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I call my music “Perpendiculous!!”. I use it as both my solo computer music alias and the pseudo-style for my compositions. The name itself, much like my music, carries a sense of levity, stemming from my deep exploration of musical theory techniques based on just intonation tuning and the harmonic series. It's a play on words in the tradition of American music, reminiscent of how jazz musicians name their pieces or how Pauline Oliveros would employ wordplay in her compositions. I'm drawn to the creative naming conventions often found in American music.

"Perpendiculous!!" acknowledges and playfully embraces the fun, curiosity, and borderline absurdity in my extensive exploration of just intonation tuning and the way that I apply it to musical parameters beyond pitch. I learned this approach, in part, from the work of Henry Cowell. I also apply these tunings to visual art. This application of tuning over the elements of pitch, rhythms, color, size and speed of movements makes a harmonic system that I employ in my work, which I perform on my instrument that I develop that I call the Horn of Plenty. These techniques, in certain perspectives, can be traced back to the work of Pythagoras, which are rooted in geometry. Pythagoras theorized about a harmony that extended beyond sound using his mathematical theories and discoveries. More accurately he proposed music with a harmonic system that reflected to scale various proportions in our solar system and then the universe.

To be clear, I am not creating a unifying theory of all art and music. I strive to make meaningful connections within the elements of my work, using my tools of choice which are based in computer code. I like to use coding languages because they allow me to scale parameters to one another, which makes it possible to “tune” a set of colors to the same proportions in the way that I have tuned my pitches. The process has become so thorough that I have become fascinated and dedicated to it to the point that, yes, I am aware that it is kind of ridiculous. I think that this is an excellent starting place for my music.

While I'm uncertain if there's a strict geometry to music, I'm certain there's a shape to sounds. The sounds I use can be proportionally scaled to create colors and shapes, which I incorporate into the visual art within my multimedia work. Here is the first region of my tuning system:

1/1 7/6 4/3 3/2 5/3 11/6 2/1

This six-note tuning serves as both a scale of pitches and a set of rhythmic durations. The 1/1 is the fundamental, and this scale contains the two perfect intervals commonly known as the perfect fourth and fifth in Western equal temperament tuning (4/3 and 3/2, respectively). The 5/3 represents a well-tuned major sixth at 884 cents. Ratios from the three and five limits will sound familiar to Western ears and evoke a sense of precision often associated with modes in Western equal temperament. The 7/6 falls between a minor third and a major second at 266 cents, while the 11/6 represents a neutral seventh at 1049 cents.

I draw heavily from Henry Cowell’s work on rhythms based on the harmonic system. The realization of this system lead to the commission of an instrument called the Rhythmicon which was made by Leon Theramin. My performance system, the Horn of Plenty can be viewed as a type of rythmicon.

With this approach, each note has its own unique duration as well as pitch. The 1/1 serves as the rhythmic fundamental, and in the first region of my tuning there are six beats per measure. The 7/6, positioned between the major second and minor third at 266 cents, plays a polyrhythm of 7 against 6. The 4/3 and 3/2 are from lower limits. They divide into six beat measures, so the results are are 8 and 9 beats to a measure. 5/3 is a higher limit; it has more color than the the two perfect intervals but it stills divides into six beats, so we have 10 against 6. The 11/6 of course is an 11 against 6 polyrhythm. When these polyrhythms, offset from one another by one beginning at six and ending at eleven, are played together in their simplest form, create a gesture that unfurls much like a sound from nature where the overtones are very present.

I don’t attempt to create a unifying musical system. In building upon Cowell's work that led to the Rhythmicon, I do, however, see parallels with total serialism, which emerged at Darmstadt in the 1950s. The intertwining of musical parameters such as duration and pitch creates opportunities for meaningful musical connections. It is the use of these connections that move them beyond arbitrary to meaningful expression, not the connection itself. I find the mapping very interesting, however it is valuable because it is so useful for the way that I like to make music.

When I began to incorporate digital art into my work, I began by applying my tuning to colors:

Region one color spectrum. Notice that each shape’s width is scaled to its corresponding ratio.

My approach is multimedia, which I achieve by applying my musical methods to the color spectrum, size and scale of shapes and at times speed of motion. This results in a tuned set of colors and corresponding geometric proportions, establishing a cohesive tuning system that I apply to pitch, rhythm, color, shape, and the speed of movement.

When it comes to just intonation tuning, I adopt Henry Cowell's approach to rhythms based on the harmonic series. Cowell commissioned an instrument, the Rhythmicon, created by Leon Theremin, to play these tuned rhythms. The instrument I've developed, known as the "Horn of Plenty," is a modern version of the Rhythmicon, programmed using SuperCollider and Processing.

My musical objectives center around using unequal temperament tuning and corresponding rhythms. I employ just intonation tuning to obtain these notes intentionally avoiding a system that creates an equal scale of quarter tones or third tones. I use ratios, and to establish a coherent rhythmic system, the denominators of the ratios in a particular region of my tuning must divide evenly. Currently, I use ratios up to 13-limit, which yields eight regions within an overall 53-note tuning system. Region 1, for example, has 6 as a common denominator:

Region 1

1/1 7/6 4/3 3/2 5/3 11/6 2/1

I find that using notes in small groups suffices for my music. There's no need for me to employ all 53 notes in a single piece; instead, I use them to create cycles of works with connections to explore.

This six-note tuning serves as both a scale of pitches and a set of proportions applied to rhythm and other elements of my work. The 1/1 is the fundamental, and this scale contains the two perfect intervals commonly known as the perfect fourth and fifth in Western equal temperament tuning (4/3 and 3/2, respectively). The 5/3 represents a well-tuned major sixth at 884 cents. Ratios from the three and five limits will sound familiar to Western ears and evoke a sense of precision often associated with modes in Western equal temperament. The 7/6 falls between a minor third and a major second at 266 cents, while the 11/6 represents a neutral seventh at 1049 cents.

In the realm of rhythm, each note has its own unique duration. I didn't set out to create a comprehensive musical system, but in addition to building upon Cowell's work that led to the Rhythmicon, I see parallels with total serialism, which emerged at Darmstadt in the 1950s. The 1/1 serves as the rhythmic fundamental, featuring six beats per measure. The 7/6, positioned between the major second and minor third at 266 cents, plays a polyrhythm of 7 against 6. The 4/3 will play eight notes in its fundamental state, but within a measure, it will produce four half notes rather than quarter notes.

One way to perceive this music is as a conscientious objection to Western European classical music. My initial intention wasn't an outright rejection of European music, but rather a need to move beyond its core tonality, which ceased to serve me artistically. By reducing its influence in my work, I experienced a sense of liberation, extending to my use of unevenly subdivided rhythms. However, this extends beyond musical theory. Shedding elements of a musical tradition also constitutes a rejection of that music's culture and values. The Western European classical music I refer to coincides with the colonial era that continues to influence our world. "Perpendiculous!!" isn't created with a piano and isn't necessarily tied to a concert format where the audience quietly observes. It offers potential for something different, and its lack of tradition continues to provide me with artistic freedom.

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