**2. AEFs in relation to the peak amplitude of the ACF,** *φ***<sup>1</sup>**

#### **2.1. AEFs in relation to IRN**

MEG has been used to investigate how features of sound stimuli related to pitch are represented in the human auditory cortex. For instance, tonotopic organization of the human auditory cortex has been investigated as a spatial representation of pure tone in the auditory system according to frequency [16–18]. The frequency of pure tones has been found to influence the source location of AEF response components, such as the N1m, in the human auditory cortex. The periodicity of pitch-related cortical responses has been investigated as part of the temporal structure of sound [19, 20]. However, it is currently unclear whether periodic pitch is reflected in the location of the source of the AEF response in the human auditory cortex.

**Figure 5.** Temporal waveforms (left panels) and power spectra (right panels) of the IRN with different delay times (*d*) and number of iterations (*n*). (a) *d* = 2 ms, *n* = 2; (b) *d* = 2 ms, *n* = 32; (c) *d* = 4 ms, *n* = 32.

To evaluate responses related to the first maximum peak of the ACF, *φ*1, which corresponds to pitch strength, in the auditory cortex, we recorded the AEFs elicited by IRNs with different iteration numbers. We anticipated that the N1m amplitude would increase with *φ*1. The N1m is a typical component of the AEFs, which is generated in the auditory cortex approximately 100 ms after stimulus onset, offset, or a change in sound [21]. A large number of physical and psychological parameters have been reported to influence N1m responses, including intensity, frequency, interaural level or time difference, threshold, states of arousal, and selective attention. For example, the N1m is correlated with basic sensations such as loudness and pitch [1].

Ten normal-hearing listeners (22−36 years; all right-handed) took part in the experiment. We produced an IRN using a delay-and-add algorithm applied to BPN that was filtered using fourth-order Butterworth filters between 100 and 3500 Hz. The number of iterations of the delay-and-add process was set at 2, 4, 8, 16, and 32, and the delay was set to 2 and 4 ms, corresponding to pitch values of 500 and 250 Hz, respectively. The stimulus duration was 0.5 s, including rise and fall ramps of 10 ms. The sounds were digital-to-analog (D/A) converted with a 16-bit sound card and a sampling rate of 48 kHz. Sounds were presented at a SPL of 60 dB through insert earphones inserted into both the left and right ear canals. **Figure 5** shows the temporal waveforms and the power spectra of some of the IRN used in this experiment. **Figure 6** shows the ACF waveform of some of the IRN used in this experiment. The *τ*1 value of IRN is the same value with the delay of the IRN. The *φ*1 value increases as the number of iterations increases.

**2. AEFs in relation to the peak amplitude of the ACF,** *φ***<sup>1</sup>**

MEG has been used to investigate how features of sound stimuli related to pitch are represented in the human auditory cortex. For instance, tonotopic organization of the human auditory cortex has been investigated as a spatial representation of pure tone in the auditory system according to frequency [16–18]. The frequency of pure tones has been found to influence the source location of AEF response components, such as the N1m, in the human auditory cortex. The periodicity of pitch-related cortical responses has been investigated as part of the temporal structure of sound [19, 20]. However, it is currently unclear whether periodic pitch is reflected in the location of the source of the AEF response in the human auditory cortex.

**Figure 5.** Temporal waveforms (left panels) and power spectra (right panels) of the IRN with different delay times (*d*)

To evaluate responses related to the first maximum peak of the ACF, *φ*1, which corresponds to pitch strength, in the auditory cortex, we recorded the AEFs elicited by IRNs with different iteration numbers. We anticipated that the N1m amplitude would increase with *φ*1. The N1m is a typical component of the AEFs, which is generated in the auditory cortex approximately 100 ms after stimulus onset, offset, or a change in sound [21]. A large number of physical and psychological parameters have been reported to influence N1m responses, including intensity, frequency, interaural level or time difference, threshold, states of arousal, and selective attention. For example, the N1m is correlated with basic sensations such as

and number of iterations (*n*). (a) *d* = 2 ms, *n* = 2; (b) *d* = 2 ms, *n* = 32; (c) *d* = 4 ms, *n* = 32.

**2.1. AEFs in relation to IRN**

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loudness and pitch [1].

**Figure 6.** ACFs of the IRN with the delay time of 4 ms and number of the iterations: (a) 2 and (b) 32.

The AEFs were recorded using a 122 channel whole-head DC superconducting quantum interference device (DC-SQUID) magnetometer (Neuromag-122TM; Neuromag Ltd., Helsinki, Finland) in a magnetically shielded room [15]. The IRNs were presented in a randomized order with a constant interstimulus interval of 1.5 s. To maintain listeners' attention level, listeners were instructed to watch a self-selected silent movie and ignore the stimuli during the experiment. The magnetic data were sampled at 0.4 kHz after being bandpass filtered between 0.03 and 100 Hz, then averaged approximately 100 times. The averaged responses were digitally filtered between 1.0 and 30.0 Hz. We analyzed a 0.7 s period starting 0.2 s prior to the stimulus onset, and an averaged 0.2 s prestimulus period served as the baseline.

