Math as Art: Part 1

I often bounce ideas off my husband, sometimes to get his initial gut reaction to something musical, and other times I use him to verbalize concepts I have difficulty realizing in practice.  Often with the later, I see his eyes glaze over as he just nods and smiles while I talk AT him…usually once I start referring to frequencies and algorithms and nested loops.  You see, my husband has an incredible innate gift of musicality.  He understands music theory and form intuitively.  And he is a man of patience to humor my intellectual ramblings:

“Look at these two axioms and how they interrelate when they are used recursively!”

“Oh, yeah…cool. That’s really interesting.”

“I hypothesize that the resulting melody will actually be tonal and aesthetically pleasing because we, as human beings tend to like things built recursively. Just look at the Golden Mean, and fractals, and flower petals…”

…and I’ve lost him.

Now, if I were to by-pass all the jargon and formula and just play the resulting music for him, he would just GET it.  He would understand exactly what is happening and even point out weaknesses and how I might make it stronger.  He is magic and I am a mere mortal who has to explore and research and use trial and error to figure out how to make these ideas a musical reality. So, I decided to try sparing him the process so he can savor the result.  What better sounding board to use freely with little to no guilt than a blog?  Over the course of the next few weeks, I plan to use this blog to help me through my latest obsession: Fractals.

And so it begins…

Fractal: A definition

A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are “the same from near as from far”. Fractals may be exactly the same at every scale,  or they may be nearly the same at different scales. The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself. (Wikipedia:

Inspired by the study of weather patterns and Strange Attractors, I decided to use 2 axioms which at first glance are similar, but have very slight differences. Once repeated recursively, given a set of rules, these differences will explode into 2 very unique sets.
As an example:

Axiom 1

{A, B, A, B, C, A, B}


Axiom 2

{A, B, A, B, D, A, B}


A = AB


C = BC

D = AC

Step 1

Axiom 1 {A, B, A, B, C, A, B} =

{A, B, A, B, C, A, B, A, B, C, B, C, A, B, A, B, C}

Axiom 2 {A, B, A, B, D, A, B} =

{A, B, A, B, C, A, B, A, B, C, A, C, A, B, A, B, C}

At this point, the differences have been abstracted further by the use of recursion. It is difficult to see, and even more difficult to hear the differences between the two.

Step 2

Axiom 1 {A, B, A, B, C, A, B, A, B, C, B, C, A, B, A, B, C} =

{A, B, A, B, C, A, B, A, B, C, B, C, A, B, A, B, C, A, B, A, B, C, B, C, A, B, C, B, C, A, B, A, B, C, A, B, A, B, C, B, C}

Axiom 2 {A, B, A, B, C, A, B, A, B, C, A, C, A, B, A, B, C} =

{A, B, A, B, C, A, B, A, B, C, B, C, A, B, A, B, C, A, B, A, B, C, B, C, A, B, B, C, A, B, A, B, C, A, B, A, B, C, B, C}

Now, just at the 2nd iteration, we can see the similarity grow farther apart:

{A, B, A, B, C, A, B, A, B, C, B, C, A, B, A, B, C, A, B, A, B, C, B, C, A, B, C, B, C, A, B, A, B, C, A, B, A, B, C, B, C}

{A, B, A, B, C, A, B, A, B, C, B, C, A, B, A, B, C, A, B, A, B, C, B, C, A, B, B, C, A, B, A, B, C, A, B, A, B, C, B, C}

This is a very simple example, using only 4 rules on 3 variables, but it gives the general idea behind this new piece I’m working on. I’m thinking the working title “Strange Attractors” is appropriate.


sarah j ritch, pyr interview!


sarah in the red room

When did you first become interested in music?

Hmm, you’re asking for a bit of family history here. I can’t remember becoming interested in music. It has just always been there, probably because of my family. My Mom was an amateur cellist until her early 20′s, my Dad is a brass player and conductor (notably of the U.S. Army band in San Francisco during the final days of the Presidio), my Grandma sang opera, one brother plays violin, another played sax and flute, plus various other relatives who played various other instruments (including auto-harp!). Music is just part of life, like air and sunshine and thunderstorms. Please don’t judge me for the cheesiness of that line, but it’s true! I’ve always loved moving to music and making sounds.

Man, that’s a lot of music in your family, it seems like it was pretty much inevitable that you would start playing. Although, you could’ve also rebelled by completely rejecting it too I suppose. With all those musicians on hand, did your family ever play music together?

My brothers and I joked around about starting a grungy Hanson type band, but no. The closest we ever came to playing music together was solfegging the violin and cello parts to various symphonies on many long drives between Vegas and Reno (nerd alert).

What was it that drew you in to music?

