How many songs can you make?

The song Do-Re-Mi has the following section:

Now, children, Do-Re-Mi-Fa-So and so on Are only the tools we use to build a song Once you have these notes in your heads You can sing a million different tunes by mixing them up

How many different tunes could you make?

Let’s make some arbitrary choices so that this question has a precise answer:

• The entire song is 7 beats long
• Notes can be any integer number of beats long
• Let’s limit the available notes to the 8 notes in Do-Re-Mi-Fa-So-La-Ti-Do

Solution