## Music meets Math

So what happens when music, graph theory and network theory meet. An awesome way to coordinate automation for music. Although I’m posting this while on bus via phone I’ll try my best to explain this. First for non sound engineers, automation is where you change a parameter, such as volume, as if you had an imaginary hand turning a knob as the song plays.  This is seen in the program as a simple graph like the diagram as the top to the left of the bar (well,  its a simple, directed graph since it moves forward in time, which comes in play near end). The second graph right of the partition is what I call an “isomorphic superposition”. Lets break this down. Isomorphism in graph theory simply means that all the connection between points are exactly the same when two graphs are compared. Superposition is fancy for placed over top off.  What I do is draw original graph, then draw a second graph starting from beginning of the first BUT I draw the second graph as if  the 2nd point in the original graph is the beginning. What this does is gives me the ability to see how the original graph will progress relative to any point simultaneously. It also creates subgraphs related to the progression of the original creating automation patterns that tie multiple parameters  in predictable patterns because of their relation to each others movement. (I can also make pleasant sounding  melodies and counterpoint if I map this to notes but only if they are within the same scale. ) Finally the last part the big box at the bottom. In network theory, it studies the connections between points in a graph. The number of connection a point has is called its degree of connection. The special feature of directed graphs is they has inputs and outputs. This tells us how many points progress to a given point (input) and how many possible points the same point can move to (output). The big chart is called an input/output matrix and map ALL possible connections between points of a graph. “I” is input, “O” is output and the zero with slash means impossible because self referential loops are impossible in real practice using automation. Blank spaces mean there is no connection but still possible. The amazing thing is out of the 729 (27 squared the area of the I/O matrix) possible connections between the 27 points.  there are only 66 I/O connections in this example, reducing unrelated information by over 10 times saving the engineer time instead of trying all possible unrelated or related connections . Sorry for the dense article hope it leveled up your math skills.

## 7 thoughts on “Music meets Math”

1. This was a really neat connection. Being an undergraduate student of mathematics and an amateur musician, I always wanted to learn more about how math can be applied to music. Luckily I was able to understand most of your mathematical concepts.

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1. Yeah the crazy part is I made the connection while pondering a Goethe misquote say “Geometry is frozen music” a couple years ago. I’m glad you understood, I was afraid of messing up especially since I was churning it out on my phone while on the bus to work. I’ll have to post more often on my math/music theories so we can maybe discuss topics that piques your interest. A couple weeks ago after rediscovering a series called “Introduction to higher mathematics” on Youtube. It helped me come up with a single axiom for what music is mathematical. A sequence of notes or Music = (Notes being an ordered pair consisting of its musical interval and duration)
Since sequences are ordered sets, I’ve been using set notation to define things like chords, scales in short math expressions and has me excited for what may come of this, whether from my mind or another.

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1. That is a very apt misquote for this topic. I like that your details were accessible to an undergraduate like me while reinforcing how applicable math is (even if it is pure). I’m really looking forward to further thoughts on this as well as your descriptions of music theory using sequences and sets. Really fascinating stuff!

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