Limits...
A Structural Theory of Pitch(1,2,3).

Laudanski J, Zheng Y, Brette R - eNeuro (2014)

Bottom Line: For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics.While this proposition also attributes pitch to periodic sounds, we show that it predicts differences between resolved and unresolved harmonic complexes and a complex domain of existence of pitch, in agreement with psychophysical experiments.We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institut D'etudes De La Cognition, Ecole Normale Supérieure , Paris, France ; Scientific and Clinical Research Department, Neurelec , Vallauris, France.

ABSTRACT
Musical notes can be ordered from low to high along a perceptual dimension called "pitch". A characteristic property of these sounds is their periodic waveform, and periodicity generally correlates with pitch. Thus, pitch is often described as the perceptual correlate of the periodicity of the sound's waveform. However, the existence and salience of pitch also depends in a complex way on other factors, in particular harmonic content. For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics. Here we examine the theoretical proposition that pitch is the perceptual correlate of the regularity structure of the vibration pattern of the basilar membrane, across place and time-a generalization of the traditional view on pitch. While this proposition also attributes pitch to periodic sounds, we show that it predicts differences between resolved and unresolved harmonic complexes and a complex domain of existence of pitch, in agreement with psychophysical experiments. We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.

No MeSH data available.


Harmonic resolvability and cross-channel structure. A, Amplitude and phase spectrum of two gammatone filters. Only a pure tone of frequency f (“Input” waveform) is attenuated in the same way by the two filters (red and blue waveforms: filter outputs). At that frequency, the delay between the outputs of the two filters is δ = Δφ/f. B, If several harmonic components fall within the bandwidths of the two filters, then the outputs of the two filters differ (no cross-channel similarity). C, Excitation pattern produced on the cochlea by a harmonic complex. Top, Amplitude versus center frequency of gammatone filters. Bottom, Spectrum of harmonic complex and of gammatone filters. Harmonic components are resolved when they can be separated on the cochlear activation pattern. Higher-frequency components are unresolved because cochlear filters are broader. D, Resolved components produce cross-channel similarity between many pairs of filters (as in A). Unresolved components produce little cross-channel structure (as in B). E, Thus, the vibration pattern produced by resolved components displays both within-channel and cross-channel structure (left), while unresolved components only produce within-channel structure (right).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4596137&req=5

f2: Harmonic resolvability and cross-channel structure. A, Amplitude and phase spectrum of two gammatone filters. Only a pure tone of frequency f (“Input” waveform) is attenuated in the same way by the two filters (red and blue waveforms: filter outputs). At that frequency, the delay between the outputs of the two filters is δ = Δφ/f. B, If several harmonic components fall within the bandwidths of the two filters, then the outputs of the two filters differ (no cross-channel similarity). C, Excitation pattern produced on the cochlea by a harmonic complex. Top, Amplitude versus center frequency of gammatone filters. Bottom, Spectrum of harmonic complex and of gammatone filters. Harmonic components are resolved when they can be separated on the cochlear activation pattern. Higher-frequency components are unresolved because cochlear filters are broader. D, Resolved components produce cross-channel similarity between many pairs of filters (as in A). Unresolved components produce little cross-channel structure (as in B). E, Thus, the vibration pattern produced by resolved components displays both within-channel and cross-channel structure (left), while unresolved components only produce within-channel structure (right).

Mentions: To build a group of coincidence detector neurons tuned to periodic sounds with fundamental frequency f0, we consider the synchrony partition of the complex tone made of all harmonics of f0, i.e., tones of frequency k · f0. For each harmonic, we select all pairs of channels in our filter bank that satisfy the following properties (Fig. 2D): (1) the gain at k · f0 is greater than a threshold Gmin = 0.25 (Fig. 2D, dashed line), (2) the two gains at k · f0 are within ε = 0.02 of each other, and (3) the gain at neighboring harmonics (order k − 1 and k + 1) is lower than the threshold Gmin (resolvability criterion). For each selected pair of channels, we connect the corresponding input neurons to a single coincidence detector neuron. The connection from the neuron with higher CF has an axonal delay δ = Δφ/kf0, where Δφ is the phase difference between the two filters at k · f0 [which is known analytically for a gammatone (Zhang et al., 2001)]. In addition, for each channel, multiple neurons receiving inputs from the same filter project to a single coincidence detector neuron with axonal delays δ = k/f0 (as in Licklider’s model), where k in the integer varying between 1 and a value determined by the maximum delay δmax.


