The electromagnetic field in absence of charges and current is described by a wave equation. The solutions of the wave equations in a general setting (without symmetry contestants and without boundary conditions) are plane waves with a fixed frequency and momentum. These are purely sinusoidal $\propto \sin(k x-\omega t)$. Similarly, sound waves are the solution of the wave equation which describe the phonon excitations in a media. Phonons are quantum of sounds, analogously to photons which are quantum of light. So, sound and light are described by very similar mathematical objects. The main difference is the speed of propagation, that is, speed of light vs speed of sound. A common and important feature of all wave equations is linear superposition. That means that if there are two solutions $\propto \sin(k x-\omega t)$ and $\propto \sin(k' x-\omega' t)$ then their superposition is also a solution of the wave equation. Now, the timbre of a musical instrument is given by the superposition of several harmonics. That means that every note of a musical instrument is not a monochromatic wave but a superposition of many frequencies, which are usually multiple of each other. This superposition changes the "shape" of the wave. The relation between the shape of the wave and its harmonics is expressed by a mathematical operation, the Fourier transform. So, a monochromatic ray of light is analogous to a very pure sine wave sound, something like the sound of a whistle or of a flute. These are described by a single sinusoidal wave. A non monochromatic ray of light is analogous to the sound of an instrument which has a more complex timbre. These are described by a superposition of sinusoidal waves. But at the end of the day, everything can be described as a superposition of pure sinusoidal waves.
Pure colors are the colors which correspond to a single frequency. Usually colors of real objects are always a superposition of several monochromatic frequencies. This is because the color of objects correspond to the complex interaction between light and matter. As a consequence, if you shine white light on a Yves Klein painting, some frequencies are absorbed, and some deflected. The blue that you see is a complex combination of the frequencies of the visible spectrum which have been reflected by the painting. However, this is not the full story, because the human eye cannot resolve all monochromatic frequencies separately, but has only 3 receptors which are sensible to a range of frequencies which are centered around blue, green, and red (if I remember correctly). The human ear is so much more sophisticated in this sense, because it is able to resolve single frequencies, also frequencies which are very close to each other.