Thank you for that essay. I have been hoping to find one such as this. It also opens the door to connections with others who are realizing that music has much to do with physics, especially quantum physics.
In your essay you mention:
In physics the most groundbreaking ideas are the simple ones.
This is a principle held by many, including Einstein. However, the mathematics used to define such things as quantum mechanics is horrendous. When we consider fields as continuous in nature and mass as composed of infinitesimal points it follows that the mathematics will be very complex.
Musical mathematics, although it can become quite complex, can be reduced to very simple precepts. The structures of music are defined by the Enharmonic System. If you look up enharmonic in a dictionary it will define enharmonic as - notes that sound the same but are written differently. This is the exact opposite of what enharmonic actually means. In an enharmonic system we are dealing with notes that are written the same but sound differently.
Even a simple scale, called a diatonic scale in music, has intervallic problems. It actually takes three diatonic scales to create perfect harmony. It takes 38 scales to allow for proper tuning of the chromatic system. Most musicians do not understand the enharmonic system. If they did we certainly would not have the tonometric system. I described the tonometric system in the essay. Let me reiterate a simple example. In the tonometric system the perfect fifth (with the exception of the octave the most basic interval) looks like this:
Whereas the perfect fifth is simply:
Not only can everything in music be defined by positive integers the entire enharmonic system is comprised of the powers and multiples of just three numbers; 2, 3 and 5.
I cannot help wondering that if so much of quantum mechanics appears to be musical in nature how much could it be simplified if we really used musical principles.