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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.


Related in: MedlinePlus

Domain of existence of pitch. A, Within-channel structure produced by a periodic sound can be decoded if the sound’s period is smaller than the maximal neural delay δmax. When δmax = 4 ms, it occurs for sounds of fundamental frequency greater than 250 Hz. B, A pure tone or resolved harmonic produces cross-channel structure with arbitrarily small delays between channels, corresponding to the phase difference between the two filters at the sound’s frequency: here a 100 Hz tone produces two identical waveforms delayed by δ = 2 ms, while the sound’s period is 10 ms. C, A transposed tone with a high-frequency carrier (>4 kHz) modulated by a low-frequency envelope (<320 Hz) elicits a very weak pitch (Oxenham et al., 2004a) (top: f0 = 120 Hz). Such sounds produce only within-channel structure because they only have high-frequency content (middle). The structural theory of pitch predicts an absence of pitch when the envelope’s periodicity is larger than δmax, which is consistent with psychophysics if δmax< 3 ms. D, A pure tone with the same fundamental frequency (f0 = 120 Hz) produces cross-channel structure with short delays. The structural theory of pitch predicts the existence of pitch in this case, consistently with psychophysical results (Oxenham et al., 2004a). E, Complex tones with f0 between 400 Hz and 2 kHz and all harmonics above 5 kHz elicit a pitch (Oxenham et al., 2011) (top, spectrum of a complex tone; middle, temporal waveform). Such tones produce only within-channel structure in high frequency (bottom), and the structural theory of pitch predicts the existence of pitch if the sound’s period is smaller than δmax, which is consistent with psychophysics if δmax > 2.5 ms.
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f3: Domain of existence of pitch. A, Within-channel structure produced by a periodic sound can be decoded if the sound’s period is smaller than the maximal neural delay δmax. When δmax = 4 ms, it occurs for sounds of fundamental frequency greater than 250 Hz. B, A pure tone or resolved harmonic produces cross-channel structure with arbitrarily small delays between channels, corresponding to the phase difference between the two filters at the sound’s frequency: here a 100 Hz tone produces two identical waveforms delayed by δ = 2 ms, while the sound’s period is 10 ms. C, A transposed tone with a high-frequency carrier (>4 kHz) modulated by a low-frequency envelope (<320 Hz) elicits a very weak pitch (Oxenham et al., 2004a) (top: f0 = 120 Hz). Such sounds produce only within-channel structure because they only have high-frequency content (middle). The structural theory of pitch predicts an absence of pitch when the envelope’s periodicity is larger than δmax, which is consistent with psychophysics if δmax< 3 ms. D, A pure tone with the same fundamental frequency (f0 = 120 Hz) produces cross-channel structure with short delays. The structural theory of pitch predicts the existence of pitch in this case, consistently with psychophysical results (Oxenham et al., 2004a). E, Complex tones with f0 between 400 Hz and 2 kHz and all harmonics above 5 kHz elicit a pitch (Oxenham et al., 2011) (top, spectrum of a complex tone; middle, temporal waveform). Such tones produce only within-channel structure in high frequency (bottom), and the structural theory of pitch predicts the existence of pitch if the sound’s period is smaller than δmax, which is consistent with psychophysics if δmax > 2.5 ms.

Mentions: We start by analyzing the domain of existence of within-channel structure (Fig. 3A). Since this is just the periodicity structure, its domain of existence is the same as in standard temporal theories of pitch. When the sound’s period exceeds the maximum delay δmax, periodicity cannot be detected anymore. Therefore, the lower limit (minimum f0) is the inverse of the maximum delay: f0 = 1/δmax.


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

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

Domain of existence of pitch. A, Within-channel structure produced by a periodic sound can be decoded if the sound’s period is smaller than the maximal neural delay δmax. When δmax = 4 ms, it occurs for sounds of fundamental frequency greater than 250 Hz. B, A pure tone or resolved harmonic produces cross-channel structure with arbitrarily small delays between channels, corresponding to the phase difference between the two filters at the sound’s frequency: here a 100 Hz tone produces two identical waveforms delayed by δ = 2 ms, while the sound’s period is 10 ms. C, A transposed tone with a high-frequency carrier (>4 kHz) modulated by a low-frequency envelope (<320 Hz) elicits a very weak pitch (Oxenham et al., 2004a) (top: f0 = 120 Hz). Such sounds produce only within-channel structure because they only have high-frequency content (middle). The structural theory of pitch predicts an absence of pitch when the envelope’s periodicity is larger than δmax, which is consistent with psychophysics if δmax< 3 ms. D, A pure tone with the same fundamental frequency (f0 = 120 Hz) produces cross-channel structure with short delays. The structural theory of pitch predicts the existence of pitch in this case, consistently with psychophysical results (Oxenham et al., 2004a). E, Complex tones with f0 between 400 Hz and 2 kHz and all harmonics above 5 kHz elicit a pitch (Oxenham et al., 2011) (top, spectrum of a complex tone; middle, temporal waveform). Such tones produce only within-channel structure in high frequency (bottom), and the structural theory of pitch predicts the existence of pitch if the sound’s period is smaller than δmax, which is consistent with psychophysics if δmax > 2.5 ms.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Domain of existence of pitch. A, Within-channel structure produced by a periodic sound can be decoded if the sound’s period is smaller than the maximal neural delay δmax. When δmax = 4 ms, it occurs for sounds of fundamental frequency greater than 250 Hz. B, A pure tone or resolved harmonic produces cross-channel structure with arbitrarily small delays between channels, corresponding to the phase difference between the two filters at the sound’s frequency: here a 100 Hz tone produces two identical waveforms delayed by δ = 2 ms, while the sound’s period is 10 ms. C, A transposed tone with a high-frequency carrier (>4 kHz) modulated by a low-frequency envelope (<320 Hz) elicits a very weak pitch (Oxenham et al., 2004a) (top: f0 = 120 Hz). Such sounds produce only within-channel structure because they only have high-frequency content (middle). The structural theory of pitch predicts an absence of pitch when the envelope’s periodicity is larger than δmax, which is consistent with psychophysics if δmax< 3 ms. D, A pure tone with the same fundamental frequency (f0 = 120 Hz) produces cross-channel structure with short delays. The structural theory of pitch predicts the existence of pitch in this case, consistently with psychophysical results (Oxenham et al., 2004a). E, Complex tones with f0 between 400 Hz and 2 kHz and all harmonics above 5 kHz elicit a pitch (Oxenham et al., 2011) (top, spectrum of a complex tone; middle, temporal waveform). Such tones produce only within-channel structure in high frequency (bottom), and the structural theory of pitch predicts the existence of pitch if the sound’s period is smaller than δmax, which is consistent with psychophysics if δmax > 2.5 ms.
Mentions: We start by analyzing the domain of existence of within-channel structure (Fig. 3A). Since this is just the periodicity structure, its domain of existence is the same as in standard temporal theories of pitch. When the sound’s period exceeds the maximum delay δmax, periodicity cannot be detected anymore. Therefore, the lower limit (minimum f0) is the inverse of the maximum delay: f0 = 1/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.


Related in: MedlinePlus