I began to think about rhythm, when I was about seven or eight years old. I remember saying to my father: it would be amazing if you could know all the possible permutations of a beat. Such a musician could play anything! Such a musician would be a universal rhythm god!

My father, who was a musician and crane operator, said: this was impossible, because the space between one beat and the next is infinite. So you would be required to know the infinite. Impossible.

I hadn’t thought much about the infinite. I wasn’t sure what it was. I was envisioning superheroes behind a drum set. But, infinite options of where to place a beat seemed pretty rational, and likely impossible to know even for a superhero. I would have to live within my mortal bounds.

Twenty years later I attended a workshop by Efrain Toro and this conversation on rhythm and the infinite was expanded greatly. The workshop was held at the University of Toronto. I listened as Mr. Toro explained the concept of harmonic rhythm – rhythm built upon the harmonic series.


The harmonic series is in both math and music. All things vibrate in this sequence. Imagine a space of time. It could be one second or one day or one year. Divide the unit of time in 2 then in 3 then in 4 and so on to infinity. That’s the harmonic series. This what the harmonic series looks like from one to seven within the length of a string :


Hearing is Believing

Efrain sat down at a drum kit and proceeded to play the harmonic series. He started with a slow simple beat of one. Then, layering the frequencies on top, he added 2 beats then 3, 4, 5, 6, 7 and eventually topped 8 with 9. All played within the same space of time. I could hear each pulse, individually, like they were meant to be together. Together yet distinct. Together then not together. Kind of like an optical illusion.

Here he is with an updated version of what I saw that day:

I ordered all of his books:


When I received the package of books, I scanned the first in the series: ‘All of Rhythm’. It is 47 pages long and begins with a 12-page introduction to E.T.’s approach to rhythm. The next 35 pages consist of practice sections of incredibly simple notation. An accompanying audio track is included to listen and play along.


That’s it, some words and a non-infinite number of pages encapsulating the entirety of rhythm. Somehow I thought there would be more to it. I imagined MORE: more pages, more writing, more notes. I mean, it is all of rhythm, shouldn’t it be a bit closer to infinitely incomprehensible and dense?

As I continued to read, I found some simple yet profound concepts:

“Rhythm is the most basic element of nature. It is the frequency in which an event happens. When this frequency occurs at a rate that we can perceive, it can be a pulse, a sound or light.” – All of Rhythm.

What does this mean? I understand that rhythm is in nature. Rhythm happens in the repeating patterns of plants, animals and the environment. I understand that repeating patterns or frequency are in the pulse of a drummer’s beat. But how are sound and light defined by rhythm? Sound and light are also measured by frequency. When we talk about something being ‘high pitched’ or ‘hitting a low note’, technically we are referring to how frequently they are vibrating in time. High notes vibrate the air and our ear drums very quickly. When we talk about colours of light, we are talking about how quickly the light vibrates the receptor cones in our eyes. Red light and Blue light vibrate at different frequencies. Sound and light are measured by how frequently they vibrate in time: Hertz (Hz).

If I play one beat every second on a drum, I am playing at a rate of 1 Hz. If I play at 440 beats a second, I would be playing the musical tone A (440 Hz). Mike Mangini holds the world record for fastest drumming at 1247 beats a minute. That’s 21 beats a second held for a minute, which is the note E (21 Hz). If some human could play the drums at 540 trillion Hz they’d be playing the colour orange… and their drums would be on fire, with an orange hue.

Octaves of Frequency

In order to relate these different frequencies to one another we use octaves. One octave represents a doubling of frequency. Hearing and sight are two ways that humans experience these octaves. Humans can hear roughly 2-3 octaves of pulse and 8 octaves of pitch . We see one octave of light. The reason red and violet, on opposite ends of this spectrum seem to be congruent is that they are an octave apart in frequency. Here is a chart showing the relative frequency of light laid over a piano keyboard:

So, what does this have to do with the harmonic series or music for that matter? To answer that question we have to look at what the harmonic series is where it exists. To do that we need to go back in time. We need to look at the beginning of the harmonic series at the beginning of time.


