plenty of features that all work together to get the sound out of the instrument and into its listener’s ears. No matter the note, a vibrating wooden box processes the sound. This box is automatically set to a specific size, and it chooses which frequencies it “favors” and which it does not. The favored frequencies are produced more loudly (naturally) than the others, which is why the higher up one travels on the E string, the scratchier the sound that is produced. This “favored choosing” of the frequencies is known as formant.
Refer to Figure 2 below. The violinist recorded a C#5, played on the A string, and put it through a feedback system that connected with the computer. This project was completed to complete a timbral analysis (timbre is just a fancy word of characteristic of sound heard) in regards to orchestration. The audio file (in .wav format) lasted about 0.8 seconds, and from the graph it can be determined that sound can naturally dissipate rather quickly. It requires extra force and push on the bow to keep the sound and tone even throughout. Additionally, the beginning of the curve tends to waver a bit more; thus the act of vibrato, or physically moving one’s finger back and forth to waver the note, is more compact at the beginning of the performance .

Figure 2.
The mechanics of the violin are vastly different to that of other stringed instruments. Unlike a guitar or a lute, which calls for the player to pluck their strings, the violin’s tone is often controlled with a bow (see Figure 3), which drags across the strings to make the string vibrate, thus producing the warm tone heard today. The initial pressure of the act of initially drawing the bow across the string “excites” the string into producing pitch—as if the string were being plucked one thousand times a second. In slow-motion, if one were to pluck the string, the string is first pulled out in one direction, but, by Newton’s Third Law, which states that every action has an opposite and equal reaction, aided by the fact that the string is held down by the bridge and the tuning pegs, the string is forced to bounce back the other way, thus creating its vibration. This event occurs many times over again even after the string has long been plucked, until it finally bounces back and forth to an equilibrium state—back to its natural setting parallel with the fingerboard. The same thing occurs even with a bow—only it is much faster and is able to sustain the pitch; as the bow is drawn across the string, until it is taken off the string or stopped entirely, the string is constantly “resetting” itself over again before it has a chance to bounce to its equilibrium state.

Figure 3.
Music is a very powerful idea, and the violin a very powerful object in which to continue its flow. One of the most incredible things about the violin is in the way it was designed, using the analysis of Pythagoras and other philosophers to create an antique object (no matter when it was made!) that still fascinates and amazes the world today. It is still used in full flow and glory even today, superseding the need for the lute, which is incredible in its own right. Let the science speak for itself unto why music is so miraculous.

Sources
http://www.cs.princeton.edu/courses/archive/spring10/cos233/assignments/dsp/
http://www.physicscentral.com/explore/action/fiddle.cfm
https://ccrma.stanford.edu/~jmccarty/hcipage.htm
How Music Works by John Powell

Pictures and graphs courtesy of Google Images.

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CSO Concert/Spring Film

This afternoon from 1pm-3pm I got to see the Chicago Symphony Orchestra playing live! The theme was all of Beethoven’s works (so, symphonies 4, 5, 8, and 9, plus his violin concerto). It was also a family community concert, which educational quips in between pieces about Beethoven as a person. Each piece had a different emotion to it, which made the concert very well-rounded, and I was analyzing each piece in my head as I listened. It was also cool because up until today, I had just been listening to recordings of these pieces; to hear them live is an experience like no other, which is why I always love live orchestras. I know especially how awesome it was during the last couple of summers, seeing concerts during warm summer evenings, and I think we’re going to try to go to some concerts as a family this summer, too. :)

Also, since I’ve never really talked about this before, in Spanish class we got a ‘final project’ which is to make a film (see it below). Of course, this was right up my alley, because I love film and obviously want to become a film composer. Luckily, I got good group-mates who were as eager as me about this (one member was a really good director in planning out the film, and maybe wanted to go into directing, so I asked him to recommend me for music when he did). Anyways, we had a lot of fun recording, and after last Wednesday night, the project turned to me for editing and music. I wrote down my ideas on the piano in my notebook, then transferred them into the film, making sure each moment hit at the right accent points. It was so cool when the puzzle pieces snapped into place as I was working! Last night I had my friend edit two of the four tracks in the film. By edit, I mean put into a software he uses to make Finale’s MIDI into an amazing orchestration that sounds incredible! I hope you’ll enjoy it when you watch the film. In any case, enjoy!

On one final note, this Tuesday is our Pops Concert! This year’s theme is Classic Rock, and during the actual concert, we’re going to have, along with the orchestra of acoustic instruments, a quartet of electric instruments, electric guitar, electric bass, and drums. It’ll be a cool night, especially for the parents! Mr. Burck has been showing us his old record player and how records like the 45 work. It’s very interesting stuff, too… In a way, I think the old record players are even cooler then today’s technology, but you know.

Anyways, thanks for reading! Sorry it’s been so long since I last posted, I’ve just been so busy. Enjoy the film if you watch it! I guess I'll call it the spring film, if we're still doing something this summer.... :)

https://www.youtube.com/watch?v=y0j57ESx38s

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