There is always a moment in my daily life at itnig when a startup asks for a video. Sometimes it’s an ad, sometimes an event, sometimes it’s just a tutorial, but no matter what it is, it comes with the need of creating a sound that represents the company and can be played at the start of the video along with the appearance of their corporate logo.

This short sound must represent their essence, it has to have their DNA reflected somehow: a representation of their values, their culture or maybe even something related to their name or logo. It is mainly an artistic process that requires inspiration but in some cases the startup name and culture is *geeky* enough to allow some rational thinking into the music composition process. Last week I crafted the sound for our startup Factorial, inspired by the mathematical operation their name represents.

## Assigning values to notes and choosing the first note

Putting a mathematical operation into sound requires a bit of imagination as well as a set of rules to get started. The first step was assigning values to notes. I decided to assign **C4** the value **1**. It is the middle key in a piano and also the middle **C** according to the International Pitch Notation so it seamed and appropriate value for that key.

Piano keys, notes and assigned values

Now we had to decide which factorial operation to represent. That is, choosing an ** x** to which we would perform

**and represent it. Being the startup name Factorial and given that it starts with an**

*x!***F**, it made sense to perform the operation on

**F4**, the first

**F**we would find after

**C4**.

## Performing the n! operation

Now that we had chosen to start at **F4** we just had to assign notes to the operands in the operation and put them in the score.

4! = 4*3*2*1 = F4 E4 D4 C4

Now we had a simple downwards scale without much musical interest but how could we enrich the melody and still make it part of the factorial operation?

## Making the middle operations sound too

As we manually start to calculate the factorial operation of a number and before we get the result, we obtain partial operands that are part of the process. How would the melody sound if we added those partcial numbers to the score?

The size of the partial operands makes the need to place them on a staff above obvius. Also because of the sequentiality of the operation we put the partial operands once we have been able to obtain the result, that is after the first note and while the second note is playing.

The first partial operand is obtained after multiplying **F4 **and** E4 **wich is the same as **4*3 **which equals** 12 **that represents a** G5 **if we check the keyboard note to number assignation.

F4 * E4 * D4 = G5 * D4 = 12 * 2 = 24 = E7

If we keep calculating we obtain the note E7, which is the result of multiplying **F4 * E4 * D4**.

Finally, we obtain the same **E7 **after multiplying the previous result by **C4**, which has the value **1**.

## Final result

If you are curious to listen to how this mathematical representation of the factorial operation sounds like, play the video below.