Part three: making the music happen (surprise, it's Math!)

Once I had chosen a basic design, it was time to start dialing in the tone generation. I would need 12 555 times, one for each note. I used this chart to find the frequencies I would need:

You can find a link to an interactive version of this chart in the resources tab.

I chose to start in Octave 6: I wanted at least three octaves. By using a frequency divider circuit, I could hit Octave 6, Octave 5, and Octave 4.

Now I needed to calculate the proper values of R & C for the 555 (which uses two RC circuit with two comparators to generate a square wave). There are two different values set by the 555 timer: frequency and duty cycle. Here are the formulae I used:

And my spreadsheet of values:

You can find a link to this spreadsheet on the resources page.

Seeing the range I would need on the pot in order to make small adjustments, I opted for a 5k pot.

Now that I had my values, the design was next!