This improvisational piece is mainly inspired by Terry Riley's In C.

This piece is based on the dynamical system Brusselator. For more details see Brushed Brusselators - Construction Principles.

The fundamental core of this piece is a ladder of thirteen notes. The distance between the notes is a semitone lower at each step upwards. This is “orbit 0”. From this, 25 further orbits are formed according to certain rules. 20 orbits were used. These orbits appear as (arpeggiated) chords in all sections except section D. The order of the orbits was chosen such that two consecutive orbits have the same starting or ending point. In sections E-G, the order of the orbits in sections A-C is reversed. In section D, all permutations of all combinations of three points of orbit 16 are played.

This piece is also based on the concept of the self-similar melody by Tom Johnson. There is a theme as a self-similar melody with abstract notes that are realized acoustically in different ways (variations). For more details see wistful wisdom - Construction Principles.

A dynamical system (again the Frenkel-Kontorova Model with five particles) reacts to the sounds of the viola. And the viola reacts to the resulting sound of the dynamical system. The dynamical system has saddle-node bifurcations. These are the tipping points ("Kipppunkte" in german) where it tips and produces acoustic outbursts.

These pieces are based on the idea of self-similar melody by Tom Johnson. For details see Erläuterungen zu Selbstähnlichen Sequenzen.

This piece is about permutations of note lengths and intervals as well as combinations of articulations. All permutations and combinations are played in a sequence so that changes only occur in small steps. Various mathematical algorithms and concepts such as the Hilbert curve are used for this purpose. For more details see weird weaving - Principles of Construction.

This piece is based on the sequence of digit sums to base 2 of the integers from 0 to 2ⁿ-1 with n from 0 to 9. This leads to the ten equal-length sections of the composition separated by general pauses. In each section, the previous section is repeated. In addition, the notes for the new section n are added. The length of the notes added is smaller by a factor of two each time, so that the total length remains the same despite the doubling of the number of notes. The digit sum determines the pitch as an index in an ascending sequence, which is constructed in such a way that the intervals of two successive notes decrease by a semitone each time. The initial tone, which therefore belongs to the digit sum 0, is one semitone lower for n than for n-1. This guarantees that there are no common tones of the series for different n. In the diagram above, different colors are assigned to the different n: Red for n=0, Orange for n=1, etc.

This work is a variation of the famous I Am Sitting in a Room by Alvin Lucier. I was sitting on a chair in an almost cubic room (3.3m x 3.3m x 2.6m) with smooth walls, floor and ceiling and two large windows on one side. There wasn't much in the room to muffle the sound. I sat on the opposite side of the windows with my computer on my lap. There was a Bluetooth speaker on the window sill. I sang "I am singing in a room" with lots of glissandi to sample many resonant frequencies of the room. I recorded my singing with my computer's built-in microphone. I saved the recording and played it through the speaker. At the same time, I made the second recording. I repeated this several times. In the end, I had 13 recordings. Each was 27-28 seconds long. Finally, I stitched them together and saved the audio signal in reverse time order.

This very simple algorithmic piece is based on the sequence of digit sums to base 3 of the integers from 0 (Graphical representation

×

Digit sums to base 3 of integers from 0 to 3^6-1=728

). This sequence determines the pitch of all three voices. The duration of each note is fixed: 1/4 for the lowest voice, 1/8 for the middle, and 1/16 for the highest. Together with a relatively fast tempo, this is responsible for the "frantic" feeling. This is further enhanced by the rising tendency of the melodic lines. When the pitch is higher than Eb in the bass voice, note durations are augmented in all voices. Doubled at E, quadrupled at F, etc. This logic has the effect of interrupting the rush. The interruptions become more frequent and longer toward the end of the piece. The piece calms down by the end due to the slowing down by a factor of 16.

The piece has five movements. Each movement has a special character. In some movements special playing techniques for the euphonium are required (1st movement: multiphonics by singing, 4th movement: quarter tones). Prime numbers are used for almost all aspects of the composition. The 4th movement is based on examples that fulfill Goldbach's conjecture (any even number greater than two is the sum of two prime numbers).

The basis of this piece is the following Lindenmayer system: A ⇒ A B, B ⇒ B C, C ⇒ A with the start A. The words generated by this rule determine many aspects of the composition, from phrasing and motives to the overall structure.

The Norwegian title could be translated as "triad progression crowding". Only major, minor triads and augmented triads occur. The progression is generated by layering six polyrhythmic Thue-Morse sequences. The additional notes form a tritone or fifth (upper voice) or fourth (lower voice) with the lowest voice of the triads. Except for a few manual octavatings, all notes are calculated.

The Norwegian title means "simultaneous probability". The whole piece is determined by a few rules involving the Thue-Morse sequence.

