Discrete Time 1-bit Music

This paper covers theoretical bases of 1-bit music composition. Boolean algebra is introduced as the foundation of 1-bit music. Several models of 1-bit sequences are presented: deterministic models in the form of phasors and Xenakis sieves, and stochastic models in the form of finite state machines.
Music composition patterns (sequential and parallel composition, 1-bit counterpoint, modulation, hierarchies) are also discussed.

Discrete Time 1-bit Music: foundation and models

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8 impulse generators + 4 MIDI player pianos

Premiered April 30, 2010 in Miller Theatre, New York.

Fonoptera: from Greek, fono “sound” + pteron “wing”, or “sounding insect”.

Fonoptera is a word that my good friend Gildardo Cruz-Rojas invented many years ago as we were brainstorming for a name for a music society. Because the piece follows along the lines of the Tepozchiquilichtli (metalic cidadas) etudes, I decided “Fonoptera” would be a great name for the piece.

The piece is for eight home made 1-bit instruments and four “deaf” MIDI pianos. The 1-bit instruments are build out of dot matrix printheads, wood, plastic caps and wire. All twelve instruments are controlled by a single computer or micro-controller.


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This is an analysis of Xenakis’s percussion piece Psappha. I focus on the statistical properties of the data and the derivation of finite state machines. Sieves are briefly discussed to introduce Xenakis’s composition method and serve as a point of reference and comparison for the stocastic machines derived.

Xenakis’ Psappha

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Descarte’s third maxim (code of morals)

My third maxim was to endeavor always to conquer myself rather than fortune, and change my desires rather than the order of the world, and in general, accustom myself to the persuasion that, except our own thoughts, there is nothing absolutely in our power; so that when we have done our best in things external to us, all wherein we fail of success is to be held, as regards us, absolutely impossible: and this single principle seemed to me sufficient to prevent me from desiring for the future anything which I could not obtain, and thus render me contented; for since our will naturally seeks those objects alone which the understanding represents as in some way possible of attainment, it is plain, that if we consider all external goods as equally beyond our power, we shall no more regret the absence of such goods as seem due to our birth, when deprived of them without any fault of ours, than our not possessing the kingdoms of China or Mexico, and thus making, so to speak, a virtue of necessity, we shall no more desire health in disease, or freedom in imprisonment, than we now do bodies incorruptible as diamonds, or the wings of birds to fly with. But I confess there is need of prolonged discipline and frequently repeated meditation to accustom the mind to view all objects in this light; and I believe that in this chiefly consisted the secret of the power of such philosophers as in former times were enabled to rise superior to the influence of fortune, and, amid suffering and poverty, enjoy a happiness which their gods might have envied. For, occupied incessantly with the consideration of the limits prescribed to their power by nature, they became so entirely convinced that nothing was at their disposal except their own thoughts, that this conviction was of itself sufficient to prevent their entertaining any desire of other objects; and over their thoughts they acquired a sway so absolute, that they had some ground on this account for esteeming themselves more rich and more powerful, more free and more happy, than other men who, whatever be the favors heaped on them by nature and fortune, if destitute of this philosophy, can never command the realization of all their desires.

Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences
Rene Descartes

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Octopus: an 8 channel electret microphone device to be used in the performance of “La espiral quebrada” [Mvltiplexor III], for spatially diffused solo flute.

I built the 8 channel power supply + preamp based on these schematics and it works pretty well for a home made device.

Pulpo mic

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Cuepatlahto and Lascaux: Two approaches to the formalized control of musical score

Cuepatlahto and Lascaux are two systems for the formalization and transcription of musical score. Developed independently, both systems implement a set of modules, classes and procedures written in the Python programming language as higher level wrappers around the LilyPond open source system for automated music engraving. In this article we discuss the background and motivations to our work, introduce the components and workflow of both systems, and provide examples of both systems operating on numeric “seed” input together with the musical score produced as output.

Cuepatlahto and Lascaux: Two approaches to the formalized control of musical score

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Hierarchical Music Structure Analysis, Modeling and Resynthesis

I approach the problem of inductive modeling of high level musical structures from a dynamical systems and signal processing perspective, focusing on motion per se independently of particular musical systems or styles. The point of departure is the construction of a state space that represents geometrically the motion characteristics of music. I address ways in which this state space can be modeled deterministically and ways in which it can be transformed to generate new musical structures.

Hierarchical Music Structure Analysis, Modeling and Resynthesis: A Dynamical Systems and Signal Processing Approach music-structure-modeling

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