Autonomous Birdsong

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Experimental synthetic birdsong:

Musical automata as dynamical systems

David M. Michael

University of Sussex, Brighton [email protected],

http://www.hksintl.com/birdsong

Abstract. This paper is intended to form the basis for a dynamicalsystems approach to musical automata (or generative music systems).Because the songbird’s vocalization and neural mechanisms have beenso extensively studied, it makes an ideal model system. Presented herein

are control experiments and dynamical analysis of a nonlinear oscilla-tor model of the avian syrinx, which will serve as the actuator for theproposed musical automata.

1 Introduction

This paper is both a proposal and an initial experiment en route to a dy-namical systems approach to autonomously generated music. Currently affectingmany recent efforts in generative music is the structure/novelty problem, whichappears in any purely symbolic system [8]. To overcome this issue, it is pro-posed that a generative music system be based on situated, embodied dynamics,following similar moves in the disciplines that now contribute to a dynamical

systems framework for understanding life, cognition, and adaptive behaviour [3,5,12, 20].

In particular, this paper explores the songbird and its musical actuator, thesyrinx, as a possible agent template for this system concluding with an evaluationof how this research might be extended to realize an embodied physical agent.The songbird is an ideal model system on which to explore this approach togenerative music because the songbird’s vocalizations and neural mechanismsfor song learning and control are extraordinarily well studied, providing a wealthof data for our modeling efforts.

To begin creating a sensory-motor loop for generative music systems, effortswere concentrated on the modeling and dynamical analysis of the syrinx, whosestructural dynamics will both constrain and inform the production of musicalsonic forms. The labial masses responsible for sound production in the syrinx

are modeled using modified nonlinear oscillators after the work of Garner, Laje,Mindlin and colleagues [18, 22, 23]. In addition to the realistic reproduction of birdsong, the syrinx oscillator acts as an appropriate actuator for the proposedautonomous musician. Manipulation of the model’s parameters can affect rich,non-discrete sonic dynamics including a continuum of frequencies, rhythms, and


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Fig. 1. Advances in basket weaving . Phase dynamics of the syrinx oscillator showingstable limit cycles and point attactors.

tonal characteristics commonly associated with music such as portamento, vi-brato, and tonal stacks (chords). Any potential control system will need to beable to learn to control the dynamics of the oscillator, rather than predefinedmusical entities.

To control the syrinx oscillator parameters, simple sine waves are used asa stand-in for what will ultimately be output from an artificial neural networkcontroller. The oscillations are rough approximations of the neuromuscular ges-tures produced by the nucleus robustus archistriatalis (RA) which coordinatethe movements of syringeal muscles. In addition to mimicking the neuromuscu-lar dynamics of syrinx, it is with specific interest to the author that potentialcontrol systems possess dynamics which will explore the parameter space of thesyrinx oscillator model.

Before further description of the model and the experiments are discussed,we will look at the motivations for this project, which are rooted in a shareddesire for improved autonomous behaviour in generative music systems.

2 Toward musical automata as dynamical systems

A major issue afflicting current approaches to autonomous generative musicsystems has been identified as the “structure/novelty tradeoff” [31] whereby anincrease in the rules defining the generative process (and thus the musical struc-ture) results in decreased novelty of sonic output and ultimately to predictablepieces. Conversely, as the rules of musical structure are loosened (or specified


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by proxy1), the sonic novelty increases often at the detriment of musicality. Sowhile a pre-programmed, expert knowledge of music theory guarantees musi-cal results, it also guarantees that the system will not create anything novel orunexpected. In fact, it is acknowledged by many researchers that recent effortsin autonomously generated music are decidedly unmusical [31]. Miranda sumsthe shared malaise of this situation perfectly: “Can we possibly discover what isneeded to improve these systems?” [26].

The structure/novelty trade-off in generative music systems is indicative of a larger issue, one that was identified by W. Ross Ashby as Descartes dictum:“how can a designer build a device which outperforms the designer’s specifica-tions?” [8, 2]. As Ashby noted, in order to outperform its initial specification, adevice must be informationally open and capable of interacting with the worldindependently of its designer. The lesson of dynamics extends beyond only andevice’s interaction with its environment and into a device’s internal operationas well. Dynamics have been proposed to overcome limitations of the internal

use of symbols and pre-programmed representation which has been convincinglyargued are inadequate for the creation of adaptive novel behaviours in a sys-tem [7]. Traditional approaches to artificial intelligence (AI)2 seem to confirmthis limitation [6], leading researchers toward a more dynamic and embodiedapproach to the modeling of the properties of living systems.

