In today’s science news: In search of universal properties of musical scales.

The thesis of the authors is that musical scales have one of the following properties, when represented (in some manner) in a 2-dimensional space:

• Most scales are convex sets
• Of those that aren’t convex, most are at least star-convex.

At a high level, there is a hypothesis that:

• The musicality of elements of music is a function of the geometrical properties of 2-dimensional representations of that music.

This same high-level hypothesis underlines the “constant patterns of activity” hypothesis of my super-stimulus theory of music, which states that:

• The musicality of music is a function of constant activity patterns within cortical maps (which are essentially 2-dimensional), in particular of a maximum border region between active areas and inactive areas, and where “constant” means over a time-scale of about 1 to 10 seconds.

Which leads me to the question:

• Can the “constant activity patterns” hypothesis explain the convex/star-convex property of musical scales?

(And I will point out that the CAP hypothesis does provide a plausible explanation of why we have musical scales at all, and as far as I know no other attempt at a scientific theory of music does this without just assuming the existence of scales a priori.)

For a graphical explanation of how convexity may be explained by the CAP hypothesis, see my next post.