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Sensory Systems/Auditory System/Pitch Processing

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Pitch Perception edit

This section reviews a key topic in auditory neuroscience: pitch perception. Some basic understanding of the auditory system is presumed, so readers are encouraged to first read the above sections on the 'Anatomy of the Auditory System' and 'Auditory Signal Processing'.

Introduction edit

Pitch is a subjective percept, evoked by sounds that have an approximately periodic nature. For many naturally occurring sounds, periodicity of a sound is the major determinant of pitch. Yet the relationship between an acoustic stimulus and pitch is quite abstract: in particular, pitch is quite robust to changes in other acoustic parameters such as loudness or spectral timbre, both of which may significantly alter the physical properties of an acoustic waveform. This is particularly evident in cases where sounds without any shared spectral components can evoke the same pitch, for example. Consequently, pitch-related information must be extracted from spectral and/or temporal cues represented across multiple frequency channels.

Investigations of pitch encoding in the auditory system have largely focused on identifying neural processes which reflect these extraction processes, or on finding the ‘end point’ of such a process: an explicit, robust representation of pitch as perceived by the listener. Both endeavours have had some success, with evidence accumulating for ‘pitch selective neurons’ in putative ‘pitch areas’. However, it remains debatable whether the activity of these areas is truly related to pitch, or if they simply exhibit selective representation of pitch-related parameters. On the one hand, demonstrating an activation of specific neurons or neural areas in response to numerous pitch-evoking sounds, often with substantial variation in their physical characteristics, provides compelling correlative evidence that these regions are indeed encoding pitch. On the other, demonstrating causal evidence that these neurons represent pitch is difficult, likely requiring a combination of in vivo recording approaches to demonstrate a correspondence of these responses to pitch judgments (i.e., psychophysical responses, rather than just stimulus periodicity), and direct manipulation of the activity in these cells to demonstrate predictable biases or impairments in pitch perception.

Due to the rather abstract nature of pitch, we will not immediately delve into this yet unresolved field of active research. Rather, we begin our discussion with the most direct physical counterparts of pitch perception – i.e., sound frequency (for pure tones) and, more generally, stimulus periodicity. Specifically, we will distinguish between, and more concretely define, the notions of periodicity and pitch. Following this, we will briefly outline the major computational mechanisms that may be implemented by the auditory system to extract such pitch-related information from sound stimuli. Subsequently, we outline representation and processing of pitch parameters in the cochlea, the ascending subcortical auditory pathway, and, finally, more controversial findings in primary auditory cortex and beyond, and evaluate the evidence of ‘pitch neurons’ or ‘pitch areas’ in these cortical regions.

Periodicity and pitch edit

Pitch is an emergent psychophysical property. The salience and ‘height’ of pitch depends on several factors, but within a specific range of harmonic and fundamental frequencies, called the “existence region”, pitch salience is largely determined by regularity of sound segment repetition; pitch height by the rate of repetition, also called the modulating frequency. The set of sounds capable of evoking pitch perception is diverse and spectrally heterogeneous. Many different stimuli – including pure tones, click trains, iterated ripple noises, amplitude modulated sounds, and so forth – can evoke a pitch percept, while another acoustic signals, even with very similar physical characteristics to such stimuli may not evoke pitch. Most naturally occurring pitch-evoking sounds are harmonic complexes - sounds containing a spectrum of frequencies that are integer multiples of the fundamental frequency, F0.  An important finding in pitch research is the phenomenon of the ‘missing fundamental’ (see below): within a certain frequency range, all the spectral energy at F0 can be removed from a harmonic complex, and still evoke a pitch correlating to F0 in a human listener[1]. This finding appears to generalise to many non-human auditory systems[2][3].

 
Pitch of the missing fundamental. Audio spectrographs for the melody of 'Mary had a little lamb'. (Left) Melody played with pure tones (fundamental), (middle) melody played with fundamental and first six harmonic overtones, (right) melody played with only harmonic overtones, with the spectral energy at the fundamental frequency removed. As demonstrated in the corresponding audio clips to the left, these three melodies differ in timbre, but pitch is unchanged, despite the missing fundamental and pure tone melodies having no spectral components in common.



