Composing a song using Mathematics

In particular using Fibonacci numbers. I’ve been interested in this since hearing a few compositions by Tool, some of their melodic pieces are created this way, also the spiral principle is observed.
This run through by Paul Davids is explanatory, very interesting!
I’m working on some ideas at the moment for relaxing background music and are looking into this idea because it is supposedly capable of giving relaxation and pleasure. In my case as I don’t sing it’s easier also I don’t really see how it could be applied to lyrics.

As a help to understand some of it a review of a particular Tool song (Lateralus) by one of my subscribed channels


Hi Darrell, it will be interesting to hear what you come up with. Paul Davids is usually interesting and IMHO a very good teacher.


Interesting to watch how a spark can grow.

Cheers Darrell

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Here’s an interview of a composer and mathematician that teamed up to write an album. They took a different approach to each song. Pi and children’s songs took center stage.


I just found several other music related episodes done by numberphile.

A lot on Fibonacci and the related golden ratio so looks like you’re on to something!


Have just stumbled across this thread when searching the forum for discussions on the relationship of maths to the guitar. This Paul Davids video is really enjoyable to watch and is setting off lots of ideas. Did you manage to progress any further with exploring it yourself?

Great find. Are you experimenting with incorporating any of this yourself?

I’m still a beginner but found myself noodling over number patterns at the weekend when thinking of different ways to learn notes on the fret board. Thinking of intervals reminded me of the golden ratio and the Fibonacci sequence. Then I started thinking of patterns of how one might play or write music. Next thing I’d fallen down a :rabbit: :hole:, all be it a happy one.

Years ago I was viewing a residential house as part of the Open House weekend in London. The home had a really grand stair case that spiralled up over several floors. The walls going up the stairs had artwork placed in sync with the Fibonacci sequence with each piece of artwork become larger as you went up. That’s stayed with me.

@Sound_Bound, It all started for me with the book “Nature’s Numbers”. Among many other things, the author shows how patterns in nature such as the spirals on a pineapple and the number of petals in a flower are related to the Fibonacci sequence.

An interior designer with a numerical mind. That would have caught my eye too. The “golden ratio”, which architects and designers reference, comes into play here too because the ratio of two adjacent numbers in the Fibonacci sequence approach the golden ratio as the sequence increases.

I haven’t tried mixing fibonacci with guitar. My playing sounds a bit “off” just trying to play normal stuff ;-).

One challenge might be that the underlying scales are sort of “man made” as opposed to “natural”. However, it might be interesting to make up your own tunings where the frequencies of each string are fibonacci numbers. It might not be kind to our western ears, but it could be something even better (definitely weirder).

Interesting subject.

I have actually toyed with the idea of using mathematics for music myself. My thoughts come from bell ringing (specifically method ringing) which is about using unique permutations, and which has its roots in mathematical group theory.

I’m starting from the basics, at this point (because that’s really where I am with method ringing) and looking at how I could use patterns like plain hunt and plain bob in a musical context.