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.

Rhythm necklaces with their shadows

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.

Two representations of Bembé

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.

Circles of fifths and half-steps

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.

Major scale rhythm

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.

Dorian mode rhythm

Here’s an example of Bemba.

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:

Lydian mode rhythm

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

Mixolydian mode and Yoruba

Mixolydian mode rhythm

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

Natural minor rhythm

Locrian and Bembé-2

Locrian mode rhythm

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

Lydian dominant mode rhythm

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

Major pentatonic scale rhythm

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

Minor pentatonic scale and Bemba

Minor pentatonic scale rhythm

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!

10 thoughts on “Beats and scales

  1. Pingback: Rhythm is Key | C4D

  2. For a collection of African rhythms, try to find materials by the artist Guem. I believe he is also a professor in music at some university in France. Wikipedia has nothing on him and Spotify just one record. Youtube has a lot more, but in disjointed fashion. If you can locate some of his early 70s records (I have some on vinyl…) he has collections of African and Afro Cuban rhythm rudiments, or simples as you call them (I am not sure which word is better for this material).

  3. What a great post, thanks Ethan!

    I can’t believe I never thought of teaching rhythms in a circle. I’m curious about how you would teach any of these rhythms to an early-level student. In my experience, the most useful way of learning any rhythmic group, including phrases and cycles, arrives at hearing and feeling the rhythm with your own voice. However, there might be various pathways to reach that point, which may include counting, clapping and voicing, starting slowly or going straight to full tempo. If you have standard ways of teaching rhythmic patterns to students, it might be informative for you to put this in a post (if you haven’t already).


    • I put on a drum loop at a slow tempo and have the student follow it. Sometimes I break it down analytically but I prefer to go by ear. The different visualization schemes have mostly been for my own benefit so far, but my research group at NYU is going to be rolling out some interactive stuff this summer.

    • He had the big cross over “Rum and Coca Cola” and “Shame and Scandal”. I am partial to the calypso of the 50’s and 60’s even though some of the recordings are rough and some of the topics a bit too local. Try Lord Melody. The recent “University of Calypso” recording captures some of the 50’s early 60’s magic. I lived in Barbados from ’66-71 and played bass in guitar bands doing covers of Sparrow, Kitchener (whose offerings were in the rhythm section with horns backing the calypsonian mode) and the calypso guitar bands, the Merrymen and the Tradewinds. Helped to arrange a calypso showcase at Studio 54 in NYC in the early 80’s with many of the musicians recording at Charlie’s Records studio

  4. Be sure to check out Charlie’s Records on Fulton Street near you in Brooklyn. Much of the calypso and soca of Trinidad and Tobago in the 80’s was recorded there. It may not still be happening, but I bet there is still a TNT scene in Brooklyn. Also a Haitian scene around the band Tabou Combo.

  5. Wonderful post, Ethan! I plan to return and review at greater leisure. Absolutely remarkable that the Bembé pattern maps precisely to the major scale, etc. Could we be equating and responding similarly (or analogously) to the same pattern presented in such different representations as pitch and time? My mind is boggled. Thank you.

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