Much of the work in autonomous generative music systems, past and present,has been based on AI techniques and in many ways can be seen as an extensionof the AI field in general. When generative music originally adopted the tech-niques of symbolic AI, it subsequently inherited the structure/novelty problem.Indeed, when asked in an interview if a body3 would be critical in an artificialcomposer of music, Marvin Minsky, co-founder of MITs AI Lab, responded bysaying, “I dont think that this will be important” [4]. So while researchers in thefields of adaptive behaviour, artificial life, and autonomous robotics (togethercharacterized as new AI) have looked to dynamics as a break-out strategy to ad-dress Descarte’s dictum - a strategy originally formulated by the cyberneticists,predating classical AI - research in autonomous generative music still overwhelm-ingly deals with closed, purely symbolic systems.

This is not to say that work in generative music has been practicing only clas-sical AI for the last twenty years. Indeed many researchers have incorporated theevolutionary [31] and agent-based approaches [10] associated with new AI, butthe systems still heavily rely on expert knowledge, such as the pre-programmingof musical notes and the symbolic manipulation of musical relationships. Fur-thermore, these systems are not connected to the environment and have no sense

1 This is the mapping of algorithm to musical phenomena [26]. It can also sometimesbe seen as the sonification of arbitrary algorithms.

2 Also characterized as classical AI, Good Old Fashioned AI (GOFAI), or symbolicAI, this approach to AI focused almost purely on symbolic systems, often with theintent that they would be connected to the world at some point in the future

3 Referring to the tenet of embodiment in new AI.


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of the world or their impact on it. In a way, it has missed the most importantpoint. Music, like all behaviour, is an embodied activity.

The work described herein builds on the conviction that embodiment (theability for a system to sense and act on the world) is a necessary considera-tion in the automation of the compositional process as well as the creation of autonomous artificial composers able to produce novel and appropriate musicalworks. From a dynamical and embodied perspective, autonomous adaptive mu-sic can be generated without the pre-specification of music theory. Furthermore,the musical behaviour is inherent in the dynamics of the brain-body system.Eventually, musical context (also important for musicality) can be learned byan embodied, situated musical automata through its interaction with the sonicenvironment.

Extending the credo of new AI, the first steps toward creating an artificialcomposer with human level proficiency may lie in the study of simpler qualita-tively examples of musical behaviour from the biological world. For this, the most

familiar and well studied of biological musicians has been chosen as a model; thesongbird. It is beyond the scope of this paper to build the entire device, ratherit is intended to provide an account of how musical structures can arise from thedynamics of the embodiment alone.

3 The songbird as autonomous instrument

This research on synthetic birdsong comes from a very long tradition. Asit turns out, the songbird has been the subject of automatic music4 for thou-sands of years. In addition to being the subject of self-playing hydro-mechanicalconstructions [33] and musical clockwork automata (such as Droz’s famous me-chanical singing birds), the songbird has also been used in the flesh, trained tosing popular tunes of the period, a practice known as “bird fancying” [1].

Bird fancying involves live songbirds, kept as captive musicians and trainedto sing modified tunes at the “delight” of human audiences. Interestingly, thepractice of bird fancying revealed some key insights into bird learning, songdevelopment and behaviour long before modern science was was to pry apart(literally) the neural and physiological mechanisms of the songbird [1].

In this historical context, we can view the efforts here as more closely resem-bling a bird fancying paradigm of musical automata than the purely computa-tional systems of generative music.

4 Birdsong structure and dynamics

What kind of music can we expect from an autonomous instrument modeledon the songbird? In this section, we examine the acoustical structure of natu-ral birdsong. Spectrographic analysis will show us what types of sounds naturalbirds can make and how these sounds are structured. This will ultimately leadus toward the best choice of models to serve as musical actuators in our system

4 Automatic music concerns the automatic playback of pre-specified tunes.


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Fig. 2. Spectrogram of the song of the White-crowned Sparrow (sound courtesy of theMacaulay Library of Natural Sounds).

as well as give us a foundation in which to compare our modeled results withthat of the biological phenomena.

