# Expressing musical patterns as a mathematical model?

My goal here is to compare visual symmetry and express the temporal symmetry of music in a similar visual manner.

I'm not very well versed at math and hence I'm not sure how to go about this.

UPDATE: I've attached a few examples I worked on in mathematically trying to express the varying patterns. The chromatic notes have been expressed numerically in a way that C = 0, C# = 1........C'= 12 - I've divided the various segments of the melodies into smaller bits like motifs, repeating melodic sequences and etc. I've noticed a few patterns in each of the melodies which i've denoted. 'D.M' = Descending Motif 'A.M'= Ascending Motif 'X.M' = A motif that's neither descending nor ascending and 'Desc' refers to a non-motival segment that's descending.

The value of x, unless stated explicitly, is the value M1 or S1 of any given sequence or motif. For example; x in a sequence {1,2,5,6} would be 1 and x in a sequence {4,5,9} would be 4. But in the first melody, x is given the value a = -3 and e = 4 at certain phrases.

Square parentheses indicate a motif phrase and round parentheses represent the conjunct movement (though this only appears in one of the scores attached)

Can you assist me on whether or not this is a satisfactory way of expressing a pattern based relationship within a melody? Is there a better and neater way? And if I wanted to graph these relationships, how do I go about it?

Thank you!

• Notes come in sequences (except when they come together). You might want to mention the quadrivium on how medieval education saw music (in particular harmony) as on a level with arithmetic, geometry and astronomy: I like the description "the study of number and its relationship to space or time: arithmetic was pure number, geometry was number in space, music was number in time, and astronomy was number in space and time." – Henry Jan 11 at 18:18
• This is beautiful! I will definitely use this in the beginning of my presentation. – user401747 Jan 11 at 18:21

There are too many aspects of music that you can talk about: tonality, dynamics, nuance, timbre, etc.

It is not so simple to map all of them simultaneously. You have to narrow it down. There are some items from physics, signal processing, and acoustics: harmonics (ratios of intervals as they relate to signals).

3Blue1Brown, a YouTube creator with a strong math background, very elegantly presents this here: Music and Measure Theory

Hope this helps, and if you need more ideas, I have enough background in both music and math to be helpful.

• I was thinking of talking about popular music melodies and expressing the various patterns present in the melody that makes it so catchy to them (on the fundamental of repetition, predictability and surprise). – user401747 Jan 11 at 18:21
• That's not a bad idea at all. Especially since most pop music is very formulaic, using very well-known chord progressions and "hooks". You can also compare the structure of pop music as it evolved, and see that overall, not much has chanced. Let me try and remember a few references or videos I have seen about this. – ex.nihil Jan 11 at 18:23
• Great! Mind if I message you some music I have notated and segmented musically? So that you can assist me on its mathematical translation? – user401747 Jan 11 at 18:38
• Sure, I can help verify if your method is correct. – ex.nihil Jan 11 at 18:48
• Thank you so much!! – user401747 Jan 11 at 18:50