We conducted source analysis for the measured field distribution based on the model of a single moving equivalent current dipole (ECD) [15]. Source estimates were based on a subset of 40–44 channels over each hemisphere. The dipole with the maximal goodness-of-fit over the analysis time window was chosen for further analysis. Only dipoles with a goodness-of-fit of more than 80% were included in the further analyses. The source waveforms for all stimuli were calculated using the best‐fitting dipole in each hemisphere. The peak amplitudes and latencies of the N1m reported in the following sections are based on the source waveforms.

**Figure 7.** Typical waveforms of AEFs from 122 channels in a listener.

**Figure 8.** Mean amplitude of the N1m (± standard error) across 10 listeners and hemispheres as a function of the num‐ ber of iterations with a delay time of 2 ms (○) or 4 ms (●).

Clear N1m responses were observed in both the left and right temporal areas in all listeners as shown in **Figure 7**. The N1m latencies were not systematically affected by the number of iterations of the IRN. **Figure 8** depicts the mean N1m amplitude across 10 listeners as a function of the number of iterations. A greater number of iterations of the IRN, i.e., a larger *φ*<sup>1</sup> value, produced a larger N1m amplitude. This suggests that a stronger pitch produces a larger N1m response. This result is consistent with previous studies [22, 23]. Previously, the amplitude of the AEF component elicited by periodic stimuli was compared with simulated peripheral activity patterns of the auditory nerve [24]. The researchers reported that the amplitude of the N1m was correlated with the pitch strength, estimated on the basis of auditory nerve activity. This finding is consistent with the present results.

more than 80% were included in the further analyses. The source waveforms for all stimuli were calculated using the best‐fitting dipole in each hemisphere. The peak amplitudes and latencies of the N1m reported in the following sections are based on the source waveforms.

**Figure 8.** Mean amplitude of the N1m (± standard error) across 10 listeners and hemispheres as a function of the num‐

**Figure 7.** Typical waveforms of AEFs from 122 channels in a listener.

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ber of iterations with a delay time of 2 ms (○) or 4 ms (●).

**Figure 9** shows the relationship between *φ*1 of the IRN and the N1m amplitude. A larger *φ*<sup>1</sup> value produced a larger N1m response, with a correlation coefficient of 0.76 (*p* < 0.05). However, we found another factor that appears to influence N1m amplitude. To calculate the effects of each ACF factor on AEF responses, we conducted multiple regression analyses with the N1m amplitude as the outcome variable. We used a linear combination of *φ*1, *τ*1 and *τe* as predictive variables in a stepwise fashion. The final version indicated that *φ*1 and *τ*1 were significant factors:

$$\text{N l'm amplitude} \approx a\_1 \, ^\ast \phi\_\text{l} + a\_2 \, ^\ast \tau\_\text{l} + b\_\text{l} \tag{3}$$

**Figure 9.** Relationship between *φ*1 and mean N1m amplitude. The delay time of the IRN of 2 ms (○) or 4 ms (●).

The model was statistically significant (*p* < 0.01), and the correlation coefficient between the measured and predicted values was 0.88. The standardized partial regression coefficients of the variables *a*1 and *a*2 in Eq. (3) were 0.77 and 0.44, respectively. These results indicate that both the ACF factors *φ*1 and *τ*1 had significant effects on N1m responses, although *φ*1 had a stronger effect.

#### **2.2. AEFs in relation to BPN**

To evaluate responses related to *φ*<sup>1</sup> in the auditory cortex, we also recorded the AEFs elicited by BPN with different bandwidths. Eight normal-hearing listeners (22–28 years; all righthanded) took part in the experiment. We produced BPN by repeated digital filtering of 10 s white noise signals. We set the magnitude of the Fourier coefficients to a cut-off slope of 200 dB/octave outside the desired bandwidth. For stimuli with a center frequency of 500 or 1000 Hz, the stimulus bandwidth was set at 1, 40, 80, 160 or 320 Hz. For stimuli with a center frequency of 2000 Hz, the stimulus bandwidth was set at 1, 40, 80, 160, 320 or 640 Hz. The maximum bandwidth was wider than the critical bandwidth for each center frequency [25]. The stimulus duration was 0.5 s, which we took from the 10 s BPN signal and set rise and fall ramps of 10 ms. The sounds were D/A converted with a 16-bit sound card and a sampling rate of 48 kHz. They were presented at a SPL of 74 dB through insert earphones inserted into both the left and right ear canals. **Figure 10** shows the temporal waveforms of the stimuli with a center frequency of 1000 Hz. As the bandwidth of the BPN increases, fluctuations in the envelope of the BPN waveform decrease. The ACF can characterize the BPN, that is, *τ*<sup>1</sup> corresponds to the center frequency of the BPN and the *φ*<sup>1</sup> value increases as the filter bandwidth decreases.

