Thelonius Monk’s Shapeshifting Chord


One of my part-time hobbies is being a Monk interpreter. A Monk interpreter not only learns how to play Monk’s compositions, but also makes a point of getting into the head of this eccentric man. The reason to do this is that Monk was an improvisor – and he was driven by an inner vision. If you can tap that inner vision, then you can generate Monk-like music – and improvise on it…even while playing Beatles songs.

I wrote a piece in 2013 about Monk as a mathematician.


Math can be about patterns (visual or sonic). Math does not always have to be expressed in numbers. Monk once said,“All musicians are subconsciously mathematicians”.

A Symmetrical Chord

The chord I’m talking about has four notes. It is typically used as a dominant chord – which naturally resolves to the tonic. Unlike the classical dominant-seventh, this chord has a flatted fifth – which makes it slip into a symmetrical regime – as shown in the picture above – inscribed in the circle of fifths.



According to Wikipedia, this chord is called the “Dominant Seventh Flat-Five Chord“. The cool trick about this chord is that it can resolve to either of two different tonics – each being a tri-tone apart.

So for instance, a chord with these notes:     Eb   F   A   B      can resolve to either Bb or E as the home key.

This chord also happens to contain 4 of the 6 tones in a whole tone scale, which Monk famously used (often as a dominant arpeggio).

If you are not familiar with music theory, you may still appreciate the beauty of sonic geometry and how it can generate such variety. If you apply similar concepts to rhythm as to harmony then you have a wonderfully rich canvas for endless musical expression. I like the way Monk wove these geometries together in a way that makes the foot tap and the ear twinge – and the brain tweak.

Monk was of course not the only one to apply these ideas – but he did accomplish something remarkable: the application of embodied math. If you have spent as much time as I have learning his language, listening to him improvise can cause a smile – or the occasional giggle – to pop out. Like an inside joke.

There is plenty of material on the internet about Monk. Here’s one voice among the many who have acquired an appreciation for Monk:  How to Listen to Thelonius Monk – by George H. Jensen, Jr.


Thelonius Monk was an Applied Mathematician

All musicians are subconsciously mathematicians” – Monk

MonkThe history of mathematics is full of white men.

In my ongoing exploration of an underlying mathematics of the body, mathematics without numbers, and mathematics of nature, I have come to believe that there is an alternate story of math. This story cannot be told with one-dimensional strings of numbers or words. It is not a text.

einsteinyoungIt is a Mathematics expressed in picture, sound, and movement. People with dyslexia understand this kind of mathematics, and routinely engage it . While they struggle in school to get through Algebra, some of them manage to grow up to become brilliant scientists (like Einstein). It is wonderful that there are people who know how to keep school from interfering with their education.

There are several notable black mathematicians listed in Wikipedia. My favorite black mathematician is Thelonius Monk, but he is not in this list.

When my friend Gary Moran, an artist and jazz musician, introduced me to Monk, my reaction was typical: “he’s playing all the wrong notes!” But I soon started to hear something logical inside of the illogical. I’ve been studying – and playing – the music of Thelonius Monk now for over 25 years. He transformed the piano keyboard into a palette of symmetries and abstractions of traditional harmony and rhythm. And most of all: syncopation. I am reminded of the empty spaces of a Cantor Dust or the semi-periodic stuttering of prime numbers. In Monk, silence is used as a tool. Figure and ground are often swapped in the middle of a passage…and the mind is jolted (into discomfort…or joy, depending on your taste for syncopation).


Take another important jazz figure: John Coltrane. He created one of the most celebrated mathematical gems of all time. Giant Steps, a sonic fractal that strides through the octave (in giant steps) … in two time-periods.

Let’s overcome, at least for a moment, our prejudices and preconceptions of what kinds of people can make an impact on the world of mathematical ideas. I’m not saying we should try to understand certain creative people in terms of math as it is usually understood, but rather to expand our idea of math to incude a larger sphere of creativity.

Math is all about abstraction. But abstraction – by definition – has a concrete origin. Body, sound, and movement is where it all starts.