4.1 Song structures

The structure of birdsong is quite diverse. The frequency range of songs istypically small, with fundamental frequencies in the range of 2 to 6 kHz. Struc-turally, the song can be divided into hierarchical levels consisting of elements or notes as elementary building units. Several elements are combined to make

up syllables which last from a few to a few hundred milliseconds. Syllables, inturn, are combined to form longer phrases which often repeat. Many phrases arecombined to form the song. Phrases and songs are often subject to individualand regional variation [9].

The structure of any synthetic reproduction of birdsong will necessarily bebased on the natural song hierarchy as it is assumed that the form of the birdand its vocal and neural mechanisms are selected for by evolution (most likelyby means of sexual selection [11, 27]) to be conducive to song in this form.

Though the reader is likely to be intimately familiar with the quality of manybird’s songs, for this paper, it will be helpful to quantify the spectral contentof the sounds in a way that will allow for systematic investigation of naturaland synthesized song. A look at the spectral content and structure of naturalbirdsong will show what can be expected sonically from a model.

The standard representation of spectral content is the spectrogram, as shownin Figure 2. By examining the spectrogram, one can see the syllables and phrasesof the song structure. It is also the spectrogram which can reveal many of thenonlinear dynamics as will be discussed.


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4.2 Nonlinear dynamics in birdsong

Typical song has been shown to have components which can be purely tonal,harmonic, inharmonic, and even contain complex and coupled amplitude andfrequency modulations. More specifically, spectrograms of birdsong contain the“fingerprints of nonlinear dynamics” [13]. Under spectrographic analysis, spe-cific nonlinear dynamical signatures can be observed such as frequency dou-blings or sudden jumps (as shown in Figure 2), transitions between harmonicand inharmonic frequency stacks and even deterministic chaos (which appear asspectrographic noise).

These dynamics are reproducible with a class of dynamical system callednonlinear oscillators. Nonlinear oscillators have been used frequently to modelbiological sound production and can roughly approximate the motion of themembranous structures found in the windpipe of vertebrates. In the songbird,the anatomical feature that contains these vibratory structures is the syrinx.

While filtering by the trachea and beak also play roles in sound quality, thesyrinx is responsible for much, if not all of the sound source.

5 The syrinx: anatomy and models

The quality and structure of vocalizations in the songbird are obviously inti-mately related to the physical and neural structures of the bird. Fortunately forour purposes, few in the animal kingdom have enjoyed as much intensive studyas the songbird. Many hundreds of studies have been carried out on localizingthe muscles, membranes and neural pathways which contribute to song produc-tion. For the current paper, we are most interested in the structures involved insound generation, the syrinx.

5.1 Syrinx physical anatomy

The avian vocal organ responsible for the physical production of sound is thesyrinx. Though there are a wide variety of syrinx morphologies, they all sharesome basic structures relevant to the production of sound.

The syrinx is located at the junction of the bronchi, projecting from the lungs,and the trachea. It is composed of cartilaginous and membranous structures aswell as a series of specialized muscles. The inaccessibility of the syrinx due to itssize and place in the bird have historically made studies difficult.

The classical model [17] attributes the sound production based on morpho-logical observations to vibrations in the syringeal medial tympaniform membrane

(MTM) in each bronchi which vibrate through the Bernoulli effect [14]. Recentlythough, direct endoscopic observations of the syrinx during sound production byGoller and Larsen [19], show that at least in those species studied, sound is gen-erated by connective tissues called the medial and lateral labia, located at thecranial end of each bronchus [30]. Surgical disruption of the MTM was not shown


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Fig. 3. The syrinx . The actual structure, removed and cleaned, reprinted from [15]

(left ). Major anatomical features, slightly modified and reprinted from [29] (right ).

to have significant effect of the sound produced by the syrinx.

