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Measuring the resolution of Torus

How many shape characters does Torus need to identify tunes? Currently it uses an average of 12.9 characters, although the number needed varies between 7 and 23.

Looking in more detail, suppose we pick tunes in the database uniformly at random and give Torus the first k characters of their shape strings, for some fixed k. Then we can define two possible measures:

We can express each of these measures as a number between 0 and 1: the higher the value, the better Torus is at identifying tunes by using k shape characters. We can then plot these measures against k to get an idea of the number of shape characters we might need to use:

The graph above suggests some puzzles: What shape should we expect the curves to be? Do they approach each other as the number of tunes becomes large?

This page is maintained by Thomas Bending, and was last modified on 7 November 2018.
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