December 28th, 2022

The Fractal Structure of John Coltrane's Solo on Countdown

This animation is a follow-up to my work on Trane's famous solo on his groundbreaking composition Giant Steps (see the August 29th entry below).  Similar to that solo, this one also possesses fractal characteristics.

Watching the animation, one can get an intuitive sense of the fractal structure by looking at the distribution of the vertical spacings between the  pink saxophone notes. Overall, there are lots of small jumps and fewer medium-sized jumps. These are all punctuated by relatively few large jumps. This relationship between count and size can be accurately captured by a power-law.

Here's a new article on Medium's premier math publication, Cantor's Paradise,  that describes the analysis:

October 26th, 2022

Protect Your Designs With This Free Google Colab Notebook

The watermark in this image was generated by the Colab notebook referenced below. (Image by Author using Stable Diffusion)  

As an inventor and songwriter, I've always been attuned to issues of intellectual property protection. When I started exploring the world of machine learning and AI-generated artwork, it seemed like it might be useful to be able to include an unobtrusive digital signature to help establish the provenance of my work. When I searched for a stand-alone, ready-made tool, the pickings were slim.

So I built one. It's a free notebook that can be opened in Google Colab from directly from GitHub.  You can read a detailed description and see an example in a brand new article in Towards Data Science.  The article also illustrates how the tool can be used to explore the field of image steganography — the practice of concealing information in plain sight. 

August 29th, 2022

The Fractal Structure of John Coltrane's Giant Steps Solo

I started this animation project in an effort to explore fractal structure in John Coltrane's iconic solo on his famous, groundbreaking composition Giant Steps.  Instead of just visualizing the sax solo, I thought it would be super fun to be able to see how the entire quartet interacted.  Here's my article in Towards Data Science which describes the solo from a fractal perspective:

Giants Steps — The Fractal Structure of John Coltrane’s Iconic Solo

Please see the YouTube description for more information about the animation.

Giant Steps animation get three thumbs-up from jazz legend Ron Carter:

Nuevo artículo por Horacio Verbitsky (New article by Argentine author Horacio Verbitsky):

PASOS GIGANTES: La música que escuché mientras escribía

New article by Josh Jones on this project just published in Open Culture:

Watch a Jaw-Dropping Visualization of John Coltrane’s “Giant Steps” Solo

April 11th, 2022

Fractal Music From Randomness

Brecker 8 is a fun example of fractal music. The piano solo is a random arrangement of a fractal distribution of melodic intervals with a predetermined dimension, d=8. I improvised the piano chords to accompany the solo in a fashion that sounds natural  ( least to my ear). Last came bass and drums. For more details, check out "Fractal Music from Randomness" in the publication Towards Data Science on Medium.