Almost all of the music I have written in the last couple of years has been based around “name composition.” That is, I have been transforming the names of the players for whom a given piece is written into the basic pitched and rhythmic materials of the piece in question. In order to break out of this compositional routine I decided to try a new approach in this piece. For Two Sierpinski Pieces I used the fractal pattern commonly known as “Sierpinski’s Triangle” to generate my initial sketches. The two pieces result from two different renderings of Sierpinski Triangles as pitches – one chromatic and one microtonal. Here they are presented as movements, but they can exist on their own as well.
Technical Notes:
Relying on the names of performers as the seeds of my materials in most of the music I have composed in the last two years has made me anxious to experiment with some new approaches. One of my experiments has been to use fractals geometry as a method of generating materials. This method was used in the composition of Two Sierpinski Pieces. I will briefly outline the approach I took below.
I used Peter Elsea’s 2012 paper “Fractals in Max” as a starting point. Basically, I remade the patches as outlined in the paper so that I could reproduce the kinds of images Elsea provides as examples. For example, here is a fully rendered Sierpinski triangle generated in Max using Elsea’s method:
From here, I began feeding the Sierpinski plots into a Bach patch that translated the visual contour into a musical contour. Specifically, I mapped the Y-Axis data to pitch height and the X-axis data to time. In the case of the basic Sierpinski Triangle above, this mapping results in clusters of pitches with a registral distribution over time that resembles the shape of the fractal.
The problem with the full triangle, however, is that too many tone clusters resulted, and the output was not musically satisfying to my ear. My solution was to use only a partial rendering of the triangle so that the basic shape remains intact, but with less resolution. For example, the partial Sierpinski Triangle used to create the initial sketch for the ending of the first of the Two Sierpinski Pieces is shown below:
In translating the image into a Bach sketch, white space was filtered out and the placement of each red dot was then quantized to a semi-tone pitch grid that matches the general range of a saxophone quartet. Critically, this means that only pitches and their placement in time were computed. I made every decision of dynamics and orchestration by intuition alone.
I modified my pitch mapping algorithm to create the chorale heard in the second of the Two Sierpinski Pieces. I used partially rendered Sierpinski Triangle similar to the one shown above, but I was unsatisfied with the results of simply mapping height to a semi-tone grid. My solution was to consider the Y-axis as an axis of frequency (Hertz) that covered the general range of a saxophone quartet. The resulting frequencies were then quantized to a quarter tone grid to allow for greater harmonic complexity. This technique results in a pseudo-spectral distribution of pitches across the range of the saxophone quartet that more easily translates to a four voice chorale texture.
Performers:
Pablo González – Soprano Sax
Carlos Tena – Alto Sax
Jesús Gallardo – Tenor Sax
Javier Juanals – Baritone Sax