ALL MUSICAL NOTES ARE PRODUCED by vibrating air. That vibration can be caused by a plucked string (in the case of a piano or a harp), or by wind bouncing off the inside of a tube (a clarinet or a trumpet), or by a stick hitting a resonant object (a drum or a xylophone).
The faster the air vibrates, the higher the note; the speed at which the air vibrates is known as its frequency. Multiples of the same frequency sound good together, because the notes produced vibrate in time with each other: these multiples are called harmonics.
Go to a piano and play a low C. This note is produced by the string vibrating 130 times a second, known as 130 Hertz (Hz). It’s named after the physicist Heinrich Rudolf Hertz, who was the first man to successfully divide 1 by a second. (Not really.)
Here’s how the note C looks on a portion of a piano:
Let’s imagine that the string vibrates at 100 Hz, because it makes the maths easier. If we double that frequency to 200 Hz, we get the C an octave above. The note has the same name because it sounds so similar to the original. In effect it’s the same note, but played higher up:
Each time we double the frequency, we get the same note an octave higher. So if we double that frequency once again to 400 Hz, we get the note C an octave above:
But wait a minute: we’ve missed out 300 Hz, which falls right between 200 Hz and 400 Hz. It’s a multiple of the original frequency of 100 Hz, so will resonate in time with it. The sound produced at 300 Hz is, it turns out, the note G:
Let’s add another 100 Hz to the 400 Hz of our high C, to make 500 Hz. If we do this, we get the note E:
So starting from the bottom we have C, C, G, C, E. Rearrange those notes and you get C, E, G—the notes which make up the major chord of the key of C. That’s why the chord just sounds so right; all the frequencies vibrate in time with each other. It’s not convention, it’s physics.
You don’t have to stop with that major chord. If you kept adding 100 Hz, you’d get all the white notes on the piano. These white notes make up the scale of C.
If you started with a note other than C, then you’d get the harmonics arising from that note, which would include black notes. Start on A, for instance, and the major chord would include A, C sharp, and E.