5.2 Syrinx oscillator models

The experiments by Goller and Larsen [19], having convincingly shown thelabia as the sound source in the syrinx through direct videography and MTMdestruction, has inspired the development of oscillating models of bird soundproduction. Because of the evidence that syrinx labia function in a way which is

similar to the human vocal folds (also in [19]), one of the first oscillator models tobe produced by Fee et al. [16] was based on a classic two-mass model of humanvocal fold oscillation by Ishizaka and Flanigan (1972). This model was furthertaken up by Mergell et al. [24].

The strength in the Ishizaka and Flanigan based models is the ability toaccount for transitions to chaotic vibrations and period doubling as observed in vivo [16]. To its detriment is the model’s complexity. Not only are the equationsdescribing the system complex, this complexity translates into prohibitive com-putational and coding demands, making them impractical for use as phonator(sound source) in the proposed larger projects.

More recently, Gardner, Laje, Mindlin and collegues [18, 22, 23] have beendeveloping variants of a model originally introduced by Titze, thereby extendingtheir previous work on human vocal fold oscillations [21]. They claim the Titze

model is one of the simplest models to account for the transfer of kinetic energyto vocal fold oscillations. As simple as the Titze model is, Garner et al wereable to arrive at an even simpler equation for a nonlinear oscillator which canproduce the periodic dynamics observed in Canaries, and extended to Sparrows.With simple sweeps of two control parameters representing the stiffness of the


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oscillator and the bronchial pressure, they could mimic the song of the ChingoloSparrow (Zonotrichia Capensis ).

The strength of the Titze-based model is its utter simplicity which makesdynamical analysis, implementation, and integration into other systems easier.Unfortunately though, this model initially seems incapable of producing chaoticdynamics [23] without some further modification. Another drawback may be alack of biologically supportable parameter values, though this is not somethingof great concern for our current purposes. Though highly simplified, these basicmodels can provide insights into how a simplified system operates, and can becontrolled.

Body abstraction and sensory-motor simplification is central in the studyof adaptive behaviour of which this paper is a part, and can be seen in manyworks viewing the body as a state-dependent agent with simple actuators (suchas Beer’s minimally cognitive agents [5], among countless others). Similarly, theobject of actuation in our study is ultimately a nonlinear oscillator, based on

the songbird’s syrinx. By understanding the syrinx oscillator’s dynamics, we notonly get a picture of how our autonomous instrument will sound, but we arealso better prepared to analyze how a control system exploits these dynamics insound production.

6 Dynamics of the syrinx oscillator

6.1 Syrinx as nonlinear oscillator

The syrinx oscillator model chosen for these experiments is the one developedby Garner, Laje, Mindlin and colleagues which appears in [22], extended fromthe original model proposed in [18]. It was chosen on the basis of simplicity,controllability, and computational efficiency, as well as its ability to accurately

produce the sounds of songbirds.The syrinx oscillator is basically a second-order ordinary differential equation

(ODE) of the following form.

ẋ = y , (1)

ẏ = −kx − cx2y + by − f 0, (2)

where c is the linear dissipation constant representing density of the material,f 0 is the force of syringial muscle contraction, b is the bronchial air pressure,and k is the labial tension. A diagram of how these parameters relate to theidealized syrinx is shown in Figure 4. Parameters are not directly related to

specific muscles in the syrinx, but rather model the concerted efforts of themuscles in the region leading to phonation and its control.

It is interesting to note that Equations 1 and 2 are basically a slight pertur-bation of the van der Pol oscillator [22]. The syrinx oscillator and the van derPol oscillator are representative of a broad class of nonlinear dynamical systems,


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Fig. 4. The idealized syrinx . Shows the relation of parameters in the syrinx oscillator,reprinted from [22].

generally referred to as nonlinear oscillators. More specifically they are relax-ation oscillators.

6.2 Relaxation oscillators

Relaxation oscillators are dynamical systems which exhibit stable limit cy-cles and have been successfully used to model biological phenomena that haveself-sustained oscillations such as the heartbeat and neurons [28]. In fact, a largevariety of periodic biological phenomena can be characterized by relaxation os-cillations [32].

