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

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

Bottom Line: 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.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.


Related in: MedlinePlus

Pitch discriminability. A, Two neurons tuned to the same frequency (within-channel) but with delay mismatch δ = 1/f produce phase-locked spikes (red and blue crosses) in response to a tone (sine waves). When the tone frequency is f (left), the two input signals match and the difference of phases of spikes ΔΦ(f) between the two neurons is distributed around 0 (shaded curve). When the tone frequency is f + df (right), the two signals are slightly mismatched and the distribution of ΔΦ(f) is not centered on 0. B, Two neurons tuned to different frequencies (cross-channel) respond at different mean phases to tones (red and blue curves). C, The discriminability index d' is defined as the distance µ between the centers of be two phase difference distributions (ΔΦ(f) and ΔΦ(f + df)) relative to their standard deviation σ. D, The standard deviation of the phase distribution is related to the precision of phase locking, measured by the vector strength (dots: vector strength vs characteristic frequency for guinea pig auditory fibers; solid curve: fit). E, Mean phase of spikes produced by auditory nerve fibers of guinea pigs for different tone frequencies (data from Palmer and Shackleton, 2009), as a function of CF (crosses) with fits (solid lines). F, Weber fraction (Δf/f, where Δf is the just noticeable difference in frequency) as a function of tone frequency for cross-channel structure (colored curves) and within-channel structure (black curve). Color represent different frequency spacings between the two channels (1 − 6 semitones). Dotted lines represent the limitations implied by a maximal delay δmax = 5 ms.
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f6: Pitch discriminability. A, Two neurons tuned to the same frequency (within-channel) but with delay mismatch δ = 1/f produce phase-locked spikes (red and blue crosses) in response to a tone (sine waves). When the tone frequency is f (left), the two input signals match and the difference of phases of spikes ΔΦ(f) between the two neurons is distributed around 0 (shaded curve). When the tone frequency is f + df (right), the two signals are slightly mismatched and the distribution of ΔΦ(f) is not centered on 0. B, Two neurons tuned to different frequencies (cross-channel) respond at different mean phases to tones (red and blue curves). C, The discriminability index d' is defined as the distance µ between the centers of be two phase difference distributions (ΔΦ(f) and ΔΦ(f + df)) relative to their standard deviation σ. D, The standard deviation of the phase distribution is related to the precision of phase locking, measured by the vector strength (dots: vector strength vs characteristic frequency for guinea pig auditory fibers; solid curve: fit). E, Mean phase of spikes produced by auditory nerve fibers of guinea pigs for different tone frequencies (data from Palmer and Shackleton, 2009), as a function of CF (crosses) with fits (solid lines). F, Weber fraction (Δf/f, where Δf is the just noticeable difference in frequency) as a function of tone frequency for cross-channel structure (colored curves) and within-channel structure (black curve). Color represent different frequency spacings between the two channels (1 − 6 semitones). Dotted lines represent the limitations implied by a maximal delay δmax = 5 ms.

Mentions: To analyze the discriminability of cross-channel structure (Fig. 6E,F), we fitted an analytical formula to the phase φ(L, f, CF) of auditory nerve responses recorded at different levels L and tone frequencies f in fibers with different CF, using a data set from Palmer and Shackleton (2009), similarly to Carlyon et al. (2012). For each level, we fitted a function corresponding to the phase response of a gammatone filter bank:ϕL,f,CF= fψL,CF+narctan⁡2πτCF,Lf-CFwhere ψ(L, CF) is the initial delay of the travelling wave [a parameterized function of CF (Zhang et al., 2001, their Eq. 3)], in the order of the gammatone filter and τ(CF, L) = α(L)CFβ(L) is inversely related to the bandwidth of the filter.


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

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

Pitch discriminability. A, Two neurons tuned to the same frequency (within-channel) but with delay mismatch δ = 1/f produce phase-locked spikes (red and blue crosses) in response to a tone (sine waves). When the tone frequency is f (left), the two input signals match and the difference of phases of spikes ΔΦ(f) between the two neurons is distributed around 0 (shaded curve). When the tone frequency is f + df (right), the two signals are slightly mismatched and the distribution of ΔΦ(f) is not centered on 0. B, Two neurons tuned to different frequencies (cross-channel) respond at different mean phases to tones (red and blue curves). C, The discriminability index d' is defined as the distance µ between the centers of be two phase difference distributions (ΔΦ(f) and ΔΦ(f + df)) relative to their standard deviation σ. D, The standard deviation of the phase distribution is related to the precision of phase locking, measured by the vector strength (dots: vector strength vs characteristic frequency for guinea pig auditory fibers; solid curve: fit). E, Mean phase of spikes produced by auditory nerve fibers of guinea pigs for different tone frequencies (data from Palmer and Shackleton, 2009), as a function of CF (crosses) with fits (solid lines). F, Weber fraction (Δf/f, where Δf is the just noticeable difference in frequency) as a function of tone frequency for cross-channel structure (colored curves) and within-channel structure (black curve). Color represent different frequency spacings between the two channels (1 − 6 semitones). Dotted lines represent the limitations implied by a maximal delay δmax = 5 ms.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f6: Pitch discriminability. A, Two neurons tuned to the same frequency (within-channel) but with delay mismatch δ = 1/f produce phase-locked spikes (red and blue crosses) in response to a tone (sine waves). When the tone frequency is f (left), the two input signals match and the difference of phases of spikes ΔΦ(f) between the two neurons is distributed around 0 (shaded curve). When the tone frequency is f + df (right), the two signals are slightly mismatched and the distribution of ΔΦ(f) is not centered on 0. B, Two neurons tuned to different frequencies (cross-channel) respond at different mean phases to tones (red and blue curves). C, The discriminability index d' is defined as the distance µ between the centers of be two phase difference distributions (ΔΦ(f) and ΔΦ(f + df)) relative to their standard deviation σ. D, The standard deviation of the phase distribution is related to the precision of phase locking, measured by the vector strength (dots: vector strength vs characteristic frequency for guinea pig auditory fibers; solid curve: fit). E, Mean phase of spikes produced by auditory nerve fibers of guinea pigs for different tone frequencies (data from Palmer and Shackleton, 2009), as a function of CF (crosses) with fits (solid lines). F, Weber fraction (Δf/f, where Δf is the just noticeable difference in frequency) as a function of tone frequency for cross-channel structure (colored curves) and within-channel structure (black curve). Color represent different frequency spacings between the two channels (1 − 6 semitones). Dotted lines represent the limitations implied by a maximal delay δmax = 5 ms.
Mentions: To analyze the discriminability of cross-channel structure (Fig. 6E,F), we fitted an analytical formula to the phase φ(L, f, CF) of auditory nerve responses recorded at different levels L and tone frequencies f in fibers with different CF, using a data set from Palmer and Shackleton (2009), similarly to Carlyon et al. (2012). For each level, we fitted a function corresponding to the phase response of a gammatone filter bank:ϕL,f,CF= fψL,CF+narctan⁡2πτCF,Lf-CFwhere ψ(L, CF) is the initial delay of the travelling wave [a parameterized function of CF (Zhang et al., 2001, their Eq. 3)], in the order of the gammatone filter and τ(CF, L) = α(L)CFβ(L) is inversely related to the bandwidth of the filter.

Bottom Line: 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.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.


Related in: MedlinePlus