~ A Derivative Work - Original Noteblock ~ (No turbo mode) This piece uses an unconventional keyboard: d/dx(x²) = 2x What does this mean? How is this possible? x² and 2x are both functions that take in a variable x that I choose and output a number representing a note (frequency). They're related because for any input x, the slope of the line that touches the graph of x² at only the point (x, x²) is 2x. In other words, 2x is what's called the *derivative* of x². 2x is always lower than x² (except at (0,0), but that's not relevant to this piece), so by choosing points on the line 2x, I can make a bass line for the music. x² always plays a higher note. By choosing some random x, I can make an interesting harmony by playing both the 2x and x² notes at the same time. Many harmonies in a row makes a song -- a "derivative" song! The graph on the screen depicts x² with the curved line (the parabola) and 2x with the slanted line. The dots that move along each of the lines represent the notes currently being played -- like notes on a keyboard.
Composed in 2021 Rediscovered, finished, and shared in 2024 9/24: Thanks @Furret_Productions for curating this! (Quick note: The y axis is very squished, so the line does not look as steep as it would be if the axes had 1:1 scaling.)
