Advanced Mathematics 201: Sequences

The first semester of Advanced Mathematics has now ended. I’ve exhausted the rhythm topics I wanted to address, and I wanted to talk more about verticality. Today is sort of bridge between the two semesters, as what we’ll see can be applied to rhythm as well as harmony and melody: number sequences.

Divergent Series

Divergent series are sequences of numbers in which a term diverges from its starting point. This means that, with infinite iterations of the series, said term will reach ∞ or -∞. They are opposite to convergent series, the terms of which get closer and closer to … Read more

Advanced Mathematics 5: Introduction to Karnatic Rhythms

In today’s class, we’ll move out of the world we’re used to–the Western music world, that is–and move to South India, around the region of Karnāṭaka. We’ll have to learn much of their musical vocabulary, although we’ll try to draw parallels with European classical music as much as possible, since I assume we are all more familiar with it. But, even when parallels are drawn, the two terms are never going to mean exactly the same thing, so it’s important to keep in mind the worlds that separate Western music from Karnatic music.

This video has been the instigator of … Read more

Advanced Mathematics 4: Notes inégales

Whew, we’ve recently gone from a very new concept, microrhythms, to a fairly advanced discussion on polyrhythms, polymetres, and polytempo. I hope that this season of Advanced Mathematics is enriching to you! Today, we’re going to talk about notes inégales – uneven notes –, what kids today call “swing feel”. It goes much deeper than what you probably imagine, and I hope you’ll learn something today!

The Triplet Feel

Most prevalent in jazz and blues music, the swing feel usually involves altering the length of two consecutive and equal notes. The most common example of this is the … Read more

Advanced Mathematics 3: Polyamory

The notation used was originally made by Urs Liska over at

In music, as in life, you can have relationships with whoever you want. In both cases, however, cultural and popular acceptance of this freedom is only in its early stages. Many countries still forbid homosexual relationships, just as many musical genres frown upon polynumeric rhythms. Today, we’ll take a look at polyrhythm, polymetre, polytempo, and non-dyadic – also mistakenly known as irrational – time signatures.

If you haven’t already, please read our previous post on microrhythms.


What is a polyrhythm? Simply enough, it’s two or more … Read more

Negative Time Signatures (a Response to Adam Neely and 12tone)

Sorry, Adam. To be fair, I’m probably wrong, too…

Youtubers Adam Neely and 12tone recently posted videos about a concept they call “negative time signatures” (click on their names to see their respective videos). There is certainly no consensus on this, as far as music theory goes, and there maybe never will, but it’s an interesting hypothetical question nonetheless. I’m writing this post because I think I have a different way of seeing this concept from Adam and 12tone’s. It’s not better, it’s not worse, just different, as there is no widely accepted definition of the term. But before introducing … Read more