How Extraterrestrials Compose Music

One of the most famous sci-fi flicks of all time is "Close Encounters of the Third Kind." Below is a clip regarding those musical tones that Richard Dreyfuss kept hearing in his head. But what's up with those tones? What do they mean? Why did the extraterrestrials send them to the lead actor's head? And, most importantly, how do Extraterrestrials compose music? All these questions shall be answered soon after you're done watching the clip:

Put yourself in the extraterrestrial's shoes. You are light-years from your home planet. You and your crew are exhausted after exploring much of the galaxy. Your navigation system is on the fritz due to a meteor shower. You are lost. You pull your flying saucer up to a nearby inhabited planet so you can ask directions.

Hopefully the earthlings can tell you how to get back to the constellation where you are from:

But first you have to let them know which constellation it is. They don't speak your language and the lead actor doesn't have a clue what is happening. He keeps building mounds with his mash potatoes and the the mud in his yard. His wife thinks he's insane and leaves him. That doesn't help you at all. What can you do to get through to these earthlings? You can create a musical language that describes the stars in your constellation. You begin with an alphabet or scale: Do ray me fa so lah te do.

Each note in the scale has its own frequency. When you double the frequency (f) you raise the pitch a whole octave. If you want to go down an octave, cut the frequency in half. If you want to go up or down a half tone, multiply or divide the frequency by 1.06, respectively. There are 12 half-tones per octave, so going up an octave requires 1.06^12 times the frequency (f). Going up a perfect fifth requires (1.06^7)f. Going down one full tone requires f/1.06^2.

Once you get your universal musical language together, you match each star in your constellation with a note:

You can now tell the earthlings where you are from and hopefully they can tell you the way back home. If they don't understand at first, just keep telepathically sending those tones until the whole planet is singing them.

If they still don't understand, try taking Richard Dreyfuss for a ride in your flying saucer and show him your sheet music below:

Extraterrestrials use triangles to communicate their music. The height of the top triangles are the pitch. The base (cosine) of each triangle is the duration. The up-side-down triangles are the loudness. The bigger the sine waves the louder and higher the pitch, and vice versa.

Below I use super-complex numbers to translate the alien music. (If you are not familiar with super-complex numbers, click here.) Hopefully the diagram below will serve as a Rosetta stone. Each note is indexed by the letter u.

To simplify the math further, let's assign first-rank tensor variables (T, P, L) to each cosine and isine term.

We end up with a simple tensor equation that describes the language of the universe: music. Now that we understand what the extraterrestrials want, can someone please give them directions?