The composition process began with the drawing of a "shape," the first of the four shapes illustrated here (the "original".) The remaining shapes are derived from the original shape. The second shape is the "inverse" of the first (original, flipped upside down.) The third is the "retrograde" of the first (original, flipped backwards.) The fourth and final shape is "retrograde of the inverse," also called the "cancrizan" (original, flipped backwards and upside-down.)

These shapes are used as "control signals" in the composition. Control signals are simply numerical values that vary, sometimes slowly, sometimes rapidly, over the course of the composition. In shape01 the control signals are used to determine the rate at which tones occur, the durations and amplitudes of the tones, and the pitch of the tones.

Csound, according to computer code written by the composer, generates these tones, sometimes hundreds of overlapping tones per second. (This form of sound creation is called "granular synthesis.") The overlapping tones combine to create the ultimate sound. Since the rate of tone creation, the duration of each tone, the amplitude of each tone and the pitch of each tone are changing according to one or another of the four control signals, they don't all change together. Therefore the resulting sound is constantly evolving.

shape01 is characterized by long glissandi, which are dictated by the slanting lines in the shapes. In this piece, and most others from this period, dissonances often resolve into consonances.

While shape01 was constrained to use only four shapes as control signals, shape02 uses additional shapes, obtained by combining the original signals. The "original", "inverse", "retrograde" and "cancrizan" signals look like this:



Some of the shapes obtained by combinations are "original+retrograde", "inverse+cancrizan", "retrograde+original", and "cancrizan+inverse", to name just a few:



The use of more than just the four basic shapes made it easier to create more variety.

shape02 contains much more "static" than shape01, and no clear consonances. The emphasis is more on rhythm.

shape03, like shape02, uses the four "standard" signals as well as signals derived from them. Here are the "standard" signals (original, inverse, retrograde, cancrizan):



shape03 exploits a mixture of rhythmic events and unisons.

shape04 uses a variety of shapes to control the musical elements (note density in time, pitch, duration, amplitude, etc.). The piece has an arch-shape, starting with very slow low notes, building to rapidly occurring high pitches, then moving back to the slow, low sounds of the beginning. As with many other shapes, there is an interplay between dissonance and consonance.

shape05 uses one of several of its shapes to determine how closely each note's pitch comes to one of the tones in a dominant-seventh chord. When the notes stray from the tones in the dominant-seventh chord, dissonance results. As the pitches approach the chord, the consonance emerges more and more clearly.

shape06 is built around a conventional chord sequence. Each note played may include rapidly played ornaments (trills, mordants, turns and more complex ornaments.) The shapes in this composition determine how closely the pitch of notes approaches the pitches of the notes in the chord sequence. Other shapes determine the nature of the ornaments (how many notes, how rapidly played, etc.)

shape07 combines musical ideas used in shape04 and shape06: low notes to high notes to low notes (two cycles); proximity/distance of pitches to consonant chords, and the generation of ornaments.

shape08 further exploits the interplay of dissonance and consonance used in previous pieces. The sound source is created by the Csound opcode "pluck", which produces a wide range of pluck-like sounds.

shape09 again exploits the interplay of dissonance and consonance.

shape10 again exploits the interplay of dissonance and consonance. This piece uses ornaments similarly to some previous pieces. The control signals, again produced by various shapes, control the proximity/distance to consonance, the speed and complexity of the ornaments, and many other factors in the piece.

This piece consists of the mixing of several "soundbites", that is, several short segments of sound. The soundbites are of durations varying from about 3-tenths of a second to 20 seconds. Each of the soundbites consists of a superposition of several tones (generated by Csound.). The characteristics of each tone (frequency, amplitude, etc.) were determined at random by use of a spreadsheet's "RANDOM" function. The piece begins with the longer soundbites, progresses to the shortest soundbites, and then ends with longer soundbites.

This piece was composed for the Bohlen-Pierce Symposium held in Boston, March 2010. "Bohlen-Pierce" is the name of a microtonal scale system of special interest to some music theorists and composers. Homage To Cage uses the Bohlen-Pierce scale throughout. The structure of the piece was suggested by (but is not identical to) techniques developed by John Cage in the period when Cage was first exploring the use of random methods for composition; in particular, Cage's method of composing Music Of Changes.

First, a "source sound file" was created. This sound file includes a range of sounds produced by Lou Cohen's Csound improvisation project. The file simply contains one type of synthesized sound after another with no particular musical intention.

Next, a spreadsheet was created, using the RANDOM function, to determine (randomly) the number of sections in the composition, the length of each section, the number of sound-events, the length of each sound-event, and the portion of the source sound file from which to select each sound. Finally, the sounds selected this way were manually cut-and-pasted from the source sound file into the final composition.

The methods developed for this piece became the basis for all the Symphonies.

This piece explores the interplay of "soloist" and "orchestra" which characterizes most concertos. Because the solo instrument (such as a violin or piano) is generally much quieter than the accompanying orchestra, the composer must carefully arrange things so that the soloist's sound is not drowned out. In this piece the "solo" instrument is a combination of toy piano, clavichord and marimba samples. The "orchestra" sounds include horn, strings, baritone saxophone, bass clarinet, and tenor recorder.