When we look up at the stars we are looking back in time. A star we observe that is four light years away is from four years in the past. The light of that star travelling at 300,000 kilometres a second, took 4 years to get here. If we look further into space, we look further into the past. Looking back far enough we can see the first few million years after the big bang. At that time, matter had not cooled enough to separate into stars and planets. We can observe wave patterns on the surface of an undulating expanse of light and sound. The troughs and peaks of these waves were on a very large scale; a wave could take thousands of years to cross the expanding universe. The interaction of these waves took the form of the harmonic series. The sound of the Big Bang rang with the harmonic series. In the harmonic series the initial impact is called the fundamental. This is the ONE. All subsequent peaks are called overtones. The first overtone is TWO the second is THREE and so on. The fundamental is the energetic source from which all overtones take their sustenance. In a sense the very first fundamental was the Big Bang and everything in the universe, including all of us, are the overtones of that original event.

This story is told very well by professor Mark Whittle at the University of Virgina on his website: Big Bang Acoustics: Sounds From The Newborn Universe. Here is a graphic from that website which describes the harmonic structure of the early universe:

Take a close look at that pattern of blobs. The blobs represent high and low compression areas of matter sloshing through space. Starting at the top set of two blobs, working down to the next groups of three, four and five blobs you are looking at the harmonic series teased out of data from the early universe. This pattern is something you are familiar with even if you’ve never seen it before. This structure is embedded in our physiology, or as Daniel Levitin says in ‘This Is Your Brain on Music’:

I never understood how some people can play music by ear. How can someone who’s never learned to read music actually make music? This is the reason why. Sound and the relationships of harmony are built into our being. And these relationships are built into all resonating objects. Musical instruments have a particular sound or timbre. The sound character each instrument produces is made up of it’s own signature emphasis of the harmonic series. When you play a single note on a violin and on a flute, say the note G (392 Hz), the note G generates all the overtones, or multiples of the G fundamental. These waves ride on top of the G. You can see in the following example that the emphasis of harmonics differ between each instrument, but the frequency peaks are exactly on the multiples of the fundamental:

The difference in emphasis of overtones is how we identify the sound of a flute or violin. This is what gives a flute it’s flute-y sound and a violin it’s violin-y sound. It’s also why we can identify the sound of our mother’s voice. There is a signature to the harmonics that our mother’s voice produces. Musical instruments have been designed to maximize this harmonic potential, but all physical object have a sound signature. Even foam you ask? Why yes if you hit it hard enough…

The person who is credited with discovering this natural phenomenon was Pythagoras. The harmonic series (1,2,3,4,5,6,7,8,9…etc.) and their inter-relations were the basis of Pythagoras’ creation of harmonic music. Legend has it that Pythagoras was admiring the sounds emanating from a smithy he was walking past. Jamie James tells the story:

For the Pythagorean cult that soon formed, the universe and God were seen to be understandable through numbers and their ratio relationships. This new music was for them a direct experience of the divinity of numbers.

Back to the Beat

OK, so what does this have to do with rhythm? Well here is where Efrain comes in. What Efrain has done is take the same harmonic ratios that are used to define musical pitch relations and applied them to pulse. If you play these harmonic ratios as rhythm you get different cultural expressions of rhythm. Blues rhythms, jazz rhythms, African rhythms, Gypsy rhythms, Indian rhythms. In the same way you can feel the mood of a scale (a minor scale is said to be sad), pulse too can have different ‘feels’.

To understand what these ‘feels’ are, one must start at the beginning of the harmonic series. It begins with the fundamental which is one. Then comes the octave which is two times the frequency of the fundamental. Together these create a downbeat and an upbeat. One and two. Or up-down, right-left, strong-weak, and next is three. Efrain claims in All of Rhythm: “The first perceivable rhythmic pattern in pulse involves the use of two frequencies; three pulses and two pulses played at the same time.”

This simple ratio of two and three is the basis of many feels of music. Swing, funk, jive, bounce, salsa all acquire their meaning from two and three. The ratio of 2:3 is called a hemiola in western music and can be applied to both pitch and pulse. It is also called cross-rhythm. In West African music it is referred to as KON and is the basic building block of all other rhythms. Acoustically it means that you can follow either the line of two or the line of three.

This is what it sounds and looks like:

According to Efrain “There is no way to proceed from playing downbeats unless you can play and fully understand the 2:3 or 3:2 relationship.”

