I would like to explore how notes on a musical scale relate to frequencies in the human hearing range. Although the science of audio frequency in music and sound engineering can get highly technical, we’re writing this article with the layperson in mind.
Having had some experience as a sound engineer, I am constantly thinking numbers in my head – music, sound effects, and sound tracks as well. So what are these numbers and how do they relate to music and the real world?
Mathematics in sound
I can’t imagine going through a day without being amazed at how most people have no thoughts of the mathematics that are involved in everything we hear. Sometimes I wonder what it might be like to just listen to music and enjoy the raw emotions stirred up, with no worries or distractions about numbers… to just be mindless and let my animal instinct react without analyzing every stinking little note! On the other hand, it is great fun to know how and why in some great electric way that this is why music works. Today, I choose to be one with the math, and I will pick some other time to pretend I am just emerging from a cave, caring only for my next meal, ugh! The wonder of knowing why that last rock to hit me in the head, resonated as a perfect C#. This is the question to answer, so here we go…
Vibration of all matter
Everything vibrates: All matter, all life, everything. The speed of these vibrations is are of extreme importance. On a subatomic level, literally everything in existence has its own fundamental vibrations.
If you can understand some of the physics involved, then you are much smarter than I. So let’s try to keep it simple. Sound is a vibration that moves the air and hits the eardrum. Slower vibrations produce lower tones; faster vibrations produce higher tones. The human ear hears the speed of the vibrations as differing notes on the musical scale.
Hertz & the sensitivity of human ear
The vibrational speed of sound is measured in waves or cycles per second. For instance, the A note vibrates at 440 times a second; in other words, the A note is 440Hz. (Hertz, abbreviated as Hz, is the standard measurement of vibrations per second.) The human ear is capable of hearing frequencies from very low notes of around 20 vibrations per second all the way up to 16,000 vibrations per second. Some engineers believe the upper range may extend up to or even beyond 20,000 vibrations per second.
Standards have been developed for audio equipment. If the manufacturer indicates a given piece of audio equipment will reproduce from 20Hz to 20,000Hz then it is safe to say it will cover the human hearing range and there for music will sound groovy. Let’s look at notes on a scale and see what frequencies are there.
The chart below compares the relative frequencies of various stringed instruments to notes on the piano. (A more detailed audio frequency chart for musical instruments is shown at the conclusion of this article.)
Although musical instruments produce similar frequencies when a given note is played, an A440 on a guitar will not have the same exact tone of an A440 on a piano, even though it’s the same fundamental frequency. The reason for this is that the two instruments are made from different materials, the surfaces of which produce varying acoustic properties and harmonics. Any instrument can produce a variety of harmonics; when a single note is played, it is also the harmonics produced by that instrument that give it its own unique character of sound.
A harmonic frequency is a multiple of a fundamental frequency. A fundamental frequency of 500Hz has a first harmonic frequency of 1000Hz, double the fundamental frequency. Its second harmonic is 1500Hz, the third harmonic is 2000Hz and so on. A musical instrument produces both fundamental and harmonic frequencies, which allows the human ear to discern the differences between instruments even if they are playing the same note.
— Definition of harmonic frequency – About.com
Have you ever watched a sound engineer on a stage tuning the sound system? I perform these tunings and checks quite often, as one might imagine. (In fact, I’ve occasionally been so detail-oriented that I’ve been accused of being nuts.) What we are doing is balancing all of the frequencies reproduced by the speakers with the room. Just like an instrument, a room is made of different materials and will sound completely different from room to room. These materials vibrate at different frequencies and have different harmonics just like an instrument. This tuning can make the difference between a great show; after all, poor sound work could mean a last gig with the band.
Suffice to say that being a musician or a sound engineer requires far more than just turning a knob or playing a few notes in sequence. Being good at either requires understanding of the science and being able to let go and enjoy the music.
 Curious individuals can easily find a great variety of interesting sound frequency charts on the web comparing this to that.