Demo: Pitch of the missing fundamental
Pure tones
Melody played in pure tones.
Full Harmonic
Melody played with fundamental frequencies and first 6 harmonic overtones.
Missing fundamental
Melody played with only harmonic overtones, with spectral energy at the fundamental frequencies removed. fhead
Problems listening to these files? See media help.



The ‘missing fundamental’ phenomenon is important for two reasons. Firstly, it is an important benchmark for assessing whether particular neurons or brain regions are specialised for pitch processing, since such units should be expected to show activity reflective of F0 (and thus pitch), regardless of its presence in the sound and other acoustic parameters. More generally, a ‘pitch neuron’ or ‘pitch centre’ should show consistent activity in response to all stimuli that evoke a particular perception of pitch height. As will be discussed, this has been a source of some disagreement in identifying putative pitch neurons or areas.  Secondly, that we can perceive a pitch corresponding to F0 even in its absence in the auditory stimulus provides strong evidence against the brain implementing a mechanism for ‘selecting’ F0 to directly infer pitch. Rather, pitch must be extracted from temporal or spectral cues (or both)[4].

Mechanisms for pitch extraction: spectral and temporal cues edit

 
Resolved and unresolved harmonics. A schematic spectrum, excitation pattern, and simulated basilar membrane (BM) vibration for a complex tone with an F0 of 100 Hz and equal-amplitude harmonics. As can be seen in the excitation pattern and BM vibrations, higher order harmonics are 'unresolved' - that is, there is no effective separation of individual harmonics. (Description adapted from original author. Available at: http://www.europeanmedical.info/auditory-nerves/resolved-and-unresolved-harmonics-341-defining-resolvability.html)

These two cues (spectral and temporal) are the bases of two major classes of pitch extraction models[4]. The first of these are the time domain methods, which use temporal cues to assess whether a sound consists of a repetitive segment, and, if so, the rate of repetition. A commonly proposed method of doing so is autocorrelation. An autocorrelation function essentially involves finding the time delays between two sampling points that will give the maximum correlation: for example, a sound wave with a frequency of 100Hz (or period, T=10 milliseconds) would have a maximal correlation if samples are taken 10 milliseconds apart. For a 200Hz wave, the delay yielding maximal correlation would be 5 milliseconds – but also at 10 milliseconds, 15 milliseconds and so forth. Thus if such a function is performed on all component frequencies of a harmonic complex with F0=100Hz (and thus having harmonic overtones at 200Hz, 300Hz, 400Hz, and so forth), and the resulting time intervals giving maximal correlation were summed, they would collectively ‘vote’ for 10 milliseconds – the periodicity of the sound. The second class of pitch extraction strategies are frequency domain methods, where pitch is extracted by analysing the frequency spectra of a sound to calculate F0. For instance, ‘template matching' processes – such as the ‘harmonic sieve’ – propose that the frequency spectrum of a sound is simply matched to harmonic templates – the best match yields the correct F0[5].

There are limitations to both classes of explanations. Frequency domain methods require harmonic frequencies to be resolved – that is, for each harmonic to be represented as a distinct frequency band (see figure, right). Yet higher order harmonics, which are unresolved due to the wider bandwidth in physiological representation for higher frequencies (a consequence of the logarithmic tonotopic organisation of the basilar membrane), can still evoke pitch corresponding to F0. Temporal models do not have this issue, since an autocorrelation function should still yield the same periodicity, regardless of whether the function is performed in one or over several frequency channels. However, it is difficult to attribute the lower limits of pitch-evoking frequencies to autocorrelation: psychophysical studies demonstrate that we can perceive pitch from harmonic complexes with missing fundamentals as low as 30Hz; this corresponds to a sampling delay of over 33 milliseconds – far longer than the ~10 millisecond delay commonly observed in neural signalling[4].    

