There are many mathematical, logical aspects to music, which is what I think was Mary's attraction to it.

**Warning: Music Geek Explanation Below**

In figured bass, you are given the soprano (melody) and bass notes, and you need to work out the alto and tenor. The bass note tells you what the chord is - let's say it's a C, and the notes in a C chord are C-E-G. So the bass is a C, and let's say the soprano is an E. That means that either the alto or tenor note must be a G (the missing note in the chord) and the other voice will double another - it can be C, E, or G.

It is these two inner voices that Mary is working out, and there are all kinds of voice leading rules as to how to do it - no parallel 5ths or octaves, for example. It is a real intellectual exercise, and I enjoyed doing it as a logic puzzle. But, you can get all the notes in and follow all the rules and still not have a pleasing, musical - as opposed to mathematical - result. (I know, for I've done it!) I'm betting this is how Mary's figured bass turned out.

This is borne out, I think, by the quote in ch. 6:

"Mary had neither genius nor taste; and though vanity had given her application, it had given her likewise a pedantic air and conceited manner, which would have injured a higher degree of excellence than she had reached. Elizabeth, easy and unaffected, had been listened to with much more pleasure, though not playing half so well;"