The string orchestra plays a sequence of hexachords characterized by the fact that none of the fifteen intervals occurs more than once. Octaves also do not occur. Two consecutive hexachords have five notes in common. The string quartet (the four solo instruments) completes these hexachords in such a way that the rule of unique intervals is observed. The string quartet is the "restless" ("ruhelos") part, and the string orchestra is the "resting" ("ruhend") part. The piece is divided into sixteen sections (of different characters). The length of the sections is determined by the golden ratio in a hierarchically organized segmentation.

This music is based on a simple, spatial one-dimensional mechanical model (Frenkel-Kontorova Model) which I studied as a theoretical physicist in the early 1990s. The motion of the mass points in this model are translated into tones. Each mass point determines the pitch and volume of a sinusoidal oscillator according to a set of parameters. The Frenkel-Kontorova model shows "avalanches" of various strengths. Acoustically, this results in "sound avalanches" of various lengths and volumes. When one avalanche has decayed, the values of the parameter set change, so that the next avalanche has a completely different sound. The sound installation should be presented in a dimly lit, ideally cuboid room with eight loudspeakers and ideally a subwoofer. All this is described in detail in quivering quicksand - principles of construction. In addition, an ultrasonic distance sensor can be placed anywhere in the room at a height of around three metres. If this measures a distance below a threshold, a change in the sound parameters is also triggered.

In the two examples above, which last about half an hour, the Frenkel-Kontorva model was solved with the same initial conditions. The same ten avalanches were generated. The difference in the examples is caused by different sound parameters. This can be clearly seen in the spectrograms. For these examples, the sound of the eight loudspeakers was reduced to two channels using Spat.

The factorization of all numbers from 1 to 2021 into prime numbers is realized musically. The version for piano and the electronic version differ a bit in the realization. In both versions prime numbers are always the lowest note. This piece is inspired by the piece "Eratosthenes Sieve" of Tom Johnson.

Various sounds are created with a sheet of paper. Finally, a pinwheel is made. The nine different recordings (improvisationally follow a score) are combined in a canon-like manner.

This piece is an exploration of "Heimat" and "Fremde". The words of the text are from Goethe's "Wahlverwandschaften" and the musical material from Schubert's song "Fremd bin ich eingezogen" (first song of "Winterreise"). I imagine this piece being played by street musicians on a lonely, windy corner in a city.

Flute, saxophone, violin, cello and piano meet in all possible combinations. Each instrument plays in a different scale (Messiaen modes). This often leads to strong friction. The percussion comments with noises and beats. An intense conversation ensues. Pauses briefly interrupt the conversation. Afterwards, the conversation takes a new turn.

Comparing the most compact 11-note chord, which neither contains an octave nor contains an interval more than once, and instrumental noises.

Short solo piece on the overtone series of F2.

A chord of eleven notes in which all intervals occur only once and which lacks octave intervals. All 2047 combinations of these tones are played in an extremely slow tempo. The sequence of combinations is determined by a balanced Gray code. The second version is the same sequence of combinations, but it begins and ends with the whole chord. This piece is similar to Tom Johnson's "Chord Catalogue."

Ten movement work. Each movement tries to implement the geometric Moiré effect musically/acoustically.

A study of continuous versus discrete change of the basic musical dimensions rhythm, pitch and sound. The complete score is calculated based on mathematical rules.

64 miniatures of the same length over the resonating overtones of the silently pressed piano keys of the notes C1, B2 and F3.

This piece is a kind of "tonal" version of "Irisierendes Irrlicht". All tones are from the C major scale. There are only three instead of five motives. The piece begins and ends with a C major chord.

My idea for this piece was this: An instrument plays a tone (within certain limits). The player of the other instrument has to hit this tone with a given interval (half or quarter tone higher or lower). The score is graphical and shows the approximate pitches and timing. Each of the five sheets of the score lasts about one minute.

Five quarter-tone motifs, each consisting of two intervals (one ascending and one descending), form the basis of the entire composition. These motifs are played one after the other. The Thue-Morse sequence decides whether a motif is repeated or not.

The idea behind this piece is that all instruments play a G. They are trapped in this G. There are several attempts to break out of this prison. At the end the escape succeeds and the piece ends in the major third F A. The piece is also suitable as a pure string orchestra.

This piece is based on a theme of sixteen bars generated by some simple rules. The well-known transformations of retrograde, inversion and augmentation generate all the notes of the piece. Everything is played in a long crescendo that extends over the entire piece.

This piece consists of 1440 almost one-minute piano pieces. When a new minute begins, one of seven different pieces of varying character is played. The sequence repeats cyclically. Each of these seven pieces is parameterized by the current minute of the day. In two pieces of the seven pieces it is possible to figure out the time of day, because five different tones or motifs are repeated. The number of repetitions is given either by the quarter of the day, the hour of a quarter, the quarter of an hour, the five minute unit of a quarter of an hour, or the minute of a five minute unit.