 
Sine-phase (left) and alternating phase (right) harmonics. These complexes have the same F0 (125 Hz) and the same harmonic numbers, but the pitch of the complex on the right is an octave higher than the pitch of the complex on the left. Both complexes were filtered between 3900 and 5400 Hz. (Description from original author. Available at: http://www.europeanmedical.info/auditory-nerves/resolved-and-unresolved-harmonics-341-defining-resolvability.html)

One strategy to determine which of these two strategies are adopted by the auditory system is the use of alternating-phase harmonics: to present odd harmonics in sine phase, and even harmonics in cosine phase. Since this will not affect the spectral content of the stimulus, no change in pitch perception should occur if the listener is relying primarily on spectral cues. On the other hand, the temporal envelope repetition rate will double. Thus, if temporal envelope cues are adopted, the pitch perceived by listeners for alternating-phase harmonics will be an octave above (i.e., double the frequency of) the pitch perceived for all-cosine harmonic with the same spectral composition. Psychophysical studies have investigated the sensitivity of pitch perception to such phase shifts across different F0 and harmonic ranges, providing evidence that both humans[6] and other primates[7] adopt a dual strategy: spectral cues are used for lower order, resolved harmonics, while temporal envelope cues are used higher order, unresolved harmonics.

Pitch extraction in the ascending auditory pathway edit

Weber fractions for pitch discrimination in humans has been reported at under 1%[8]. In view of this high sensitivity to pitch changes, and the demonstration that both spectral and temporal cues are used for pitch extraction, we can predict that the auditory system represents both the spectral composition and temporal fine structure of acoustic stimuli in a highly precise manner, until these representations are eventually conveyed explicitly periodicity or pitch-selective neurons.

Electrophysiological experiments have identified neuronal responses in the ascending auditory system that are consistent with this notion. From the level of the cochlea, the tonopically mapped basilar membrane’s (BM) motions in response to auditory stimuli establishes a place code for frequency composition along the BM axis. These representations are further enhanced by a phase-locking of the auditory nerve fibres (ANFs) to the frequency components it responds to. This mechanism for temporal representation of frequency composition is further enhanced in numerous ways, such as lateral inhibition at the hair cell/spiral ganglion cell synapse[9], supporting the notion that this precise representation is critical for pitch encoding.

Thus by this stage, the phase-locked temporal spike patterns of ANFs likely carry an implicit representation of periodicity. This was tested directly by Cariani and Delgutte[10]. By analysing the distribution of all-order inter-spike intervals (ISI) in the ANFs of cats, they showed that the most common ISI was the periodicity of the stimulus, and the peak-to-mean ratio of these distribution increased for complex stimuli evoking more salient pitch perceptions. Based on these findings, these authors proposed the ‘predominant interval hypothesis’, where a pooled code of all-order ISIs ‘vote’ for the periodicity - though of course, this finding is an inevitable consequence of phase-locked responses of ANFs. In addition, there is evidence that the place code for frequency components is also critical. By crossing a low-frequency stimulus with a high-frequency carrier, Oxenham et al transposed the temporal fine-structure of the low frequency sinusoid to higher frequency regions along the BM.[11] This led to significantly impaired pitch discrimination abilities. Thus, both the place and temporal coding represent pitch-related information in the ANFs.

The auditory nerve carries information to the cochlear nucleus (CN). Here, many cell types represent pitch-related information in different ways. For example, many bushy cells appear to have little difference in firing properties of auditory nerve fibres – information may be carried to higher order brain regions without significant modification[4].Of particular interest are the sustained chopper cells in the ventral cochlear nucleus. According Winter and colleagues, the first-order spike intervals in these cells corresponds to periodicity in response to iterated rippled noise stimuli (IRN), as well to cosine-phase and random-phase harmonic complexes, quite invariantly to sound level[12]. While further characterisation of these cells' responses to different pitch-evoking stimuli is required, there is therefore some indication that pitch extraction may begin as early as the level of the CN.

In the inferior colliculus (IC), there is some evidence that the average response rate of neurons is equal to the periodicity of the stimulus[13]. Subsequent studies comparing IC neuron responses to same-phase and alternating-phase harmonic complexes suggest that these cells may be responding to the periodicity of the overall energy level (i.e., the envelope), rather than true modulating frequency, yet it is not clear whether this applies only for unresolved harmonics (as would be predicted by psychophysical experiments) or also for resolved harmonics[4]. There remains much uncertainty regarding the representation of periodicity in the IC.

