I'm a young musician, as well as a computer programmer. My understanding of math is formed well to my needs, but I am by no means a mathematician, but the field is very interesting to me. I have come across a lot of questions in music theory relative to math. Much of it to try and make sense of the esoteric phenomenon that many great musicians have tried to make sense of. In the simplest sense some explain music as a repetitive pattern that can break or substitute itself to create tension or harmonic dissonance to resolve back to the original pattern.
The golden ratio has inspired many artists. Satie, Sonneries de la Rose + Croix no 1 is a great example of this. Where as the golden ratio is often seen as perfect, whereas dissonance is often seen as a "flaw" or break in repetition. This specific piece is interesting because it creates a pattern, breaks it in a very confusing manner, then resolves the pattern into something distinguishable which resolves back into the chorus. Bringing on a sort of epiphany
My experiment is based around Galois Field Theory. I'm looking for an algorithm to create multiple arrays of non-pattern distinguishable points, which collectively sum up to a distinguishable pattern. I aim to interpret this into a musical notation. Like I stated previously, I'm not a mathematician. So this problem is difficult for me to solve.
This leads me to my question. Would is be possible to create arrays of essentially
anti-patterns which would sum to a distinguishable pattern? For instance a Fibonacci pattern, or perhaps any pattern which could be divided up into separate
anti-patterns which could be resolved into the original pattern. If so, how? If not, why?
Inspiration came from Scott Rickard and some of his research in this area. This may clarify exactly what I'm trying to do. Take this pattern-less music concept and turn it into a way to create dissonance and tension in music which resolves in a similar manner to the piece previously mentioned by Erik Satie.
I realize my use of music jargon, and I will try and relate it to you in as mathematical terms as I can if you just ask. I know this might seem off topic, but truly this is a very mathematical topic, I'm just trying to keeps it relative to my goal and perhaps someone with similar interests can weigh in on this and perhaps aid me in making this question more geared towards the mathematician.
Additionally: Just for inspiration,
All a musician can do is to get closer to the sources of nature, and so feel that he is in communion with the natural laws. ~ John Coltrane