A Structural Theory of Pitch(1,2,3).

Laudanski J, Zheng Y, Brette R - eNeuro (2014)

Harmonic resolvability and cross-channel structure. A, Amplitude and phase spectrum of two gammatone filters. Only a pure tone of frequency f (“Input” waveform) is attenuated in the same way by the two filters (red and blue waveforms: filter outputs). At that frequency, the delay between the outputs of the two filters is δ = Δφ/f. B, If several harmonic components fall within the bandwidths of the two filters, then the outputs of the two filters differ (no cross-channel similarity). C, Excitation pattern produced on the cochlea by a harmonic complex. Top, Amplitude versus center frequency of gammatone filters. Bottom, Spectrum of harmonic complex and of gammatone filters. Harmonic components are resolved when they can be separated on the cochlear activation pattern. Higher-frequency components are unresolved because cochlear filters are broader. D, Resolved components produce cross-channel similarity between many pairs of filters (as in A). Unresolved components produce little cross-channel structure (as in B). E, Thus, the vibration pattern produced by resolved components displays both within-channel and cross-channel structure (left), while unresolved components only produce within-channel structure (right).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4596137&req=5

f2: Harmonic resolvability and cross-channel structure. A, Amplitude and phase spectrum of two gammatone filters. Only a pure tone of frequency f (“Input” waveform) is attenuated in the same way by the two filters (red and blue waveforms: filter outputs). At that frequency, the delay between the outputs of the two filters is δ = Δφ/f. B, If several harmonic components fall within the bandwidths of the two filters, then the outputs of the two filters differ (no cross-channel similarity). C, Excitation pattern produced on the cochlea by a harmonic complex. Top, Amplitude versus center frequency of gammatone filters. Bottom, Spectrum of harmonic complex and of gammatone filters. Harmonic components are resolved when they can be separated on the cochlear activation pattern. Higher-frequency components are unresolved because cochlear filters are broader. D, Resolved components produce cross-channel similarity between many pairs of filters (as in A). Unresolved components produce little cross-channel structure (as in B). E, Thus, the vibration pattern produced by resolved components displays both within-channel and cross-channel structure (left), while unresolved components only produce within-channel structure (right).
Mentions: To build a group of coincidence detector neurons tuned to periodic sounds with fundamental frequency f0, we consider the synchrony partition of the complex tone made of all harmonics of f0, i.e., tones of frequency k · f0. For each harmonic, we select all pairs of channels in our filter bank that satisfy the following properties (Fig. 2D): (1) the gain at k · f0 is greater than a threshold Gmin = 0.25 (Fig. 2D, dashed line), (2) the two gains at k · f0 are within ε = 0.02 of each other, and (3) the gain at neighboring harmonics (order k − 1 and k + 1) is lower than the threshold Gmin (resolvability criterion). For each selected pair of channels, we connect the corresponding input neurons to a single coincidence detector neuron. The connection from the neuron with higher CF has an axonal delay δ = Δφ/kf0, where Δφ is the phase difference between the two filters at k · f0 [which is known analytically for a gammatone (Zhang et al., 2001)]. In addition, for each channel, multiple neurons receiving inputs from the same filter project to a single coincidence detector neuron with axonal delays δ = k/f0 (as in Licklider’s model), where k in the integer varying between 1 and a value determined by the maximum delay δmax.

Bottom Line: For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics.While this proposition also attributes pitch to periodic sounds, we show that it predicts differences between resolved and unresolved harmonic complexes and a complex domain of existence of pitch, in agreement with psychophysical experiments.We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institut D'etudes De La Cognition, Ecole Normale Supérieure , Paris, France ; Scientific and Clinical Research Department, Neurelec , Vallauris, France.

ABSTRACT
Musical notes can be ordered from low to high along a perceptual dimension called "pitch". A characteristic property of these sounds is their periodic waveform, and periodicity generally correlates with pitch. Thus, pitch is often described as the perceptual correlate of the periodicity of the sound's waveform. However, the existence and salience of pitch also depends in a complex way on other factors, in particular harmonic content. For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics. Here we examine the theoretical proposition that pitch is the perceptual correlate of the regularity structure of the vibration pattern of the basilar membrane, across place and time-a generalization of the traditional view on pitch. While this proposition also attributes pitch to periodic sounds, we show that it predicts differences between resolved and unresolved harmonic complexes and a complex domain of existence of pitch, in agreement with psychophysical experiments. We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.

No MeSH data available.