1. High and Low Sounds Depend on How Many Times Something Vibrates per Second
When you pluck a guitar string, it moves back and forth so fast that you cannot see it. This movement is called vibration. The number of times it vibrates in one second is called frequency. The unit for frequency is Hz (Hertz).[1]
In most cases, a higher number of vibrations means a higher-pitched sound. The standard "A" note is 440Hz, which means the string vibrates 440 times in one second.[1] Since 1Hz equals one vibration per second, the number directly tells you the count.
You can imagine the difference by waving your hand twice in one second versus ten times. However, real sound vibrations are much faster and finer than your hand can move. To change this frequency, you must change the string itself. Let us look at what happens when you press a string in the middle.
2. Pressing a String at the Middle Raises Its Pitch by One Octave
If you make a string half as long, its frequency doubles. When you press the center of a string, the vibrating part becomes half the original length. This makes the vibration count twice as high as before. This new note is exactly one octave higher.[1]
An octave is defined by a frequency ratio of 2:1. The "A" note at 440Hz has an octave above it at 880Hz.[2] Whether you go from 440Hz to 880Hz or from 880Hz to 1760Hz, the sound feels like the "same note, just higher." Pitch increases by doubling, not by adding numbers.
So far, we only changed the length. But are there other things that change pitch? Let us look at what else affects how high or low a string sounds.
3. String Length, Tension, and Thickness All Affect Pitch
The frequency of a string is inversely proportional to its length. It is also proportional to the square root of the tension (the force pulling the string tight) and inversely proportional to the square root of the mass per meter.[2] This means shorter, lighter, and tighter strings make higher sounds.
Be careful with tension. If you double the tension, the frequency does not double. Because of the square root relationship, you must quadruple the tension to double the frequency.
This relationship was shown by Mersenne in his book Harmonie universelle in 1636. Galileo had similar results, but the law is named after Mersenne because he verified it with experiments.[2] How do instrument makers use this? Let us look at how pianos produce low notes.
4. Why Low Piano Notes Use Thick, Heavy Wound Strings
To make a low sound, you must either make the string longer or make it thicker and heavier. If you double the length of a string, the pitch drops by one octave. If you tried to make low notes with thin strings, the instrument would become too large.[7]
In the low range of a piano, strings are wrapped with copper wire to make them thicker and heavier. Heavier strings vibrate more slowly, creating lower sounds even if the string is short. This changes the "mass" part of Mersenne's law to save space on "length."[3]
Wound strings (strings with metal wire wrapped around them) first appeared in violins in Italy around 1660. They appeared in pianos between the late 18th century and 1820. These dates are approximate and vary by source.[7]
We have established that pitch depends on vibration counts. But is the pitch you hear always the same as the vibration count?
5. How We Can Hear a Low Note That Is Not Actually Played
A single sound contains a fundamental frequency (the main pitch) and multiples of that frequency called harmonics. It is known that if you remove the fundamental frequency but leave the harmonics, the perceived pitch hardly changes.[6]
For example, if you play 1000Hz and 1200Hz together, you may hear a 200Hz pitch. 1000Hz is 5 times 200Hz, and 1200Hz is 6 times 200Hz. The explanation is that the brain finds the common fundamental frequency from the relationship between the heard harmonics.[6] However, this explanation does not fully define the specific processing happening in the brain.
This shows a distinction: pitch is a subjective quality felt by people, while frequency is a measurable physical quantity.[2] Usually, they match, so we do not notice the difference. Frequency and heard pitch do not always overlap perfectly. So, who decided on the standard "A=440Hz"?
6. When Did A=440Hz Become the International Pitch Standard?
The standard for pitch has changed over time and place. In the 1860s, France set 435Hz as the standard, and many countries and groups adopted it. In May 1939, representatives from various countries met at the BBC Broadcasting House in London to discuss concert pitch.[7]
The proposal to use A=440Hz was adopted as Recommendation R16 by the International Organization for Standardization (ISO) in 1955. It became the official standard ISO 16 in 1975.[7]
The difference between 435Hz and 440Hz is 5Hz. For sounds below 500Hz, people can usually tell the difference if the change is about 3Hz for pure tones (sine waves) or about 1Hz for sounds with mixed frequencies.[2] This ability varies by person and condition, but a 5Hz difference is large enough to be heard in comparisons.
For example, Leonard Bernstein is said to have often tuned the New York Philharmonic to A=442Hz. Real-world performance standards are not always exactly 440Hz.[7]
Pitch is created by three things overlapping: the physics of vibration counts, the pitch humans feel, and agreements between people.
7. A Rubber Band Experiment You Can Try at Home
You can try this today. Hook a rubber band around the edge of a box and stretch it. Pluck it gently with your finger. Then, press the middle of the rubber band with your finger and pluck it again. Listen to see if the sound becomes higher when you press it.
After that, pull the rubber band tighter and pluck it. Compare the sound of a thick rubber band with a thin one. It is hard to tell with your ears if the frequency doubles exactly, but you should hear the change in pitch. Do not pluck rubber bands near your face or eyes.
If you visit a school music room and can see inside a piano, look at how the low-note strings differ from the others.