Pitch coding in the auditory cortex edit

Thus, there is a tendency to enhance that representations of F0 throughout the ascending auditory system, though the precise nature of this remains unclear. In these subcortical stages of the ascending auditory pathway however, there is no evidence for an explicit representation that consistently encodes information corresponding to perceived pitch. Such representations likely occur in ‘higher’ auditory regions, from primary auditory cortex onward.

Indeed, lesion studies have demonstrated the necessity for auditory cortex in pitch perception. Of course, an impairment in pitch detection following lesions to the auditory cortex may simply be reflect a passive transmission role for the cortex: where subcortical information must ‘pass through’ to affect behaviour. Yet studies such as that by Whitfield have demonstrated that this is likely not the case: while decorticate cats could be re-trained (following an ablation of their auditory cortex) to recognise complex tones comprised of three frequency components, the animals selectively lost the ability generalise these tones to other complexes with the same pitch[14]. In other words, while the harmonic composition could influence behaviour, harmonic relations (i.e. a pitch cue) could not. For example, the lesioned animal could correctly respond to a pure tone at 100Hz, but would not respond to a harmonic complex consisting of its harmonic overtones (at 200Hz, 300Hz, and so forth). This suggests strongly a role for the auditory cortex in further extraction of pitch-related information.

Early MEG studies of the primary auditory cortex had suggested that A1 contained a map of pitch. This was based on the findings that a pure tone and its missing fundamental harmonic complex (MF) evoked stimulus-evoked excitation (called the N100m) in the same location, whereas components frequencies of the MF presented in isolation evoked excitations in different locations[15]. Yet such notions were overcast by the results of experiments using higher spatial-resolution techniques: local field potential (LFP) and multi-unit recording (MUA) demonstrated that the mapping A1 was tonotopic – that is, based on neurons’ best frequency (BF), rather than best ‘pitch’[16]. These techniques do however demonstrate an emergence of distinct coding mechanisms reflective of extracting temporal and spectral cues: phase-locked representation of temporal envelope repetition rate was recorded in the higher BF regions of the tonotopic map, while the harmonic structure of the click train was represented in lower BF regions[17].Thus, the cues for pitch extraction may be further enhanced by this stage.

 
Schematic illustration of multi-peaked neurons. Blue dotted line shows a classical tuning curve for a 'single-peaked' frequency selective neuron with a best frequency (BF) at around 500Hz, as illustrated by the maximal response of this neuron to frequencies around this BF. The red solid line shows a schematic response of a multi-peaked neuron identified by Kadia and Wang (2003). In addition to a BF at 300Hz, this neuron is also excited by tones at 600Hz and 900Hz - i.e., frequencies in harmonic relation to the principal BF. Although not illustrated here, responses of such neurons to harmonic complexes (in this case, consisting of 300, 600, and 900 Hz for example) often had an additive effect, eliciting responses greater than that of a pure tone at the BF (i.e., 300Hz) alone. See reference [18]

An example of a neuronal substrate that may facilitate such an enhancement was described by Kadia and Wang in primary auditory cortex of marmosets[18]. Around 20% of the neurons here could be classified as ‘multi-peaked’ units: neurons that have multiple frequency response areas, often in harmonic relation (see figure, right). Further, excitation of two of these spectral peaks what shown to have a synergistic effect on the neurons’ responses. This would therefore facilitate the extraction of harmonically related tones in the acoustic stimulus, allowing these neurons to act as a ‘harmonic template’ for extracting spectral cues. Additionally, these authors observed that in the majority of ‘single peaked’ neurons (i.e. neurons with a single spectral tuning peak at its BF), a secondary tone could have a modulatory (facilitating or inhibiting) effect on the response of the neuron to its BF. Again, these modulating frequencies were often harmonically related to the BF. These facilitating mechanisms may therefore accommodate the extraction of certain harmonic components, while rejecting other spectral combinations through inhibitory modulation may facilitate the disambiguation with other harmonic complexes or non-harmonic complexes such as broadband noise.