This simple relationship is central to an experience of rhythm. In music the 2:3 relationship represents a perspective position. When you can play around this relationship and switch between two and three, you are on your way to understanding the orientation of many kinds of music and the feeling of up and down. Here is an example from Efrain showing the different ways this simple relationship can be perceived and played:

Rhythm is Harmony and Harmony is Rhythm

Efrain’s view is that the archetype of rhythm is the same whether expressed as pitch or pulse. Using C as the fundamental Efrain outlines the pyramid shape of frequencies generated from one to seven :

If you open the image in another window you can see that the octave is C (Two) and the fifth is G (Three). Each note up the scale is the same harmonic multiple of the fundamental. Seen this way, what we call harmony is a manifestation of rhythm. But western music does not generally describe pulse according to this rhythmic archetype. Instead as Efrain says:

“The idea of a well tempered scale and military drumming comes from the same concept, in which there is no variation or there is a fixed space between notes. Western popular music today is mostly based on a military approach. The notes are played in perfect spaces between one another and this creates a one dimensional sound.” All of Rhythm.

Every year at school when I was a kid, we’d get our photos taken and I prided myself on providing consistent photos year after year. Photos you could rely on. Photos that said “I care”. Actually I’m not sure I was aware of what was going on. Probably I was just adequate at taking orders from a photographer who had hundreds of kids to process. Tilt head. Smile. Next.

From a manufacturing point of view, standardization is perfection. When Starbucks promises that ‘your drink should be perfect every time’ what they mean is it should be the same every time. No variation. Could your beverage experience be better? Divine even? Perhaps, but your whole day would be thrown off. You’d come to expect divinity in your coffee every morning. And then you’d get bored and switch to crack.

In music production there are ways to perfect music. Using a technique called ‘quantization’ a musical performance that is ‘off’ can be forced into line. But the ‘line’ that everything is brought into is perfectly even. In the case of pulse, western notation represents the duration of notes in a system that halves or doubles their length: whole notes, half notes, quarter notes, eighth notes, etc. And so, predominantly we play the octaves of pulse. Even when writing in an odd time signature the notes you use are half notes, quarter notes and eighth notes. Three-quarter time means, three quarter notes per bar. 5/8 time means 5 eighth notes per bar. Odd numbers have been boxed in by twos and fours and eights. Perhaps this is because even numbers are easier to work with. The symmetry of the human body makes it more difficult to dance to odd rhythms, as our feet and brain have to switch sides (or emphasis) every bar. Dancing a waltz in ¾ time does exactly this. So odd is defined by evenness in western music. There are no 1/5 notes or 1/7 notes. These divisions of time simply aren’t contemplated. But in a natural approach to rhythm they are actually played!

Natural Rhythm

“On the other hand many other styles such as Afro-Caribbean, Brazilian, Nigerian and north and south Indian music, are played with a more natural approach. The sounds or notes are played with all the divisions and subdivision of time allowing for fluctuations. All the layers of rhythms from one to nine all happening at the same time.” All of Rhythm

The Malinke rhythms from Guinea and Mali are a prime example of this natural approach to rhythm. Here is the excellent short documentary called FOLI that illustrates this approach to rhythm:

This ‘natural approach’ to rhythm is in harmony with a universe extending over 72 octaves, from the origins of galaxies and planets up into the vibrations of DNA, electrons and, rationally speaking, into thought. That there could be one unifying concept that extends across all these scales is beyond my capacity to analyze. However I find it extraordinary that humans have built music out of it. And a natural approach to music provides us with the means to plug into this rhythmic network, this vibrational matrix or groove grid if you will. Through rhythm and harmony you can experience this universal structure. You can play in the infinite.

My father passed away 8 years ago. I’ve tried to imagine where he was going and what that experience was, as his worldly tether stretched ever more thinly. In his last moments my mom was singing to him by his side (it is said that hearing is the last sense to leave consciousness). I see in that moment, his essential self accelerating to the speed of light, time slowing and the harmony of the stars mingling octaves below and above my mother’s voice.

This is my mother and father singing Pete Seeger’s Ode to Joy together:

Ode to Joy

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