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.

9 thoughts on “Music meets Math

    1. James Revels Composer

      Yeah this is a dense one >.< I'll try to clarify only because I'm working on codifying it. So Say I varied an instruments volume as the song progressing using an automation pattern which in a program looks like the simple graph on left of bar (here a QUICK paragraph from the developer of the program I record on with picture of automation if you aren't familiar now say I have 33 other instruments and want to automate but each pattern must be unique, how do I chose from the infinite amount of patterns? Now, imagine the points as cities on a globe tracking as you travel from your city all the way around the world and back home. You can only move left to right due to the rail line being one way rail (like music move one way through time) so you must go through each city in a specific order. Since the distance (duration) from one city to the next is the same. We can take pictures the round trip from each city, super impose them to create a chart (the second complex graph) which tells us when any train (volume value) will reach any city (instrument) and then. Because math, There are only 33 possible patterns each train can created in this rail system, whether they leave simultaneously or not ,because they share the same one way rail. With this the rail company can create identical one way rails so that more trains arrive at bigger cities more often than the smaller one ( or in music I can make more instruments crescendo simultaneously when I want although each instrument has its own unique volume changing pattern). In short I used 1 pattern to turn a common mixing/mastering problem with infinite answers into one with 33 possible choices.

  1. Dranor Zylander

    Thats really amazing, its like engineering music. If you could turn that into an algorithm and then incorporate into an app i think that’d be winwin. Im thinking who knows what musical masterpieces it could churn out.

    1. James Revels Composer

      Thanks for the reblog! I was thinking the same thing about the algorithm and app. It would streamline calculation and probably reveal some cool properties. I use Microsoft visual studio for dabbling in code a little and will eventually attempt to make a prototype for when I meet a real programmer. As for the masterpieces, I am excited to hear these as well and see if real mathematicians can apply it to something beyond music. All this stemmed from a Goethe Misquote saying “Geometry is frozen music”

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