 
Putative 'pitch regions' in human supratemporal plane. (A) Lateral view of the left hemisphere, with STG indicated in red. (B–D) Top view of left supratemporal plane, after removal of a large part of the parietal cortex. PP, HG, and PT are indicated in blue, yellow, and green, respectively. Major sulci are outlined in black (FTS, first transverse sulcus; SI, sulcus intermediate; HS, Heschl's sulcus; HS1, first Heschl's sulcus; HS2, second Heschl's sulcus). Panels include hemispheres with one HG, an incomplete separation of HG, and two HG in (B–D), respectively.

However, given that the tendency to enhance F0 has been demonstrated throughout the subcortical auditory system, we might expect have to come closer to a more explicit representation of pitch in the cortex. Neuroimaging experiments have explored this idea, capitalising on the emergent quality of pitch: a subtractive method can identify areas in the brain which show BOLD responses in response to a pitch-evoking stimulus, but not to another sound with very similar spectral properties, but does not evoke pitch perception. Such strategies were used by Patterson, Griffiths and colleagues: by subtracting the BOLD signal acquired during presentation of broad-band noise from the signal acquired during presentation of IRN, they identified a selective activation of the lateral (and to some extent, medial) Heschl’s gyrus (HG) in response to the latter class of pitch-evoking sounds[19]. Further, varying the repetition rate of IRN over time to create a melody led to additional activation in the superior temporal gyrus (STG) and planum polare (PP), suggesting a hierarchical processing of pitch through the auditory cortex. In line with this, MEG recordings by Krumbholz et al showed that, as the repetition rate of IRN stimuli is increased, a novel N100m is detected around the HG as the repetition rate crosses the lower threshold for pitch perception, and the magnitude of this “pitch-onset response” increased with pitch salience[20].

There is however some debate about the precise location of the pitch selective area. As Hall and Plack point out, the use of IRN stimuli alone to identify pitch-sensitive cortical areas is insufficient to capture the broad range of stimuli that can induce pitch perception: the activation of HG may be specific to repetitive broadband stimuli[21]. Indeed, based on BOLD signals observed in response to multiple pitch-evoking stimuli, Hall and Plack suggest that the planum temporale (PT) is more relevant for pitch processing.

Despite ongoing disagreement about the precise neural area specialised for pitch coding, such evidence suggests that regions lying anterolateral to A1 may be specialised for pitch perception. Further support for this notion is provided by the identification of ‘pitch selective’ neurons at the anterolateral border of A1 in the marmoset auditory cortex. These neurons were selectively responsive to both pure tones and missing F0 harmonics with the similar periodicities[22]. Many of these neurons were also sensitive to the periodicity of other pitch-evoking stimuli, such as click trains or IRN noise. This provides strong evidence that these neurons are not merely responding any particular component of the acoustic signal, but specifically represent pitch-related information.

Periodicity coding or pitch coding? edit

Accumulating evidence thus suggests that there are neurons and neural areas specialised in extracting F0, likely in regions just anterolateral to the low BF regions of A1. However, there are still difficulties in calling these neurons or areas “pitch selective”. While stimulus F0 is certainly a key determinant of pitch, it is not necessarily equivalent to the pitch perceived by the listener.

There are however several lines of evidence suggesting that these regions are indeed coding pitch, rather than just F0. For instance, further investigation of the marmoset pitch-selective units by Bendor and colleagues has demonstrated that the activity in these neurons corresponds well to the animals' psychophysical responses[7]. These authors tested the animals’ abilities to detect an alternating-phase harmonic complex amidst an ongoing presentation of same-phase harmonics at the same F0, in order to distinguish between when animals rely more on temporal envelope cues for pitch perception, rather than spectral cues. Consistent with psychophysical experiments in humans, the marmosets used primarily temporal envelope cues for higher order, unresolved harmonics of low F0, while spectral cues were used to extract pitch from lower-order harmonics of high F0 complexes. Recording from these pitch selective neurons showed that the F0 tuning shifted down an octave for alternating-phase harmonics, compared to same-phase harmonics for neurons tuned to low F0s. These patterns of neuronal responses are thus consistent with the psychophysical results, and suggest that both temporal and spectral cues are integrated in these neurons to influence pitch perception.

