Neil P. McAngus Todd

A model of expressive timing in tonal music.

During a performance, a pianist has direct control over only two variables, duration and intensity (Seashore, 1938). Other factors such as pitch and timbre are determined largely by the composer and the mechanics of the instrument. Thus expressiveness imparted to a performance lies in the departures from metrical rigidity and constant intensity. In this article, the first of the two variables is considered and it is shown how a duration structure can be generated, corresponding to the rubato in a performance, from the musical structure. The main input to the model is the time-span reduction of Lerdahl and Jackendoff9s theory (1977, 1983). Also shown is an interesting analogy between this model and the algorithms of Grosjean, Grosjean, and Lane (1979). Thus the hypothesis that expression is largely determined by musical structure, and the formal parallel between time-span reduction and prosodic structure are given empirical support.

The dynamics of dynamics: A model of musical expression

A computational model of musical dynamics is proposed that complements an earlier model of expressive timing. The model, implemented in the artificial intelligence language LISP, is based on the observation that a musical phrase is often indicated by a crescendo/decrescendo shape. The functional form of this shape is derived by making two main assumptions. First, that musical dynamics and tempo are coupled, that is, ‘‘the faster the louder, the slower the softer.’’ This tempo/dynamics coupling, it is suggested, may be a characteristic of some classical and romantic styles perhaps exemplified by performances of Chopin. Second, that the tempo change is governed by analogy to physical movement. The allusion of musical expression to physical motion is further extended by the introduction of the concepts of energy and mass. The utility of the model, in addition to giving an insight into the nature of musical expression, is that it provides a basis for a method of performance style analysis.

The kinematics of musical expression

The notion that there is an intimate relationship between musical motion and physical movement is an old one and can be traced back to antiquity. Recently this idea has again received some attention, particularly in relation to musical expression. To use a modern metaphor, one can consider expressive performance to be analogous to the problems of kinematics and trajectory planning in robotics. The trajectories referred to, however, are not those of the performers limbs in physical space, but those of an abstract movement relative to a metrical grid associated with a musical score. Recent studies have attempted to substantiate this idea by comparing a model of motion with timing measurements of the final ritardandi from actual performances. This study extends these earlier analyses to include the accelerandi as well as the ritardandi from complete performances. One conclusion is that the variation of tempo in music can be reasonably compared with velocity in the equations of elementary mechanics. Further, ...

A computational model of rubato

Presented is a model of rubato, implemented in Lisp, in which expression is viewed as the mapping of musical structure into the variables of expression. The basic idea is that the performer uses “phrase final lengthening” as a device to reflect some internal representation of the phrase structure. The representation is based on Lardahl and Jackendoffs time-span reduction. The basic heuristic in the model is recursive involving look-ahead and planning at a number of levels. The planned phrasings are superposed beat by beat and the output from the program is a list of durations which could easily be adapted to be sent to a synthesiser given a suitable system.

Motion in Music: A Neurobiological Perspective

The topic of musical motion has generated a considerable amount of controversy in the past few years (P. Desain, H. Honing, H. van Thienen, & L. Windsor, 1998). In this essay it is argued that motion is central to our understanding of many aspects of music, particularly to our understanding of rhythm, and that an adequate account of motion in music requires a neurobiological perspective. Two possible mechanisms are discussed that may form a neurobiological basis for the association of motion in music: a vestibulomotor mechanism and an audio-visuo-motor mechanism. These two mechanisms in turn may mediate two distinct kinds of musical motion: gesture and locomotion.

A short latency vestibular evoked potential (VsEP) produced by bone-conducted acoustic stimulation

In this paper data are presented from an experiment which provides evidence for the existence of a short latency, acoustically evoked potential of probable vestibular origin. The experiment was conducted in two phases using bone-conducted acoustic stimulation. In the first phase subjects were stimulated with 6-ms, 500-Hz tone bursts in order to obtain the threshold V(T) for vestibular evoked myogenic potentials (VEMP). It was confirmed that the difference between bone-conducted auditory and acoustic vestibular thresholds was slightly over 30 dB. The estimated threshold was then used as a reference value in the second part of the experiment to stimulate subjects over a range of intensities from -6 to +18 dB (re: V(T)). Averaged EEG recordings were made with eight Ag/AgCl electrodes placed on the scalp at Fpz, F3, F4, F7, F8, Cz, T3, and T4 according to the 10-20 system. Below V(T) auditory midlatency responses (MLRs) were observed. Above V(T) two additional potentials appeared: a positivity at about 10 ms (P10) which was maximal at Cz, and a negativity at about 15 ms (N15) which was maximal at Fpz. Extrapolation of the growth functions for the P10 and N15 indicated a threshold close to V(T), consistent with a vestibular origin of these potentials. Given the low threshold of vestibular acoustic sensitivity it is possible that this mode may make a contribution to the detection of and affective responses to loud low frequency sounds. The evoked potentials may also have application as a noninvasive and nontraumatic test of vestibular projections to the cortex.

