Fourier discovered that we can reproduce the shape of a graph by adding together the heights of sine waves with different frequencies.

To each graph we can mark off the frequencies of the sine waves that are needed to reproduce that graph. This is called the spectrum.

The sound of the tuning fork is a pure sine wave. The spectrum consists of one mark.

The sound of the violin is built out of sine waves whose frequencies are integer multiples of the fundamental note. The spectrum consists of numbers marked off at regular intervals.

What distinguishes the graph of music against the graph of white noise is that the spectrum of the graph depicting music sampled at any moment in time consists of isolated numbers.

White noise on the other hand has a spectrum of continuous numbers. It is like recording a trombone playing a glissando of notes and then playing all the notes simultaneously.

So what does this have to do with Riemann’s imaginary landscape?