All music is
analog, even if it is created or processed digitally.
What that means is that music is a sound wave that propagates through the air to your ears, causing vibrations in your ear drum that get translated into electrical signals in your brain by the little bones and nerve stuff in your inner ear.
Having said that, there are two ways to create and store music: digital and analog.
Analog storage captures the actual waveform and creates a direct 1:1 representation of it. The best-known method of this is the phonograph record. The grooves in the record (this is a simplification) are made by a mastering needle that translates the sound vibrations picked up by the studio mike. The wiggles in the groove are a physical image of the music's sound waves.
A good way to demonstrate this is to stick a pin through the bottom of a paper cup, and touch the tip of the pin to the groove in a spinning record. You will hear the music come from the cup, proving that the groove contains an analog of the music signal.
Another method, equally popular, was magnetic storage. First created using metal wire, then plastic tape coated with metallic particles, a magnetic field, varying with the music signal, created the musical representation. Until digital storage came along, all improvements in magnetic tape involved being able to increase the density and clarity of the magnetic field that could be created and the metal heads that wrote and read the signal.