Yet, again, this study cannot definitively distinguish whether these pitch-selective neurons explicitly represent pitch, or simply an integration of F0 information that will then be subsequently decoded to perceive pitch. A more direct approach to addressing this issue was taken by Bizley et al, who analysed how auditory cortex LFP and MUA measurements in ferrets could independently be used to estimate stimulus F0 and pitch perception[23]. While ferrets were engaged in a pitch discrimination task (to indicate whether a target artificial vowel sound was higher or lower in pitch than a reference in a 2-alternative forced choice paradigm), receiver operating characteristic (ROC) analysis was used to estimate the discriminability of neural activity in predicting the change in F0 or the actual behavioural choice (i.e. a surrogate for perceived pitch). They found that neural responses across the auditory cortex were informative regarding both. Initially, the activity better discriminated F0 than the animal’s choice, but information regarding the animals’ choice grew steadily higher throughout the post-stimulus interval, eventually becoming more discriminable than the direction of F0 change[23].

Comparing the differences in ROC between the cortical areas studied showed that posterior fields activity better discriminated the ferrets’ choice. This may be interpreted in two ways. Since choice-related activity was higher in the posterior fields (which lie by the low BF border of A1), compared to the primary fields, this may be seen as further evidence for pitch-selectivity near low BF border of A1. On the other hand, the fact the pitch-related information was also observed in the primary auditory fields may suggest that sufficient pitch-related information may already be established by this stage, or that a distributed code across multiple auditory areas code pitch. Indeed, while single neurons distributed across the auditory cortex are in general sensitive to multiple acoustic parameters (and therefore not ‘pitch-selective’), information theoretic or neurometric analyses (using neural data to infer stimulus-related information) indicate that pitch information can nevertheless be robustly represented via population coding, or even by single neurons through temporal multiplexing (i.e., representing multiple sound features in distinct time windows)[24][25]. Thus, in the absence of stimulation or deactivation of these putative pitch-selective neurons or areas to demonstrate that such interventions induce predictable biases or impairments in pitch, it may be that pitch is represented in spatially and temporally distributed codes across the auditory cortex, rather than relying on specialised local representations.

Thus, both electrophysiological recording and neuroimaging studies suggest that there may be an explicit neural code for pitch lies near the low BF border of A1. Certainly, the consistent and selective responses to a wide range of pitch-evoking stimuli suggest that these putative pitch-selective neurons and areas are not simply reflecting any immediately available physical characteristic of the acoustic signal. Moreover, there is evidence that these putative pitch-selective neurons extract information from spectral and temporal cues in much the same way as the animal. However, by virtue of the abstract relationship between pitch and an acoustic signal, such correlative evidence between a stimulus and neural response can only be interpreted as evidence that the auditory system has the capacity to form enhanced representations of pitch-related parameters. Without more direct causal evidence for these putative pitch-selective neurons and neural areas determining pitch perception, we cannot conclude whether animals do indeed rely on such localised explicit codes for pitch, or if the robust distributed representations of pitch across the auditory cortex mark the final coding of pitch in the auditory system.    