Circles is one of Cohen's earliest electronic pieces, written in 2004. Various circles are described mathematically by equations in a multi-dimensional space. The dimensions represent musical elements, such as duration, amplitude, amplitude-envelope, pitch, number of simultaneous notes, and other aspects of each note.

As the path of a circle is traversed over time, the circle is traversed through space. Therefore these characteristics vary, hence the sound of the music varies. The path, in time, of each circle through space results in an audio track of sound. The equations have been set up in such a way that the circles travel through the sound-space on different paths, but are designed to come in contact with each other somewhere (and at some time) during the composition. The effect is that the sounds of the tracks are identical when the circles are in contact, but then diverge as the paths of the circles diverge. The sounds then converge again as the paths of the circles once again approach the contact points.

All the Symphonies use the same basic technique, which was first used in Homage To Cage: one or several "source sound" files was created, and then short sound sections were cut from the source files and pasted into the final composition. While the cut/paste process in Homage To Cage was performed manually, it was performed automatically in the Symphonies, by appropriate programming of Csound.

The source audio file for Symphony 1 uses synthesized sounds produced by Lou Cohen's mouse/keyboard improvisational Csound project. The piece has 24 sections; the length of each section was chosen by a random number generator. Also determined at random are the number of sound events (each taken from the source file) in each section, the durations of the events, the section of the source file from which the sounds are selected, and within each source section, the starting position of each selected sound event. The sound events are generally long enough so that hints of the original improvisation can be heard.

The source file for this piece was created by the composer improvising with his wiimote/laptop Csound project. A 56 minute source file was produced. The Symphony has 13 sections. The first section of the Symphony uses sounds from a single section of the source file. The second section uses sounds from two different sections of the source file. Each subsequent section of the symphony uses sounds from more distinct source file sections until section 7 of the Symphony. From section 8 on, the number of source file sections used is reduced until the thirteenth and final section, which once again uses only one section from the source file. As with Symphony 1, the duration of each section, the exact location and duration of each source sound event, and exact positioning of each "paste" operation was left to chance (by using a spreadsheet program's random number generator.)

The source material for Symphony 3 is taken from improvisations with Lou Cohen's wiimote/laptop project. The Symphony's structure is suggested by classical forms often found in traditional symphonies. There are 4 sections to the piece, played without pause: Introduction; Theme and Variations; Scherzo; Finale.

The source material for Symphony 4 consists of "Factory Sounds" - sounds built-in to Apple's Digital Audio Workstation Logic. The selected sounds are primarily percussion and hip-hop sounds, activated by MIDI. The composer improvised at a MIDI keyboard to create the final source audio file. The piece consists of 27 sections, each somewhat longer than 26 seconds in length. The 27 sections are divided into 3 subsections with a general A-B-A structure. Each of the subsections is in turn divided into 3 sub-subsections, each of which displays an a-b-a substructure.

Source audio material for Symphony 5 consists of samples of acoustic instruments: flute, oboe, bass clarinet, contrabassoon, horn, trumpet, tuba, viola, violin, cello, double bass and piano. These samples were activated by the composer improvising at a MIDI keyboard. The piece consists of 45 sections each 17.5 seconds long, and a final 46th section of 10 seconds. Each of the sections employs a different combination of the source instrument sounds. The combinations were determined with the help of Orthogonal Arrays (OAs.) For more about OAs, see Method of composition.

The source material for Symphony 6 consists of samples of acoustic instruments: flute, violin, viola, cello, double bass. The samples were activated by the composer improvising at a MIDI keyboard, thereby creating the source audio file. The piece consists of 36 sections, each 16.67 seconds in length. Various combinations of source sounds were selected from each section by the use of Orthogonal Arrays.

The source material for Symphony 7 is derived from synthesized sounds devised by the composer (using Csound.) These sounds were placed in a soft-sampler so that they could be activated by the composer's improvisations at a MIDI keyboard. The piece consists of 9 pairs of sections, each pair 48 seconds long.

The source material for Symphony 8 is derived from direct recordings of the composer's Steinway piano, played normally and also played by plucking and scraping the piano strings. Among other sounds, very long piano tones were recorded. These were sometimes played back with the initial attack of the note omitted, so that the sounds resemble bowed, rather than hammered or plucked strings. The composer improvised directly at the piano keyboard to create portions of the source audio file. The various types of improvisation and other piano sounds were divided into categories which were selected from different sections by means of an Orthogonal Array. There are 18 sections of 20 seconds each. There are also generally two layers of sound, one consisting of the "bowed" sounds; the other of all other recorded sounds.

The source material for Symphony 9 comes from a range of synthesized sounds readily available in Apple Computer's Digital Audio Workstation Logic and also variations on those readily available sounds. There are 13 sections of 30 seconds each. Random processes were used to determine which source sounds were used in each section.