**Figure 10.** Temporal waveforms of BPNs with a center frequency of 1000 Hz and different bandwidths, Δf, (a) 1 Hz; (b) 40 Hz; (c) 80 Hz; (d) 160 Hz; (e) 320 Hz.

We recorded and analyzed the AEFs using methods similar to previous MEG experiments using IRN. The temporal waveforms of AEFs from 122 channels showed clear N1m responses in both the left and right temporal areas in all listeners. **Figure 11** depicts the mean N1m amplitude across eight listeners as a function of the BPN bandwidths. A narrower BPN bandwidths produced a larger N1m amplitude, that is, the larger the *φ*<sup>1</sup> value, the larger the N1m response. This result is consistent with previous IRN experiments.

both the ACF factors *φ*1 and *τ*1 had significant effects on N1m responses, although *φ*1 had a

To evaluate responses related to *φ*<sup>1</sup> in the auditory cortex, we also recorded the AEFs elicited by BPN with different bandwidths. Eight normal-hearing listeners (22–28 years; all righthanded) took part in the experiment. We produced BPN by repeated digital filtering of 10 s white noise signals. We set the magnitude of the Fourier coefficients to a cut-off slope of 200 dB/octave outside the desired bandwidth. For stimuli with a center frequency of 500 or 1000 Hz, the stimulus bandwidth was set at 1, 40, 80, 160 or 320 Hz. For stimuli with a center frequency of 2000 Hz, the stimulus bandwidth was set at 1, 40, 80, 160, 320 or 640 Hz. The maximum bandwidth was wider than the critical bandwidth for each center frequency [25]. The stimulus duration was 0.5 s, which we took from the 10 s BPN signal and set rise and fall ramps of 10 ms. The sounds were D/A converted with a 16-bit sound card and a sampling rate of 48 kHz. They were presented at a SPL of 74 dB through insert earphones inserted into both the left and right ear canals. **Figure 10** shows the temporal waveforms of the stimuli with a center frequency of 1000 Hz. As the bandwidth of the BPN increases, fluctuations in the envelope of the BPN waveform decrease. The ACF can characterize the BPN, that is, *τ*<sup>1</sup> corresponds to the center frequency of the BPN and the *φ*<sup>1</sup> value increases as the filter band-

**Figure 10.** Temporal waveforms of BPNs with a center frequency of 1000 Hz and different bandwidths, Δf, (a) 1 Hz; (b)

stronger effect.

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width decreases.

40 Hz; (c) 80 Hz; (d) 160 Hz; (e) 320 Hz.

**2.2. AEFs in relation to BPN**

**Figure 11.** Mean amplitude of the N1m (± standard error) across eight listeners and hemispheres as a function of bandwidth with a center frequency of 500 Hz (□), 1000 Hz (■), and 2000 Hz (△).

**Figure 12.** Relationship between *φ*<sup>1</sup> and mean N1m amplitude. Symbols denote the center frequency of the BPN as 500 Hz (□), 1000 Hz (■), or 2000 Hz (△).

**Figure 12** shows the relationship between *φ*1 of the BPN and the N1m amplitude. A larger *φ*<sup>1</sup> produced a larger N1m response. The correlation coefficient was 0.65 (*p* < 0.05). However, we identified another factor that influences N1m amplitude. To calculate the effects of each ACF factor on AEF response, we conducted multiple regression analyses with the N1m amplitude as the outcome variable. We used a linear combination of *φ*1, *τ*1, and *τ*e as predictive variables in a stepwise fashion. The final version indicated that *φ*1 and *τ*e were significant factors:

$$\text{N l'm amplitude} \approx a\_\text{s} \, \text{\* } \phi\_\text{l} + a\_\text{4} \, \text{\* } \tau\_\text{c} + b\_\text{2} \tag{4}$$

The model was statistically significant (*p* < 0.01), and the correlation coefficient between the measured and predicted values was 0.78. The standardized partial regression coefficients of the variables *a*3 and *a*<sup>4</sup> in Eq. (4) were 0.52 and 0.45, respectively. The results indicated that the ACF factors *φ*1 and *τe* had significant effects on N1m responses.