Vestibular evoked myogenic potentials evoked by brief interaural head acceleration: properties and possible origin

The vestibular system responds to head acceleration by producing compensatory reflexes in the eyes and postural muscles. In this study, we investigated the effect of brief interaural acceleration on the vestibular evoked myogenic potential (VEMP) in 10 normal subjects and 10 patients with bilateral (bVL) or unilateral vestibular loss (uVL). The stimuli were delivered with a handheld minishaker and tendon hammer over the mastoid and produced relatively pure interaural head acceleration with little rotation (mean peak acceleration: 0.14 g at 3.3 ms). VEMPs were recorded from the neck muscles and were characterized in normal subjects by a positive/negative potential ipsilateral to the stimulated side (peak latencies: 15.1 and 22.6 ms) and a positive response contralaterally (20.3 ms), which was sometimes preceded by a negativity (14.5 ms). These peaks were absent in patients with bVL, confirming their vestibular dependence. In the patients with uVL, medial acceleration of the intact ear produced bilateral responses, an initial positivity on the intact side, and a negativity on the affected side, whereas lateral acceleration produced only a late positivity on the intact side. As the acceleration was primarily in the horizontal plane, it is likely to have activated utricular receptors. Consistent with this, we found that VEMPs are very sensitive to the direction of head acceleration and have features consistent with the utriculocollic projections demonstrated in animals.

Towards a cognitive theory of expression: The performance and perception of rubato

Expression is examined from the viewpoint of communication theory and it is argued that a proper understanding of expression involves an integrated description of both performance and perception. A framework is developed in which to couch a general theory of expression. As an example, a number of algorithms, implemented in Lisp are described which model the performance and perception of rubato. The model is based on two factors: 1) the use of “phrase final lengthening” to signal a group boundary and 2) the ability of the listener to track a variable tempo. The study shows that rubato is a rich source of information for the listener and that any realistic music parser must take this into account. On the other hand any performance model must take into account the constraints of perception.

Estimated source intensity and active space of the American alligator (Alligator Mississippiensis) vocal display

In this article the results are reported of a study to measure the intensity of the vocal displays of a population of American alligators (Alligator mississippiensis). It was found that the dominant frequencies in air range between 20 and 250 Hz with a source sound pressure level (SPL) of 91-94 dB at 1 m. The active space for the air-borne component is defined by the background and was estimated to be in a range up to 159 m in the 125-200 Hz band. For the water-borne component the dominant frequency range was 20-100 Hz with a source SPL of 121-125 dB at 1 m. The active space in water is defined by hearing thresholds and was estimated to range up to 1.5 km in the 63-100 Hz band. In the lowest frequency bands, i.e., 16-50 Hz, the estimated active space for otolith detection of near-field particle motion in water ranged to 80 m, which compared significantly with far-field detection for these frequencies. It is suggested that alligator vocal communication may involve two distinct sensory mechanisms which may subserve the functions of scene analysis and reproduction, respectively.

Single trial detection of human vestibular evoked myogenic potentials is determined by signal-to-noise ratio

Vestibular reflexes in humans can be assessed by means of acoustically evoked responses of myogenic origin. For the vestibular-collic pathway this is termed the vestibular evoked myogenic potential (or VEMP) and for the vestibular-ocular pathway the ocular VEMP (or OVEMP). Usually VEMPs require an averaging process to obtain a clear response against the background myogenic activity, but depending on the combination of target reflex and stimulus mode, in some cases clear responses can be observed in single trials without averaging. We aimed to test whether this difference in detectability was simply related to signal-to-noise ratio (SNR), or a manifestation of some other difference in the reflex pathways. In four healthy subjects we recorded VEMPs and OVEMPs in response to 2-ms, 500-Hz sound pips and 10-ms, 100-Hz transmastoid vibrations at four intensity levels, and also determined thresholds. A plot of probability of detection P vs. SNR for all subjects and conditions fell onto a single sigmoid curve. When fitted by a logistic function after linearization a regression yielded an R(2) of 0.89 (n = 64, p < 0.001), with parameter estimates of mu = 2.9 and sigma = 2.0. Three patients with superior canal dehiscence, characterized by significantly lowered thresholds for sound-activated responses, exhibited a similar detection curve. We conclude that single trial detection of evoked myogenic potentials is a property mainly determined by SNR. Thus vestibular reflexes, differing in both their response magnitude and in their levels of myogenic activity by more than an order of magnitude, can be described by a single relationship when their magnitude is expressed relative to background activity, demonstrating the fundamental importance of the SNR.