Asking ChatGPT to think about topological structures of music:.
It’s doing well. Here’s a sampling:
“For example, a trumpet’s timbre might be described as having a bright, sharp quality at the top of the topological structure, with a round, mellow quality at the bottom. The different timbres might be connected to each other by a series of curves or slopes, representing the way that the timbres flow and change over time as the trumpet is played.”
“For example, the 4/4 time signature could be visualized as a topological structure with four beats arranged in a square, with each beat connected to the others. The 3/4 time signature could be visualized as a topological structure with three beats arranged in a triangle, with each beat connected to the others. The 9/8 time signature could be visualized as a topological structure with nine beats arranged in a nonagon, with each beat connected to the others.”
and
“For example, a piece of music that starts off with a slow tempo and gradually speeds up over time could be visualized as a topological structure with the slow tempo at the bottom and the faster tempo at the top, with a gradual upward slope connecting the two. A piece of music that starts off with a fast tempo and gradually slows down over time could be visualized as a topological structure with the fast tempo at the top and the slower tempo at the bottom, with a gradual downward slope connecting the two.”