Beats and scales

I don’t know a lot about Afro-Caribbean rhythms, beyond the fact that they cause me intense joy whenever I hear them. My formal music education has focused almost exclusively on harmony, and I’ve had to learn about rhythm mostly on my own. That’s why it was so exciting for me to discover the work of Godfried Toussaint. He introduced me to a startlingly useful pedagogical tool: the rhythm necklace.

A rhythm necklace is a circular notation for rhythm. Let’s say your rhythm is in 12/8 time. That means that each cycle of the rhythm has twelve slots where sounds can go, and each slot is an eighth note long (which is not very long.) A 12/8 rhythm necklace is like a circular ice cube tray that holds twelve ice cubes.

What’s so great about writing rhythms this way? Rhythms are relationships between events that are non-adjacent in time. When you write your rhythms from left to right, as is conventional, it’s hard to make out the relationships. On the circle, the symmetries and patterns jump right out at you. I recommend the Toussaint-inspired Rhythm Necklace app to get these concepts under your fingers and into your ears.

You can’t look into Afro-Caribbean beats without coming across a bell pattern called Bembé, also known as “the standard pattern” or the “short bell pattern.” Here’s how it sounds:

I was probably first exposed to Bembé by Santana’s “Incident at Neshabur.”

Bembé’s meter is ambivalent. You can represent it as duple (4/4) or triple (6/8 or 12/8). Practitioners urge you not to think of the bell pattern as being in one meter or the other. Instead, you’re supposed to hold both of them in your head at the same time. The ambiguity is the point.

Before I got started representing rhythms on a circle, I was representing pitches that way. Every music student learns the circle of fifths. Chromatic pitch class space is circular too. Each circle is the involute of the other.

I noticed that the major scale necklace on the chromatic circle has the same pattern of filled and empty boxes as the Bembé rhythm necklace.

I’m not the only person to have noticed this coincidence. Toussaint noticed it too, and discussed it in this paper: Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines. Behind the dry title is a remarkable insight into human musical tastes across cultures.

If you rotate the major scale necklace, you get the major scale modes, all of which are valuable scales in their own right. Rotating the Bembé necklace gives you a set of widely-used beats, all of which you can hear in this super useful video:

Dorian mode and Bemba

If you rotate the major scale necklace one step counterclockwise, you get Dorian mode, the major scale starting and ending on its second note. C Dorian mode has the same pitches as the B flat major scale. Rotating Bembé one step counterclockwise gets you a rhythm called Bemba. This new necklace is distinctive for being left-right symmetrical.

Here’s an example of Bemba.

https://youtu.be/8_lLD7aKFls

Lydian mode and Tambú

Rotating one step counterclockwise from Dorian mode gives you the Phrygian mode, but that scale doesn’t map onto any widely-used rhythm. The rotation after that, however, does:

Tambú is also known as the “long bell pattern.” Here’s an example.

Mixolydian mode and Yoruba

I couldn’t find any good examples of this beat, or the next two, other than the black-and-white cowbell guy video above.

Natural minor and Ashanti

Locrian and Bembé-2

The major scale necklace isn’t the only one to line up with a bunch of rhythm necklaces. The melodic minor scale does too. The most interesting melodic minor mode/beat correspondence is this:

Lydian dominant mode and Asaadua

All five modes of the pentatonic scale make widely used beats. Here are the ones you get from the two most crucial pentatonic modes.

Major pentatonic scale and Fume-Fume

Fume-fume is also known as 12/8 clave, the triple meter equivalent of son clave.

Minor pentatonic scale and Bemba

This video isn’t as clear as the one at the top of the post, but it’s still worth watching for the performance of a lot of different rhythm necklace rotations.

Not all of the beats that Toussaint discusses map onto commonly-used Western scales, and not every scale maps onto a commonly-used beat. Still, the overlap is startling. What does it all mean?

Toussaint argues that there’s one feature uniting the world’s most popular rhythms: maximal evenness. All of the patterns above are the result of trying to fit five or seven drum hits into twelve possible slots. It can’t be done perfectly evenly, but there are many different ways to approximate it. Nearly all of the mathematically possible solutions are widely used rhythms. Many of them are also widely used scales. The odd number of hits or scale tones is important. If you divide your twelve-step necklace by three or four or six, you get perfectly symmetrical subdivisions that quickly become boring. People do use the even subdivisions, both for rhythm (e.g. four-on-the-floor kick drums) and for pitch (e.g. the whole-tone and diminished scales), but you need some asymmetry to hold the listener’s (or dancer’s) interest.

In European-descended cultures, we like our harmonies interesting and our rhythms boring. In Afro-Caribbean cultures, it’s the other way around. Either way, there’s a shared interest in using a precise blend of symmetry and asymmetry to challenge and gratify our pattern-recognition abilities. If there’s any feature that’s universal to all the world’s music, that’s probably it.

Please, if you know Afro-Caribbean music, recommend some listening to me in the comments!