There are many ways of making sound on an instrument, which we take for granted, and seldom precisely understand why each different technique yields a different sound.  In my creative project, I attempt to explain the physics behind the techniques that yield different sounds on the violin through a composition. The composition showcases different methods of making unique sounds on the violin using techniques such as col legno, pizzicato, natural harmonics, sul tasto, and chords.  I also included a few measures designed for the musical saw because of the interesting properties of its sound.

Project Description

The first step in my project was to make a list of the elements that make violin music aesthetically appealing, allowing me to pick the ones on which to focus.  The elements were timing/time signature, tempo, dynamics, key, timbre, and technique/effects.  I decided to choose technique/effects as my focal point because they are used much less frequently than the other five elements, and hence are often overlooked. The techniques I integrated into my piece are col legno, pizzicato, sul tasto and harmonics.  I also decided to include a few measures to be played on the musical saw because of its particularly interesting sound. 

The intersection of mathematics with these effects isn’t obvious.  However, these effects are made using physics, which is a branch of study that is closely involved with mathematics.  Violin music is created by vibrating a string, which creates standing waves, and by manipulating the waves in different ways, different effects are created.  

To play the violin in the most traditional way, a bow is drawn across a string.  The bow creates sound in the same way that plucking a string repeatedly creates a sound.  Drawing a bow across a string creates a slip-stick cycle where the bow grips the string and then releases it.  Rosin is generally applied to the bow hair to increase its coefficient of static friction.  Bowing the string too slowly makes it so you can hear the sticks exclusively and bowing too fast makes it so you can hear the slips exclusively.  When bowing a string, the entire range of high, low, and the fundamental harmonic are maintained and only dissipate when the bow stroke ends. There must be an equation or slip-stick frequency in relation to bow speed, though I do not know if it is linear, exponential, logarithmic… and I have not succeeded in finding it.  It can be determined that “the cycle of stick and slip on the bow has the same period as the vibration of the string” (Wolfe).  In my project, we will work out an equation to describe the time of a slip-stick cycle, and one for the amplitude of the motion of the string at the bowing point based on variables such as string length, distance from the bridge, and period of the vibration of the string.  

Having thus laid the foundation for understanding the physics behind bowing the violin in the traditional way, we transition to a discussion of the effects mentioned above.  

Sul Tasto refers to the technique in which the bow is drawn over the fingerboard to create a finer, more muffled sound.  The sound here is more muffled because the area where the string is vibrating most is positioned away from the f-holes.  The string vibrates most where the bow interfaces with the string, so positioning it away from the f-holes gives the impression of a muffled sound.  

The pizzicato technique yields a short burst of sound that dissipates quickly, in contrast with the long, sustained sound that a bow drawn across the string produces.  This is because drawing a bow across the string sustains the vibration without letting it dissipate, whereas a pizzicato only vibrates the string for an instant.  When a bow is drawn across a string, a note is maintained.  However, after a pluck, the high harmonics fade away quickly, leaving only the fundamental and some weak lower harmonics. Bowing maintains the rich harmonic spectrum.

Col Legno refers to tapping the string with the back of the bow that produces an effect similar to pizzicato, where we perceive a short burst of sound that dissipates quickly.  The sound dissipates quickly because striking the wood is not a continuous input of energy.  This sound has a different quality than pizzicato; it sounds drier and more staccato.  This is because we hear the collision of the stick and the string, which is percussive.

The word “harmonics” denotes the overtones that are present in addition to the fundamental frequency.  The standing wave pattern of a fundamental frequency contains only two nodes.  As we add nodes, we get to the second harmonic, then the third, etc..  When we know the number of waves in a string, we can derive an equation relating the wavelength of the standing wave to the string length.  On the violin, we can play a “true harmonic” without its fundamental frequency by placing a finger lightly onto a string in specific places, and drawing the bow across the string as usual.  To play an “artificial harmonic”, one simply places a finger as if to play a regular note, and places an additional finger lightly on the string four whole steps away.

Our final “effect” isn’t really an effect; it is a peculiar sound made by a peculiar instrument.  A sound by a musical saw is clearer than on most instruments because a saw usually only creates one single harmonic along with the fundamental frequency, instead of a broad range of harmonics, which is the reason why the sound carries so well on the wind and sounds much more clear. A sound is made when the bow is drawn across the saw which is curved into the S shape; this can also occur when the saw is in a C shape.  The player must find the “sweet spot” of the saw in order to make a sustained pitch.  The “sweet spot” is a flat part of the metal, and it can be moved up and down based on the curvature of the saw.  When the player drags the bow across the saw, they cause the saw to vibrate, which creates the sound.  Like bowing a violin, a slip-stick motion occurs here as well.  

This paper has attempted to explore some of the physics behind violin effects.  I wonder if this exploration will change the way I perceive my own playing, and I ask if my playing will be improved with this new knowledge.  I am curious if violin students would benefit from the knowledge of this physics and if it would improve their playing.  I wonder if I could put together a booklet on this. But that is a project for another time!

Works Consulted

Cox, Trevor. “Musical Saws and Harmonics.” The Sound Blog, 31 Dec. 2009, acousticengineering.wordpress.com/2009/12/31/musical-saws-and-harmonics/.

McNamee, David. “Hey, What’s That Sound: Musical Saw.” The Guardian, Guardian News and Media, 7 June 2010, www.theguardian.com/music/2010/jun/07/musical-saw.

“Physics Tutorial: Fundamental Frequency and Harmonics.” The Physics Classroom, 2000, www.physicsclassroom.com/class/sound/Lesson-4/Fundamental-Frequency-and-Harmonics#:~:text=The%20frequencies%20of%20the%20various,frequency%20of%20the%20first%20harmonic.

“Tonal Effects.” Strings – Orchestration Skills-Step 8, inmusica.fr/SC/Orchestration_Skills_-_Strings-Step_8.htm.

Wolfe, Joe. “Bows and Strings.” The Bowed String, The University of New South Wales, newt.phys.unsw.edu.au/jw/Bows.html.


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