Limit cycles are isolated closed trajectories in the phase space (one variableplotted against another) of a nonlinear system. As Strogatz notes, “limit cyclesare inherently nonlinear phenomena” (p.196) and the amplitude and frequencyof the system are ultimately dependent upon initial conditions and the struc-ture of the system itself. Unlike linear oscillators where any disturbance to theamplitude will persist in the system forever, nonlinear oscillators are resistantto perturbations, returning to the preferred limit cycle for a given set of param-eters [28]. For a more exhaustive treatment, the reader is referred to [32] and [28].

6.3 Dynamics specific to the syrinx oscillator

The syrinx oscillator has dynamics which are curiously different from thestandard van der Pol, as much as its relaxation oscillation is mirrored. The b

term in the syrinx oscillator leads to a Hopf bifurcation [22] of the system atb = 0. For negative values of b, representing reverse in pressure and an inhalationby the bird, the phase space of the system moves towards a fixed point attractor .Practically, this means that there is a loss of oscillatory behavior, and an ultimateloss of phonation. As can be seen in Figure 5, the shape of the limit cycle toward


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Fig. 5. Dynamics of the syrinx oscillator . (left column ) Graph of y(t) for +b showingrelaxation oscillations and phase portrait of (x, y) for solutions to Equations 1 and 2

starting from (x, y) = (0.01, 0.01). (right column ) Graph of y(t) for−

b showing a moresinusoidal waveform leading to a point attractor for Equations 1 and 2 starting from(x, ẋ) = (0.01, 0.01).

the point attractor is also quite different, more resembling a pure sine wave. Thissinusoidal waveshape appears as b moves toward 0.

High values for f 0 and c also result in loss of phonation, but for differentquantitative reasons. If c is too high all kinetic energy is lost to the medium/labia,that is, the material is too dense. If f 0 is too high, the model labia are completelyclosed, limiting airflow and thus oscillation of the membrane.

The value k, which represents labial stiffness as caused by the musculature,effects the frequency of the oscillations. As expected, high values of k results inhigh frequency oscillations and visa versa.

In order to faithfully reproduce birdsong, all parameters b and k cannot beleft at a single setting and are best served as functions of time. The original workon the syrinx oscillator was able to reproduce many features of birdsong usingsmooth oscillatory sweeps of the control parameters b and k (and later f 0 forabrupt phonation control) using a pair of coupled oscillators tracing ellipses inb, k phase space. These periodic sweeps have since been experimentally verified[25], though they are not the result of coupled oscillators.

Studies have shown that the neuromuscular response of the syringeal mus-cles follow oscillatory trajectories in response to stimulation from RA projectionneurons [30]. For the proceeding simulations, simple uncoupled sine wave oscilla-

tors were used for the continuous control parameters (b, k) on the syrinx model,thereby approximating the actions of the RA. This method follows the workpresented in [23, 18]. An understanding of how the oscillatory dynamics of thesyringeal muscles influence the sound will be of great use in defining a controlsystem and its range of operation.


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Fig. 6. Bifurcation of the syrinx oscillator. This image modified from the original whichappears in (Laje et al. 2002) [22].

It should also be noted here, but will also be pointed out in the simulationresults, that the frequency of control parameter sweeps should be much lowerthan the frequency of oscillations induced in the system as a whole.

7 Synthetic birdsong: simulation methods and results

7.1 Experimental setup

For this paper, numerical integration, visualization, and sonification of the

syrinx oscillator was done in MATLAB software by MathWorks. Simulationsoften took as long as 3 minutes render time per second of audio produced.

Using the parameter values for b,k,c, and f 0 established in [22] it was diffi-cult if not impossible to get the appropriate responses from the system. Thesevalues were replaced with value ranges that produced appropriate results overmany trials. This discrepancy could have been due to the methods of integrationused (ode45() in MATLAB) as well as from the extraction of values from thesolutions that were necessary to reformat them to a form whose amplitude couldbe transferred to the audio range [-1 1], sampled at 44100 times per second,resulting in a 22.050 KHz signal.

Parameter values for the model that worked well were as follows: b in therange of [-1 8], k in the range [0 600] ( 10:1 b), c in the range [0 50] ( 5:1 b),f 0 in the range [0 40] ( 5:1 b). These values for the model make it irreconcil-

able with experimental data beyond the shape and behaviour of the vibratorymechanisms. For the experiments, both c and f 0 were kept at fixed values andparameters b and k were driven with sine waves as previously mentioned.


