Gauss wanted to understand the graph of the prime number staircase. Using the idea of a dice he made an approximation to this graph.

What Riemann discovered was a way to change Gauss’s graph into the staircase of the primes by adding on harmonics. Each wave gradually changes the smooth graph of Gauss into the staircase of primes just like the graph of the clarinet appeared from adding on the extra harmonics.

Where did Riemann discover these waves or harmonics?

Riemann discovered that the two-coordinates marking every point at sea-level in his landscape could be used to produce a wave. The North-South coordinate told him the frequency of the wave whilst the East-West coordinate determines the height or volume of the wave.

Here are the waves corresponding to the first few points at sea-level in the landscape.