When in time of great catastrophe, human lives become numbers to be logged and forgotten. Here we honor those numbers: one thousand, six hundred and thirty-six; seven thousand, two hundred and six; seven thousand, five hundred and seventeen; ten thousand, one hundred and twenty-eight; twenty-eight thousand, four hundred and seventy-six; thirty-one thousand, five hundred and thirty-seven; thirty-five thousand, one hundred and thirteen; forty-nine thousand, seven hundred and fifty-five; fifty-three thousand, eight hundred and thirty-five; sixty-four thousand, five hundred and eighty; sixty-six thousand and ninety-nine;  sixty-six thousand, eight hundred and eighty-seven; sixty-seven thousand, eight hundred and ninety-nine; seventy-one thousand, two hundred and seventy-one…

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Program notes

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Requiem embodies my idea of performers and audience as active co-creators of the artistic event. This idea has developed over the years and has now found an evolutionary path in the concept of musical spaces as networks, that has become the foundation of my artistic and music-theoretic research in the past few years.

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In Requiem, the term “performer” must be interpreted in the most open way possible. First and foremost, “performer(s)” are co-creators, they can be humans or machines engaged in the production of sound, music, movement, light, video, etc. The “score” is then music score or dance notation, projection mapping or live coding instructions… As such, performers might be musicians or dancers, video artists, autonomous systems, etc. but all must be capable of verbal communication. The nature of the performance is naturally very improvisatory.

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The version presented in the video above is just one of the potentially infinite realizations of this piece. The scores for Requiem are produced by a generative composition software written by myself, and the end result can be controlled by particular choices of the input parameters. This particular recording has been made with an ensemble of six musicians that in turn performed the voice and instrumental parts. Two small sections include also the participation of a larger ensemble (the audience). 

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Performance notes

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The score of Requiem consists of graphs made of an ensemble of boxes (nodes) connected by directional paths: the score is, in fact, a network. Each node contains specific information on what sort of gesture the performer should execute in that place in the performance. The paths provide the direction the performer should follow in the execution of the piece. There are two kinds of nodes: verbal (gray circles) and non-verbal (white rectangles):

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When performer(s) reach a nonverbal node (white rectangle) they should interpret the gesture with an execution in their idiomatic performance practice (sound, visual, movement, etc.). Each gesture of a given node should be executed for any arbitrary amount of time and in a somewhat obsessive manner. 

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When performer(s) reach a verbal node (gray circles) they should interpret the gesture in the recitation of a text comprised of an unspecified sequence of arbitrary integer numbers. Examples of performance practices might include whispers, murmurs, speech, shouts, cries, laughter, rap, singing, etc. The execution of the “verbal nodes” should be exclusively verbal and can be done in any language. Each performer should use their unique text.

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In the nodes, the gesture is always described using four gesture keywords: register, density, loudness and dimension.
Register. [high, middle, low] Whether the gesture belongs to a high, middle or low register – of clear interpretation for a sound production mechanism, it should be freely interpreted if other means of performance are used;
Density. [high, medium, low] Indicates the density at which the gesture(s) should be executed.  In a musical context, it would correspond to the speed of execution or the duration of the events. In other performance contexts it should be interpreted accordingly;
Loudness. [piano, mezzo, forte] How loud the gesture should be. Of direct significance in a sound context, it should be interpreted accordingly for other performance media;
Dimension. [internal, external] Of free interpretation for any performer. In an instrumental context It could indicate the means of sound production, the kind of sound produced, etc.
Given the values that each keyword can assume, there are only 54 unique gestures descriptions. 
 

Timing: the performance does not require synchronization of any sort. The performer(s) will have the choice of deciding how to begin (and from where) and end the piece and when to transition from one layer to the next (if more than one have been generated). 
 

Conductor: when a conductor is present, as in the present recording, their role is to guide the performers through the enactment of the score and suggest the ensemble performance strategy (how to start/end, identity sections, how to transition from different sections, etc.). It is imperative that the conductor communicates to the ensemble the dictionary of conducting moves and their meaning. Possible examples are: 
•    Play/pause (individual performer/group or full ensemble)
•    Go to next node (individual performer/group or full ensemble)
•    Global or group dynamics
•    Global or group tempo
The conductor is encouraged to direct as many rehearsals as possible (depending on the technical and expressive level of the ensemble), to produce a performance that is musically and esthetically coherent.

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Compositional design and score generation

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In Requiem, every aspect of the performance is defined by two key elements: a network of nodes with a specific connection topology, and the determination of the optimal path that visits every link connecting any node at least once.

The score and text are dynamically generated by executing python codes (see box below) that build the network(s) of nodes with complete freedom in the choice of the parameters of the performance (type of ensemble, duration, venue, range of performance practices represented, etc.). 

The network structure used here is generated using various models for the generation of random networks of various topological characteristics. The most common is the Barabasi-Albert model that incorporates two important general concepts, growth and preferential attachment: growth means that the number of nodes in the network increases over time; preferential attachment means that the more connected a node is, the more likely it is to receive new links. Nodes with a higher degree have a stronger ability to grab links added to the network. The resulting topology is fundamental in the analysis of many musical spaces. This topology is also central to the determination of the optimal path that guides the performer through the graph: we solve here a route optimization problem to find a shortest closed path or circuit that visits every edge of the graph we have generated. When the graph has a Eulerian circuit (a closed walk that covers every edge once), that circuit is an optimal solution. Otherwise, the optimization problem is to find the smallest number of graph edges to duplicate (or the subset of edges with the minimum possible total weight) so that the resulting multigraph does have a Eulerian circuit.