Bernice Laden

Correlation dimension of woodwind multiphonic tones

A multiphonic is a regime of oscillation of woodwind musical instruments that is perceived as two or more simultaneously sounding pitches. The frequencies fl,m of the line spectral components of a measured woodwind multiphonic tone fit a biperiodic spectrum at low- to mid-playing levels. For the saxophone and clarinet multiphonics investigated, the two basis frequencies of the biperiodic spectrum are phase locked, that is, their ratio is equal to a ratio of small integers. A broadband spectrum is present in multiphonic spectra that exceeds instrumentation noise and window leakage associated with signal processing. The correlation dimension D of P. Grassberger and I. Procaccia [Physica D 9, 189-208 (1983)] is measured by embedding a single measured time series in higher-dimensional space, so as to reconstruct the phase space of the dynamical system. The time delay used in the dimensional reconstruction is chosen using information theory. For the particular multiphonics analyzed, the correlation dimension ranges from 2.5 to 2.9 for the saxophone and from 1.3 to 2.2 for the clarinet. One clarinet multiphonic shows possible additional dynamical complexity at small length scales in the embedding space, with a correlation dimension of 3.3. These results give quantitative evidence that some, but not all, multiphonic tones possess a strange attractor.

Chaotic Dynamics of Otoacoustic Emissions

The discovery of otoacoustic emissions (OAE) has encourage? a re-asessment of active mechanisms in hearing. Nonlinear oscillators are attractive candidates for understanding active processes in hearing, and otoacoustic emissions in particular. Even the simplest nonlinear oscillators used in current theories shww hmlt cycle behavior but they are also capable of more complex, chaotic, behavior. For example, the forced van der Pol oscillator utilized in models of hearing (Duifhuis et al., 1986; Tubis et al., 1988) is also known to exhibit chaotic behavior. It is unknown whether OAEs actually exhibit chaotic behavior.

The Coordination of Compensatory Tracking and Anticipatory Timing Tasks.

Abstract Two experiments investigated the presence of a coordination factor in a task consisting of compensatory tracking and anticipatory timing components. The task (Intercept task) resembles a computer game in which a rocket must be aimed and fired to shoot an incoming missile. The studies were designed to determine if a coordinating ability exists above and beyond the abilities needed to perform the component tasks alone. We also investigated the nature of coordination abilities through correlations with other types of coordination tasks and measures of intelligence. Is coordination a general cognitive ability that contributes to performance in a wide range of coordination tasks, or is coordination ability task specific? Multiple regression analyses indicated the existence of a coordination ability in the Intercept task. This coordination ability, however, was shown to be unrelated to the coordination of visual and linguistic processing and to psychometric measures of intelligence as assessed by the Armed Services Vocational Aptitude Battery (ASVAB). Coordination of visual and linguistic processing correlated with a component of the ASVAB measuring perceptual speed. We conclude that, although the ability to integrate separate components of a complex task draws on a coordination ability, this ability is domain specific and thus varies depending on the nature of the component tasks.

Representation of pitch input to neural network models of music perception

Neural networks are a general class of computational models that can be used to model a variety of music perceptual tasks. An important issue in designing a neural network is the representation of input. The choice of representation can influence the networks trainability, its plausibility as a perceptual model, and its ability to generalize to other musical tasks. Networks that have been trained either to classify musical chords or to identify musical pitch are described. Four approaches to representation are examined. The simplest is a tone‐chroma notation in which there are 12 possible input nodes, one for each tone of the Western chromatic scale. Two approaches, a harmonic and subharmonic template, are motivated by theories of complex pitch perception. Input nodes are quantized into pitch‐class categories of the Western chromatic scale, and incorporate the notion of pitch height as well as tone chroma. In the fourth approach, each input node represents a frequency bin with a one‐third semitone bandwi...

A parallel learning model of musical pitch perception

Musical pitch perception involves the ability to extract and internalize a template that represents harmonic information. Template extraction is important to other perceptual processes such as melody recognition and chord classification, although these involve extraction of intervallic information. In order to explore how templates might be learned, a parallel learning algorithm was developed. This algorithm is based on the notion that a stimulus does not need to be physically present for a response to be learned. An artificial neural network was trained with this algorithm to identify the pitch of a tone complex. The network had 116 input units (log frequency) and 88 output units (pitch). After training, it correctly identified the pitch of 88 tone complex prototypes. It was tested with a variety of incomplete patterns as well as dyads and triads. All test patterns were correctly identified, although output strength dropped when simultaneous tone complexes were presented. The results indicate the paralle...

Do octave complexes facilitate learning to identify pitch class

This research explored the ability to learn to identify the pitch class of sine and complex tones. It was hypothesized that pitch‐class identification could be improved if octave complexes were used in training. Shepard tones [R. N. Shepard, J. Acoust. Soc. Am. 36, 2345–2353 (1964)] were thought to be ideal pitch‐class exemplars because they contain only octave‐related partials and have an envelope that controls for pitch height. Three groups of undergraduate music majors participated in the study. None had absolute pitch. Subjects were given a pre‐ and post‐test of their ability to name the pitch class of sine tones, various acoustical instrument tones, synthesizer tones, and Shepard tones. Group 1 controlled for maturation effects and did not receive any training. Subjects in groups 2 and 3 attended five training sessions. Digital piano tones were used in group 2 training sessions, while Shepard tones were used for group 3. There were reliable differences between group 2 and group 1 scores. Group 3 scor...

Chaotic dynamics of woodwind multiphonics

Experimental evidence for chaos in multiphonic tones derives from measured power spectra, and more directly from the measured correlation dimension of the reconstructed phase space of the dynamical system. The frequencies fl,m of the line spectral components of a reed‐driven woodwind multiphonic fit a biperiodic spectrum of low‐ to mid‐playing levels; i.e., there exist base frequencies f1 < f2 such that fl,m = lf1 + mf2, for non‐negative integers l and m. For an alto saxophone multiphonic, these base frequencies are phase locked, namely, their ratio is equal to a ratio of small integers. Using the same nominal saxophone fingering, this measured ratio equals 8 : 5 or 7 : 4 (within 0.1%) depending upon players adjustment of embouchure and playing level. A broadband spectrum is present in the saxophone multiphonic spectra at all but the lowest levels, which exceeds instrumentation noise and window leakage associated with signal processing. A phase‐locked biperiodic spectrum superposed on a broadband backgro...

A neural network model of musical chord classification

A neural network, which models a musical task, specifically the chord classification task, was built. The model “listens” to a chord and classifies it as a major, minor, or diminished chord. Two basic approaches were taken in the development of the model: (1) pitch class, and (2) harmonic template. The pitch class approach represents chords as they are customarily represented in music notation, namely by specifying the pitch class of each tone in the chord. The harmonic template approach defines each pitch in terms of an equivalent harmonic complex, specified by the most appropriate pitch class label for each of the first five harmonics. This approach is motivated by pitch perception theories based upon pattern matching (Goldstein, 1973; Terhardt, 1974). Connection strengths between nodes in the network were derived using an error propagation learning algorithm (Rumelhart, Hinton, and Williams, 1986). The pitch class network performed poorly by classifying only 33%–72% of the musical chords correctly. The...