References edit

  1. ↑ Schouten, J. F. (1938). The perception of subjective tones. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, 41, 1086-1093.  
  2. ↑ Cynx, J. & Shapiro, M. Perception of missing fundamental by a species of songbird (Sturnus vulgaris). J Comp Psychol 100, 356–360 (1986).
  3. ↑ Heffner, H., & Whitfield, I. C. (1976). Perception of the missing fundamental by cats. The Journal of the Acoustical Society of America, 59(4), 915-919.
  4. ↑ a b c d e Schnupp, J., Nelken, I. & King, A. Auditory neuroscience: Making sense of sound. (MIT press, 2011).
  5. ↑ Gerlach, S., Bitzer, J., Goetze, S. & Doclo, S. Joint estimation of pitch and direction of arrival: improving robustness and accuracy for multi-speaker scenarios. EURASIP Journal on Audio, Speech, and Music Processing 2014, 1 (2014).
  6. ↑ Carlyon RP, Shackleton TM (1994). "Comparing the fundamental frequencies of resolved and unresolved harmonics: Evidence for two pitch mechanisms?" Journal of the Acoustical Society of America 95:3541-3554    
  7. ↑ a b Bendor D, Osmanski MS, Wang X (2012). "Dual-pitch processing mechanisms in primate auditory cortex," Journal of Neuroscience 32:16149-61.
  8. ↑ Tramo, M. J., Shah, G. D., & Braida, L. D. (2002). Functional role of auditory cortex in frequency processing and pitch perception. Journal of Neurophysiology, 87(1), 122-139.
  9. ↑ Rask-Andersen, H., Tylstedt, S., Kinnefors, A., & Illing, R. B. (2000). Synapses on human spiral ganglion cells: a transmission electron microscopy and immunohistochemical study. Hearing research, 141(1), 1-11.
  10. ↑ Cariani, P. A., & Delgutte, B. (1996). Neural correlates of the pitch of complex tones. I. Pitch and pitch salience. Journal of Neurophysiology, 76(3), 1698-1716.
  11. ↑ Oxenham, A. J., Bernstein, J. G., & Penagos, H. (2004). Correct tonotopic representation is necessary for complex pitch perception. Proceedings of the National Academy of Sciences of the United States of America, 101(5), 1421-1425.    
  12. ↑ Winter, I. M., Wiegrebe, L., & Patterson, R. D. (2001). The temporal representation of the delay of iterated rippled noise in the ventral cochlear nucleus of the guinea-pig. The Journal of physiology, 537(2), 553-566.
  13. ↑ Schreiner, C. E. & Langner, G. Periodicity coding in the inferior colliculus of the cat. II. Topographical organization. Journal of neurophysiology 60, 1823–1840 (1988).
  14. ↑ Whitfield IC (1980). "Auditory cortex and the pitch of complex tones." J Acoust Soc Am. 67(2):644-7.
  15. ↑ Pantev, C., Hoke, M., Lutkenhoner, B., & Lehnertz, K. (1989). Tonotopic organization of the auditory cortex: pitch versus frequency representation.Science, 246(4929), 486-488.
  16. ↑ Fishman YI, Reser DH, Arezzo JC, Steinschneider M (1998). "Pitch vs. spectral encoding of harmonic complex tones in primary auditory cortex of the awake monkey," Brain Res 786:18-30.    
  17. ↑ Steinschneider M, Reser DH, Fishman YI, Schroeder CE, Arezzo JC (1998) Click train encoding in primary auditory cortex of the awake monkey: evidence for two mechanisms subserving pitch perception. J Acoust Soc Am 104:2935–2955.    
  18. ↑ Kadia, S. C., & Wang, X. (2003). Spectral integration in A1 of awake primates: neurons with single-and multipeaked tuning characteristics. Journal of neurophysiology, 89(3), 1603-1622.    
  19. ↑ Patterson RD, Uppenkamp S, Johnsrude IS, Griffiths TD. (2002) "The processing of temporal pitch and melody information in auditory cortex," Neuron 36:767-776.    
  20. ↑ Krumbholz, K., Patterson, R. D., Seither-Preisler, A., Lammertmann, C., & Lütkenhöner, B. (2003). Neuromagnetic evidence for a pitch processing center in Heschl’s gyrus. Cerebral Cortex, 13(7), 765-772.
  21. ↑ Hall DA, Plack CJ (2009). "Pitch processing sites in the human auditory brain," Cereb Cortex 19(3):576-85.    
  22. ↑ Bendor D, Wang X (2005). "The neuronal representation of pitch in primate auditory cortex," Nature 436(7054):1161-5.    
  23. ↑ a b Bizley JK, Walker KMM, Nodal FR, King AJ, Schnupp JWH (2012). "Auditory Cortex Represents Both Pitch Judgments and the Corresponding Acoustic Cues," Current Biology 23:620-625.
  24. ↑ Walker KMM, Bizley JK, King AJ, and Schnupp JWH. (2011). Multiplexed and robust representations of sound features in auditory cortex. Journal of Neurosci 31(41): 14565-76 
  25. ↑ Bizley JK, Walker KM, King AJ, and Schnupp JW. (2010). "Neural ensemble codes for stimulus periodicity in auditory cortex." J Neurosci 30(14): 5078-91.    
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