Is Music Inherently Digital?

Music is by default analog. Or is it? What is the most important thing in music? Isn't it the tempo? Tempo is simply a clock, and that is the core of digital! But the instruments that play are analog, you say. That might be more so for the violin or the cello, but the piano has discrete notes that the player can use, unlike the strings instruments where the player can slide his fingers between notes giving this analog feel. If you go down into the basic notes you will get into the world of digital, which I believe is the nature of all things. Any instrument can be digitized, and that is exactly what the musical synthesizer does. In the micro world, there is no such thing as continuous time, distance or energy. Everything is quantized. Have you heard of the uncertainty principle? It states that position and velocity cannot be simulataneously measured. If you try to determine the position, you affect the particle's speed, and vice versa. Same goes for energy and time, they cannot be determined simulataneously. So inherently musical energy that we hear is quantized if time is to be continuous, and vice versa. So it is either the notes' energies are quantized or the time itself is, or both are to varying degrees. In either case, deep down in the microworld, music then must be digital.
Today music is still played with analog instruments, especially classical music. Players still perform according to the sheet music that the great composers of the previous few centuries wrote. The symphonies are still conducted in real time by the maestro of the philharmonic orchestra. But that does not mean that the same music could not be reproduced digitally. It certainly could. You could have a software program read the sheet music and play it using different instruments whose sounds are synthesized with high fidelity. You could then generate a MIDI file that could be played by the computer. You could record track on top of another track and create a vast symphonic effect, and most of all you could do all that alone, without the need for a whole orchestra.
Still nothing beats the sound of the various instruments performing together in the symphony hall, which is inarguably analog. So it is not a question of is music digital or analog, but it is a question of which is better. What do you think?