Hello mathematicians,

I am a student of musical composition and I need to solve the following problem for one of my pieces. I worked on it for a long time but I have not taken enough advanced algebra to solve it.

I am looking for the list:

such that

1.

2.

3.

4.

5.

6.

7.

8.

where

Any help solving for W would be appreciated.

Thanks,

Silly