Discrete Time 1-bit Music: foundations and models (PDF)
This paper covers the 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 discussed within the context of 1-bit music. The paper concludes with a brief description of a series of pieces created with the models and tools presented.
Hierarchical music structure analysis, modeling and resynthesis : a dynamical systems and signal processing approach(PDF)
The problem of creating generative music systems has been approached in different ways, each guided by different goals, aesthetics, beliefs and biases. These generative systems can be divided into two categories: the first is an ad hoc definition of the generative algorithms, the second is based on the idea of modeling and generalizing from preexistent music for the subsequent generation of new pieces. Most inductive models developed in the past have been probabilistic, while the majority of the deductive approaches have been rule based, some of them with very strong assumptions about music. In addition, almost all models have been discrete, most probably influenced by the discrete nature of traditional music notation.
We 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. We address ways in which this state space can be modeled deterministically, as well as ways in which it can be transformed to generate new musical structures. Thus, in contrast to previous approaches to inductive music structure modeling, our models are continuous and mainly deterministic.
We also address the problem of extracting a hierarchical representation of music from the state space and how a hierarchical decomposition can become a second source of generalization.
Xenakis’ Psappha (PDF)
My desire to carefully analyze Psappha stemmed from my interest in discrete-time 1-bit music. In this music there are only two “words” in the musical alphabet. i.e., at any given time-point we can find one of two events:
0or1. Thus, the set of all possible events available at any given time-point can be represented with just one bit. In addition, two time-points (and thus two events) can not be arbitrarily close to each other. i.e., there is a minimum time interval between events.
This smallest time interval is called the tatum (time atom) and all time intervals are integer multiples of it. The musical thinking behind Psappha is very close to this world. The elements on the page (here called strokes) have no duration. At any given time-point, there either is a stroke or not.
Abjad: An Open-Source Software System For Formalized Score Control (PDF)
The Abjad API for Formalized Score Control extends the Python programming language with an open-source, object-oriented model of common-practice music notation that enables composers to build scores through the aggregation of elemental notation objects. A summary of widely used notation systems’ intended uses motivates a discussion of system design priorities via examples of system use.
Aristoxeno: del punto, a la línea, a la dynamis (PDF)
Aristoxeno es considerado uno de los teóricos de la música más importantes e influyentes de la antigüedad. Los dos aspectos del Elementa harmonica que han sido más discutidos y analizados son su concepción aristotélica de la ciencia de la armonía y su representación del espacio de alturas, el cual parece implicar un temperamento igual. Existen, sin embargo, otros aspectos del tratado que merecen más atención. En este texto analizamos los conceptos de genus y dynamis y sus implicaciones para las nociones musicales básicas de nota y escala, de las cuales derivamos definiciones generales. Como prueba de concepto concluimos con un breve análisis musical que pone en práctica dichas definiciones.
La transformación continua de la forma de onda por medio del potencial combinatorio de sus intervalos de tiempo. (PDF)
MúSIIC-Win 3.2 (MÚSICA, SISTEMA INTERACTIVO DE INVESTIGACIÓN - CREACIÓN, versión Windows) permite investigar el potencial combinatorio de materiales musicales de orden discontinuo: intervalos de altura y deduración que pueden ser expresados bajo la forma de melodías, armon ías o ritmos. El módulo “forma de onda” genera pulsos a intervalos de tiempo definidos con números enteros para simplificar la combinatoria entre intervalos que sirven para segmentar la forma de onda. Esta última es tratada aquí como una “identidad de intervalos” de tiempo expresada bajo la forma de una serie de números enteros ordenados del menor al mayor. Por ejemplo: dada una identidad de intervalos, el conjunto de los mismos es permutado de acuerdo a un método que los ordena de acuerdo a sus relacionesde mínima distancia, “d1”, lo cual genera un permutaedro que representa el potencial combinatorio de cada identidad deintervalos. Este método constituye un nuevo modelo de transformación combinatoria continua de la forma de onda, asunto de interés en acústica. Un aspecto adicional de interés de dicha metodología es el enlace que establece entre lo melódico, lo armónico, lo rítmico y lo timbrico, universos cuya conexión estructural es a su vez un tema novedoso para la teoría musical.