Growing up, my Mom always encouraged me to pursue all my interests (probably because of my attention span issues). I’m what you would call a “high stress functioner,” or someone who needs a multitude of things going on at once in order to stay focused. If you give me one thing to focus on, I can’t. So, (through generous community support because we were dirt poor) my Mom had me in ballet, gymnastics, piano lessons, girl scouts, and various after-school academic clubs. I’m really lucky that so many people were able to make this happen for me. When I say we were dirt poor, I mean dirt. Section 8 housing, homeless shelters, WIC, food bank, seven people in a two bedroom apartment, moving every six months kind of poor. Our Christmases were provided by the churches and public donations and I remember a few occasions where I was told to go get a clean rock from the yard for stone soup. . . .

Continued at:

sarah j ritch, pyr interview!

ESPLORAZIONI: Featuring work of Aaron Einbond









I have always told my students that music is maths realized as art.  I think this always comes up because I have a tendency to explain music theory fundamentals as if I were teaching arithmetic.  Most of my students, being in the 4th Grade through Jr. High academic range always pick this up and say “Wait, is this music or math?!”  I love seeing the sparkle in their eyes when I explain my view of maths and music…it’s like I just made something boring (presumably maths) into something mystical.

So, naturally, I am drawn to the increasingly expanding field of computer music.  I’m talking low dirty dark magic computer science and skilled music composition.  There aren’t many people working in this new genre who are a genuine mix of coder/composer, but those who are give me hope for the future.  Ensemble Dal Niente is presenting a concert this Saturday which features a new work by one of these special sorts of person, Aaron Einbond.  Aaron is a composer for both electronics and acoustic instruments as well as is a researcher in computer science!  His new work Without Words combines soprano, nine players, and live electronics.

Made with CataRT

Aaron explains the above here :

“In the plot, each dot represents a short sample as performed by Amanda DeBoer, and the axes correspond to the timbral qualities of the sounds.  I explored this plot to assemble the samples into micro-montages, which I use in the electronic component of the work, or ask Amanda to recreate live.  I also map them to other audio recordings, so that the performers are asked to recreate a recording of frogs, the sun, or of Wallace Stevens reading.  Because samples of Amanda and the other players were my starting point, their unique sonic identities are woven into the fabric of the work as well.”

And how does one notate this idea? Aaron was kind enough to give us a little peek into the score:

You can check out the realization of this piece live this Saturday. Details given below.


Saturday, June 9, 2012 7:30pm

Nichols Concert Hall
1490 Chicago Avenue
Evanston, IL
Tickets: $20 general/$10 students, available at the door

Spektral Quartet: Theatre of War

Theatre of War

The Spektral Quartet

My hubby is awesome, and talented, and handsome.  I normally wouldn’t use my blog/site to gush over him, but I am so impressed and proud of his upcoming project, Theatre of War, that I felt so inclined.  The topic is one of great importance, that of passive acknowledgement of war in our modern society.  Theatre of War is not aiming to take a side, preach, or act as any kind of political protest but rather to serve as a tool to bring the wars to our active attention.  I, for one, did not pay much attention to any of our wars until my own brother was stationed in one of the most active zones in Afghanistan.  This was a direct daily assault on me and made me realize how important it is for each of us to educate ourselves on global policies and actions.  I hope you’ll be as impressed as I was with their preview trailer and make it out to the Spektral Quartet’s Theatre of War.


Intuition Vs. Algorithm essays

Intuition Vs. Algorithm





Victoria Morris

When I accepted the assignment to make a piece for this show, I was quite thrilled by the push and pull duality inherent in the phrase “Intuition/Algorithm”. After all, intuition is the deepest, rawest instinct of the human mind and we think of algorithms, when we think of them all, as the refined product of the right brained, never to be grasped easily except as part of an advanced degree. Except… we mention the latest algorithms so casually, designers wrapping them in friendly GUI to hide the bitterness of math, and make them sweet like music. They hide it when we ask our friends to “Google it” or in the marvel of a newborn learning to use his parent’s iPad, the trajectory of an angry bird. Design is increasingly the art of masking algorithm in intuition.

If the concept of the program was exciting, I was not so thrilled by Sarah’s request that I select a contemporary artist who exemplified this concept and write about them. Which is why I’m giving a speech: I dragged my heels so long that I didn’t get it printed in the program. Oops! Sorry. The difficulty wasn’t in selecting an artist. I very quickly decided that I wanted to speak about Jenny Holzer. For me, she exemplifies the theme of our show. Hers is work that can only exist in this digital era of signboard and computer typography and projection yet speaks with a loud clear voice about things we know to be true but are afraid to admit to ourselves, let alone one another. Intuition. Algorithm.

The trouble that I faced was in selecting a single piece by Holzer to discuss. Her entire body of work centers on these ideas, but I finally had to choose and I chose  “Installation for Neue Nationalgallerie” in Berlin. This marriage of art, technology and architecture was debuted in 2001 and consists of thirteen scrolling LED tickertape displays in amber installed upon exposed beams in the roof of the building. The text of the piece was written by Holzer herself, and describes a mother as she observes the changing body of her adolescent daughter.