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Fig. 7. Natural and synthetic songs . Spectrogram of the song of the Rufous-sidedTowhee (top) and spectrogram of a synthesized birdsong (bottom ) where b is varied bya low frequency sine wave and k is varied using a combination of a sine driven, adaptive

van der Pol at t


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Fig. 8. Experimental synthetic birdsong . Syrinx models oscillations (top), spectrogramshowing the frequency content (middle ), and plot of unscaled control parameters forvariables k and b, using simple sine waves.

is necessary, this model was intially unable to produce period doubling, a featurecommonly observed in birdsong.

One additional consideration was left out of these experiments, and that isthe low pass filtering effects of the trachea and beak. In other experiments mod-eling birdsong, great lengths have been taken to make mathematical tube modelsof the trachea and beak resulting in much more natural sounding synthetic song.

However, for the purposes of our applications as described previously, this shouldnot be an issue. Instantiation of this model as sound generator in physical bodywill allow for a trachea and beak that require not math, that is, a real tube canaffixed to filter the sound output from the model.


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Fig. 9. Close-up of syrinx oscillator x, y phase dynamics in Figure 1 with time plottedon the vertical axis.

8 Conclusions and future research

The syrinx oscillator seems to be quite capable of providing a basis for theproduction of musical material. Through the manipulation of parameters in this

simple dynamical system, we were able to experimentally synthesize many of thecomponents of musical sound. The bifurcation of the system at b = 0 results inthe generation of rhythm as well as having an affect on the timbre of the sound.Sweeping of the k parameter allows for access to frequencies in a sufficient rangefor varied melodic content. The results of the present experiment suggest thatthis model can provide a rich canvas to work with en route to musical automata.Moreover, these experiments suggest that the dynamics of a system can indeedgive rise to potentially musical material without musical specifications per se.

The relative ease and success of the present implementation and analysisowes much to the numerous obsessive studies and simulations of the avian vocalorgan, as well as to the birds “sacrificed” [19] in order to recreate them. Thoughthe models can effectively imitate simple song phrases, they still seem a far cryfrom the complex structures found in species such as Luscinia Megarhynchos (the

Nightengale), though it is assumed that the structures are a neural phenomenaand do not require a drastic rework of the physical model.

Now that the body of the proposed musical automata has been chosen, asuitable neural controller can be investigated. Fortunately, there is a wealthof information concerning the neural mechanisms and pathways involved in the


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control and production of birdsong. In fact, the learning of songs and mechanismsof vocalization in humans and songbird share some striking parallels. As withhuman speech, songbirds must learn their songs from tutors. This convergentevolution has made the oscine an extraordinarily well studied order of birds,much of it centered around illuminating possible mechanisms of human speechacquisition and learning.

Combining what is known about the behavioural neurobiology of birdsongwith techniques of simulated learning and artificial neural networks, the prospectsfor a complete model seem encouraging. Future research aims to combine whatis known of songbird neural architectures with the model syrinx to produce adevice that is able to sense and respond to the world, hopefully outperforming itsdesigner’s specifications (which should be little more than the dynamic structureof the system).

For many researchers, songbird vocalization and learning models allow for thetesting of hypotheses concerning how birdsongs are learned and produced, based

on experimental evidence with living specimens. To the author, birdsong modelsrepresent an opportunity to explore new possibilities of autonomously generated,adaptive music using these models as self-playing instruments, in much the sameway that eighteenth century bird fancyers used living birds but whose physicalrealization is wholly non-organic and more akin to clockwork musical automata.

Acknowledgments

This paper is dedicated to Marilyn Anne Losco Michael. Thanks to SarahAngliss for her research and turning me on to the The Bird Fancyer’s Delight, Al-ice Eldridge for discussions on nonlinear oscillators, the nightengales in Sheffieldand the Royal Pavilion in Brighton, Dr. Max Michael III, Fernando Almeida eCosta and Eduardo Izquierdo-Torres who organized the activaite.d workshop,and finally thanks to two anonymous reviewers for the helpful comments andreferences.

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