All the music we’ve ever heard comes from just 12 musical notes (ignoring octaves). Think of all the thousands of songs you’ve ever heard. And the millions you’ve never heard. Each one of them is made from just 12 notes. If you think about it, that is Kinda Bonkers!

How is it that a mere 12 notes can produce basically an unlimited supply of melodies? Daniel Levitan in This is Your Brain on Music explains: “each note can go to another note, or to itself, or to a rest, and this yields 12 possibilities. But each of those possibilities yields twelve more. When you factor in rhythm – each note can take on one of many different note lengths – the number of possibilities grows very, very rapidly.”

Similarly, musician and composer Oli Freke found that based on some reasonable assumptions that “There are around 82,500,000,000,000,000,000 melodies that are 10 notes long.” His reasoning and calculations can be found here.

A Bit of Detail on Musical Notes

Music is made up of “notes.” A “note” is the pitch and duration of a musical sound. “Pitch” is how high or low a note sounds and is dependent on the frequency of the vibrations of the sound waves the sound creates. For instance, “middle C” vibrates at about 261hz. Notes are separated by intervals which are logarithmically spaced, so the each note fundamental frequency is 2^(1/12) = 1.0595 times the previous frequency.

In western music, we use a scale of notes that consists of 12 notes.:

• Seven “natural notes”: C, D, E, F, G, A and B
• Five “altered notes”: the sharps and flats (on a piano, the “black keys”)

What are Octaves?

The 12 notes repeat at higher and lower octaves. An “octave” describes two distinct tones but are named the same note. Octaves are either half or double the value of the note an octave away. For example, the “A” above middle C is 440hz. The A octave below this note is 220hz and the octave above it is the A at 880hz. Notes of the same name but at different octaves sound the same to us – but they are merely at higher and lower pitches.

The Song Remains the Same*

An astounding thing about songs is that we still recognize them even when they are played at a different octave or the speed at which they are played is changed. Again, from the fantastic book This is Your Brain on Music by Daniel Levitin:

“Play a melody using any set of pitches, and so long as the relation between those pitches is held constant, it is the same melody. Play it on different instruments and people will still recognize it. Play it at half speed or double speed, or impose all of these transformations at the same time, and people still have no trouble recognizing it as the original song.”

*The Song Remains the Same: