Pitch and Tuning
There are three main components that determines a string's fundamental pitch:
Pitch is the frequency of the sound wave created by the vibrating string of the instrument. The string is able to vibrate because it is a harmonic oscillator. This means that its motion is repetitive and the amount of time needed to complete one cycle of this motion is dependent on the stiffness and inertia of the string.
Stiffness is how strongly the string snaps back toward its resting position when it is displaced by either bowing or plucking a string. A loose string (decreased tension) will not move back to resting position or equilibrium as quickly as a tight string. This means that the loose string completes a vibration cycle less often than a tighter string. As a result, the sound wave created by the instrument also has less cycles or a lower frequency/pitch. The opposite is true of a tighter string (increased tension). This is why guitars, violins, and other stringed instruments can be tuned by twisting the tuning heads on the instrument's head. The twisting either tightens or loosens the string, causing the fundamental pitch of the string to increase or decrease as a result of the change in string tension. See Figures 9.2.1 and 9.2.2 in Media tab.
Mass affects pitch because of a property called inertia. When the string is let go after it is displaced by plucking or bowing, it accelerates back to its resting position. Newton's Second Law of motion tells us that acceleration is equal to the force applied on an object divided by that object's mass. Or, in simpler terms, the same force on a larger object will result in less acceleration. This makes sense if you think of pushing a fully loaded grocery cart versus an empty one. The full cart has much more mass and is much harder to get going than the empty one. This same principle applies to the string. Strings of greater mass will produce a lower frequency sound wave because they vibrate less often than strings of smaller mass.
The consequence of these circumstances is that to play a different pitch other than the strings fundamental pitch and its harmonics, the individual playing the instrument must either change the tension or the mass of the string. Altering string tension during the middle of a song, like when tuning, would be very difficult. The other option, changing the mass of the string, may initially sound difficult as well. However, it is quite easy. The string itself does not have to be shortened to produce a higher pitch. A musician simply has to press the string down to the fretboard or fingerboard so that the length of the string free to vibrate decreases. This is what violinists and guitarists are doing as their fingers move up and down the neck of the instrument. They are decreasing string length in order to produce other pitches from the same string.
- Tension
- Mass
- Length
Pitch is the frequency of the sound wave created by the vibrating string of the instrument. The string is able to vibrate because it is a harmonic oscillator. This means that its motion is repetitive and the amount of time needed to complete one cycle of this motion is dependent on the stiffness and inertia of the string.
Stiffness is how strongly the string snaps back toward its resting position when it is displaced by either bowing or plucking a string. A loose string (decreased tension) will not move back to resting position or equilibrium as quickly as a tight string. This means that the loose string completes a vibration cycle less often than a tighter string. As a result, the sound wave created by the instrument also has less cycles or a lower frequency/pitch. The opposite is true of a tighter string (increased tension). This is why guitars, violins, and other stringed instruments can be tuned by twisting the tuning heads on the instrument's head. The twisting either tightens or loosens the string, causing the fundamental pitch of the string to increase or decrease as a result of the change in string tension. See Figures 9.2.1 and 9.2.2 in Media tab.
Mass affects pitch because of a property called inertia. When the string is let go after it is displaced by plucking or bowing, it accelerates back to its resting position. Newton's Second Law of motion tells us that acceleration is equal to the force applied on an object divided by that object's mass. Or, in simpler terms, the same force on a larger object will result in less acceleration. This makes sense if you think of pushing a fully loaded grocery cart versus an empty one. The full cart has much more mass and is much harder to get going than the empty one. This same principle applies to the string. Strings of greater mass will produce a lower frequency sound wave because they vibrate less often than strings of smaller mass.
The consequence of these circumstances is that to play a different pitch other than the strings fundamental pitch and its harmonics, the individual playing the instrument must either change the tension or the mass of the string. Altering string tension during the middle of a song, like when tuning, would be very difficult. The other option, changing the mass of the string, may initially sound difficult as well. However, it is quite easy. The string itself does not have to be shortened to produce a higher pitch. A musician simply has to press the string down to the fretboard or fingerboard so that the length of the string free to vibrate decreases. This is what violinists and guitarists are doing as their fingers move up and down the neck of the instrument. They are decreasing string length in order to produce other pitches from the same string.
