A Neurodynamic Account of Musical Tonality

Abstract

Science since antiquity has asked whether mathematical relationships among acoustic frequencies govern musical relationships. Psychophysics rejected frequency ratio theories, focusing on sensory phenomena predicted by linear analysis of sound. Cognitive psychologists have since focused on long-term exposure to the music of one’s culture and short-term sensitivity to statistical regularities. Today evidence is rapidly mounting that oscillatory neurodynamics is an important source of nonlinear auditory responses. This leads us to reevaluate the significance of frequency relationships in the perception of music. Here, we present a dynamical systems analysis of mode-locked neural oscillation that predicts cross-cultural invariances in music perception and cognition. We show that this theoretical framework combines with short- and long-term learning to explain the perception of Hindustani rāgas, not only by encultured Indian listeners but also by Western listeners unfamiliar with the style. These findings demonstrate that intrinsic neurodynamics contribute significantly to the perception of musical structure.

Statistical learning and probabilistic prediction in music cognition: mechanisms of stylistic enculturation

“…In this approach, metrical expectations emerge from the resonance of coupled oscillators that entrain to temporal periodicities in the stimulus. A related oscillatory approach has been used to predict cross‐cultural invariances in perceived tonal stability . Since these models naturally imply an explanation of pitch and temporal processing in terms of stimulus structure, they do not provide a compelling account of enculturation (though it has been claimed that it is potentially compatible with Hebbian learning) .…”

“…A related oscillatory approach has been used to predict cross-cultural invariances in perceived tonal stability. 75 Since these models naturally imply an explanation of pitch and temporal processing in terms of stimulus structure, they do not provide a compelling account of enculturation (though it has been claimed that it is potentially compatible with Hebbian learning). 71 It is possible that oscillatorbased models and the mechanisms of statistical learning and probabilistic processing implemented in IDyOM are complementary in simulating different aspects of expectation (e.g., enculturated versus nonenculturated processing) or by operating at different Marrian levels of description.…”

Mode locking in periodically forced gradient frequency neural networks

“…In general, low-order mode locking at a simple frequency ratio (i.e., with k and m being small integers) is stronger and more stable with a wider locking region than high-order mode locking at a more complex ratio (large k and m) [34]. This property of nonlinear resonance has been suggested to underlie the relative consonance and dissonance of musical intervals [21] and the tonal stability of pitches in musical keys [23,24]. In the latter studies, the coefficient to the input term in Eq.…”

“…It has been shown that auditory neurons modelock to acoustic stimulation [17,18], and human auditory brainstem responses include various mode-locking ratios to stimulus frequenices [19]. Mode locking in the auditory system was recently proposed as a basis for the perception of pitch [20], harmony [21,22], tonality [23,24], and rhythm and meter [25][26][27], which have been traditionally related to frequency ratios (see Section IV B for more discussion).…”

“…Individual GrFNN models can have multiple layers of oscillators that are driven by external signals and connected to other oscillators in the same and/or different layers, and the connections can be either fixed or plastic (e.g., [22,27]). GrFNN models have been used to explain auditory neurophysiological data [31,32] as well as behavioral data on music perception [22,24,27].…”