The words scroll on and on across the ceiling in a never ending loop from adulthood to the decision to keep a child, without end. The hard, unforgiving orange light industrializes a text that memorializes the sentiments of motherhood.

Spencer Hutchinson

The Photo-Programitism* of Laszlo Moholy-Nagy

I have selected, not one piece of art, but selections from the body of work of Laszlo Moholy-Nagy who’s experimentation with light as a medium used directly for the purpose image sets a visual precedent for the abstract machine inspired aesthetic and whose process is greatly aligned with the working methodology of musique-concrete and electronic sound manipulation.  While no concrete algorithms are used in the process of his work per-se, the dependence on the technology at his disposal does necessitate the mindset and approach to art-making that one is beholden to when confronted with the technological programs and limitations of electronic and mechanical media.  The photograms, collages, and photographs of Nagy when observed as a whole present the astute observer with a unique personalized aesthetic that goes beyond what was achievable by way of conventional plastic media used by other more notable artists who aligned themselves with cubism and constructivism.   By infusing, at the onset of creation, a purely intuitive placement of objects to be not represented, but rather RE-presented as mysterious entities whose embedded alien aesthetic is revealed through the impersonal photographic process, Nagy has created the first true synthesis of man/machine collaboration which has left on enduring legacy on the discipline of technological art.

*Photo-Programmitism: is a term that I invented for the purpose of talking about Nagy’s work in particular since his creative output was not limited to photography, but was rather beholden to an aesthetic that necessitated multiple approaches to image-making where the process of creation is depenedent on the use of light as a medium.

-Spencer Hutchinson, January 27, 2012

End the Silence

Since last June, I have not been incredibly active. You might say I’ve been in a creative depression, unable to get that spark ignited and unmotivated to do anything about it.  Lucky for me, people won’t let me just wither away into logic and maths.  Thanks to a few entities out there like Absence of Wax, The International Beethoven Project, and a few friends forcefully nudging me to compose and perform (I have to give my husband alot of credit here), I can say that I am coming out of my lull.


The first act of celebration is the release of my first solo album by netlabel Pan Y Rosas Discos!  It is a free download as part of the Creative Commons community to be shared freely for non-commercial purposes.  I hope you get a chance to listen and enjoy it as much as I loved making it!

Sarah J. Ritch: String Theory



Chicago Scratch Orchestra

Sometime a week or so ago, I was introduced to the idea of  a “scratch orchestra.”  For those of you who are, like me, new to the concept, below is a nice short description courtesy of Wikipedia:


The Scratch Orchestra was an experimental musical ensemble founded in the spring of 1969 by Cornelius Cardew, Michael Parsons and Howard Skempton.

The Orchestra reflected Cardew’s musical philosophy at that time. This meant that anyone could join, graphic scores were used (rather than traditional sheet music), and there was an emphasis on improvisation. The Scratch Orchestra arose from Cardew’s ‘Experimental Music’ class at Morley College, London, which served as a venue for extra rehearsals for Scratch Orchestra concerts, but Scratch Orchestra rehearsals were also held separately.

The first meeting of the Scratch Orchestra was at St. Katharine’s Dock, 1 July 1969. It was announced by means of a ‘Draft Constitution’, published in “The Musical Times” in June 1969. The Draft Constitution set out categories of musical activity: Improvisation Rites, Popular Classics, Compositions, and Research Projects. Cardew also proposed that the responsibility of programming of concerts be assigned in reverse seniority, so that the first concert, on 1 November 1969 at Hampstead Town Hall, was designed by Christopher Hobbs, an eighteen-year-old student of Cardew’s at the Royal Academy of Music.

Despite the emphasis on free improvisation, the varying experience of the members, and the ‘do your own thing’ free aesthetic of the time, the Scratch Orchestra was a disciplined ensemble. Eventually the strains of Cardew’s “reverse seniority”, tensions between musically-trained and non-musically-trained members, and an increasing interest in political aesthetics led to a gradual change in the activities, and then the outlook of the ensemble. It was effectively inoperative by 1974.


When asked if I’d be interested in joining the Chicago Scratch Orchestra for this year’s Chicago Calling Arts Festival, I read Cardew’s Draft Constitution and knew it was something I’d been waiting for!  The best part (for me, as I don’t know how well I’ll be appreciated by the other members OR the audience) is that I can pick my instrumentation….and I picked cello and/or laptop.  This is an instrumentation I’ve been experimenting with in my band, Sound Collision Alliance.  I have been pretty excited with the results while working with 2 others who I have years of experience performing with and I can’t wait to be thrown in the mix of people I’ve never even met.  If you are intrigued or frightened, I suggest you check out my Upcoming Events page for details on performances and how you can attend (or avoid).

If you are interested in the cello and/or laptop instrumentation, check out this recent Sound Collision Alliance recording with members of NU Directions Chamber Brass: