Music is produced by controlled vibrations, eg the vibration of guitar or violin strings, a saxophone reed or the lips of a trumpeter. These vibrations create sound waves. Any object which vibrates will create a sound, which could be musical or otherwise. The frequency at which an object tends to vibrate when struck, plucked, etc, is called its natural frequency. If the vibrations are big enough and if the natural frequency is within the human frequency range, then the sound can be heard. The actual frequency at which an object will vibrate is determined by a variety of factors. Each of these factors will either affect the wavelength or the speed of the vibration. Since:
frequency = speed/wavelength
an alteration in either speed or wavelength of the vibration will result in an alteration of the frequency (and the pitch of the note). The role of a musician is to control these variables and produce a given frequency from the instrument being played.
A guitar has six strings, each having a different density (the thicker strings are more dense per metre), a different tension (which is controllable by the guitarist), and a different length (also controllable by the guitarist). The speed at which waves move through a string depends on the tightness (tension) and density of the string. Changes to these properties affect the natural frequency of a particular string. The vibrating bit of the string can be shortened by pressing the string against one of the frets on the neck of the guitar; by changing the length of the string you change the wavelength of the wave, the frequency the string vibrates at and the pitch of the note produced. The same principles can be applied to any string instrument – the piano, harp, violin, guitar… OR SAW!!!!! All objects have natural frequencies, which are the frequencies at which standing wave patterns are established within the object. These vibration patterns produce the highest amplitude (loudest) vibrations with the least input of energy, and they consist of whole numbers of waves. Some examples are given to the right, but note that the string has got to have a start and an end – remember this when we look at AB/BC on the saw: When a guitarist wants to play, he or she tunes the guitar by tightening or loosening the tuning screws to get each string to the right tension. Once the guitar is tuned in this way, the only thing that changes the pitch of the note is the position of the fingers on the fret board which change the length of the string. The same is true of a violin. The volume of the sound can be increased by plucking or bowing harder or faster. However, a saw player will tell you that this is a piece of cake! The strings stay the same length unless they are stopped by an accurately placed finger, and the tension stays the same. It only gets complicated when you come to play several strings at once.
Compare a“string” instrument to a saw blade. Because the blade is an S-shape, you have created three virtual strings, the sections AB, BC and CD. The outer strings, AB and CD, are much shorter than the main string BC. These strings produce higher notes and often harmonics (Squeaks). Changing the pitch of the note is achieved by changing the length of the string and/or through applying additional tension.
Tension is created by:
1. Moving your thumb, wrist OR hand position and combining it with where you place the bow on the blade.
2. Moving your arm can completely change the shape of the S, and positions of B and C. This can either bring those two positions closer together to raise the pitch or move them apart to lower it. When you get the hang of this instrument you can even merge two virtual strings together. The extended string produces low pitched notes.
3. If you change the bowing position, you can swap between the two strings . This sometimes can produce accidental chords based loosely upon major/minor 3rds and 6ths.
Confused? The good news is that when you play the saw, you don’t have to do the calculations every time you play a note, you go by instinct. It just helps to have an idea of the theory and a musical ear.
A word about rosin: Any violinist will tell you that before you put horsehair to catgut, you need to smear your bow liberally with rosin, to make the bow “sticky”. Saw players do the same. The principle is the same as the wine glass trick – see below.
The wine glass trick: Obtain a wine glass and clean your fingers. Gently slide your finger over the rim of the glass. You may be able to set the glass vibrating by means of slip-stick friction. Like a violin bow being pulled across a violin string, the finger sticks to the glass molecules, pulling them apart at a given point until the tension becomes too great. The finger then slips off the glass and finds another microscopic surface to stick to; the finger pulls the molecules at that surface, slips and then sticks at another location. This process of stick-slip friction is sufficient to set the molecules in the glass into vibration at its natural frequency. The result is enough to impress your dinner guests. Try it at home!!
For further information regarding the musical saw why not watch this wonderful video featuring Mairin Ryan, from Athlone in Ireland. She talks to Discover Science & Engineering about her project on The Physics of the Musical Saw at the BT Young Scientist & Technology Exhibition 2010.