# Belles: An Experiment in Marathon

An idealized visual representation of the rhythms in “Belles”. The vertical axis represents the beats of the composition and the horizontal axis the time at which each note is played inside the rhythmic pattern. Each colour represents a different note in the piece.

Ever since I started visually representing microrhythms, for example in my last post about Marathon, I’ve had the idea of creating rhythms based on visuals, instead of the other way around. For this experiment, I was thinking about the full extent of the Gnawa rhythm going back and forth and overlapping with itself to create this … Read more

# Marathon: Analyzing the Extents of the Gnawa Morph

You’ve already seen a similar figure if you’ve read my post Marathon: Understanding Ratio Morphing. Here, I’ve added subdivisions of time from 5 to 8, but in practice they also include subdivisions of 2, 3, and 4, and we’re going to look over them relatively succinctly today.

First, how to read this graph. It’s important to know that it’s read from left to right. The leftmost boundary is the start of a measure, and the rightmost one the end of it. If you’ve ever used Guitar Pro or a similar notation software, you can easily imagine a cursor moving … Read more

# Marathon: Understanding Ratio Morphing

I’ve already written a bunch of posts on microrhythms and have since created a little free program to help create microrhythm in MIDI files. Now, I want to try and give a better explanation on how morphing works.

Morphing occurs when you put two rhythms in opposition. Let’s take the fairly easy example of the traditional Gnawa three-note rhythm. The two conflicting rhythms here are the straight triplet and a quintuplet feel “swing” version of itself. This conflict is made abundantly clear by Malcolm Braff’s conception of it.

Triplet notes (below) conflicting with a quintuplet swing version of itself

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# Advanced Mathematics 202: Decimal Music

The French Revolution brought humanity many things, among which are the values of liberty, equality, and secularism. However, in their hot-blooded revolt, they also brought the widespread use of the decimal system, taking the place of the old-fashioned Carolingian system, which resembled somewhat the Imperial system of today’s USA. They even thought of bringing up decimal time, and a decimal calendar, where the twelve months of the year each had three “weeks” of ten days. At the moment of writing these lines, we are Octidi the 28th of Messidor (Monday, July 16th, 2018). Each of these days would … Read more

# 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