# Binaural beats through the auditory pathway: from brainstem to connectivity patterns

Hector D. Orozco Perez, Guillaume Dumas, Alexandre Lehmann

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## To cite this version:

Hector D. Orozco Perez, Guillaume Dumas, Alexandre Lehmann. Binaural beats through the auditory pathway: from brainstem to connectivity patterns. eNeuro, 2020, pp.ENEURO.0232-19.2020. 10.1523/ENEURO.0232-19.2020. pasteur-02484658v2

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Research Article: New Research | Cognition and Behavior

# Binaural beats through the auditory pathway: from brainstem to connectivity patterns

https://doi.org/10.1523/ENEURO.0232-19.2020

**Cite as:** eNeuro 2020; 10.1523/ENEURO.0232-19.2020

Received: 18 June 2019

Revised: 23 December 2019

Accepted: 20 January 2020

This Early Release article has been peer-reviewed and accepted, but has not been through the composition and copyediting processes. The final version may differ slightly in style or formatting and will contain links to any extended data.

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# Binaural beats through the auditory pathway: from brainstem to connectivity patterns

**Abbreviated Title:** Binaural Beats through the auditory pathway

Hector D Orozco Perez¹,², Guillaume Dumas³,⁴ and Alexandre Lehmann¹,⁵,⁶

¹ Laboratory for Brain, Music and Sound Research (BRAMS), Montreal, Canada (H2V 2S9).

² McMaster University, Department of Psychology, Neuroscience and Behavior, Hamilton, Canada (L8S 4L8).

³ Human Genetics and Cognitive Functions, Institut Pasteur, UMR3571 CNRS, Université de Paris, Paris, France (75015).

⁴ Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL, USA (FL 33431).

⁵ Department of Otolaryngology Head & Neck Surgery, McGill University, Montreal, Canada (H3A 0G4).

⁶ Centre for Research on Brain, Language and Music (CRBLM), Montreal, Canada (H3G 2A8).

**Author contributions:** HO, AL, and GD designed research; HO and AL performed research; GD contributed analytic tools; HO and GD analyzed data, HO wrote the paper; AL and GD provided edits and comments for the paper.

**Correspondence should be addressed to** [hector.dom.orozco@gmail.com](mailto:hector.dom.orozco@gmail.com)

**Acknowledgements:** The authors of this paper would like to thank Pierre Rainville and Bérangère Houze for sharing the E-SAS scales; Mihaela Felezeu for all the help and support during data acquisition; and our participants for volunteering their time to perform the experiment.
27 Authors report no conflict of interest

28

29 Funding sources: GD was financially supported by the Institut Pasteur

30

31 Abstract

32 Binaural beating is a perceptual auditory illusion occurring when presenting two neighboring

33 frequencies to each ear separately. Several controversial claims have been attributed to binaural

34 beats regarding their ability to entrain human brain activity and mood, in both the scientific

35 literature and the marketing realm. Here, we sought to address those questions in a robust

36 fashion using a single-blind, active-controlled protocol. To do so, we compared the effects of

37 binaural beats with a control beat stimulation (monaural beats, known to entrain brain activity but

38 not mood) across four distinct levels in the human auditory pathway: subcortical and cortical

39 entrainment, scalp-level Functional Connectivity and self-reports. Both stimuli elicited standard

40 subcortical responses at the pure tone frequencies of the stimulus (i.e., Frequency Following

41 Response), and entrained the cortex at the beat frequency (i.e., Auditory Steady State Response).

42 Furthermore, Functional Connectivity patterns were modulated differentially by both kinds of

43 stimuli, with binaural beats being the only one eliciting cross-frequency activity. Despite this, we

44 did not find any mood modulation related to our experimental manipulation. Our results provide

45 evidence that binaural beats elicit cross frequency connectivity patterns, but weakly entrain the
46 cortex when compared to monaural beat stimuli. Whether binaural beats have an impact on

47 cognitive performance or other mood measurements remains to be seen and can be further

48 investigated within the proposed methodological framework.
# Visual Abstract

1. Binaural beats occur when presenting two neighboring frequencies to each ear separately

<figure><img src="image_3.png" /></figure>

In both the scientific literature and the marketing realm, there are claims that Binaural Beats modulate brain activity and mood through brain entrainment

2. Both gamma and theta binaural beats entrain the cortex, but less so than a rhythmic "sham" stimulus

Power [dB] at 7 ± 0.5 Hz elicited by theta conditions

<figure><img src="image_4.png" /></figure>

Binaural

Monaural

Power [dB] at 40 ± 0.5 Hz elicited by gamma conditions

<figure><img src="image_5.png" /></figure>

Binaural

Monaural

3. Both stimuli (sham and binaural) modulated long and short range connectivity patterns differentially, with binaural beats being the only one eliciting cross-frequency activity.

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

4. No stimuli, however, modulated subjective experience.

<figure><img src="image_9.png" /></figure>

Whether the patterns reported here have, or not, any impact on cognition or mood remains an open question

50

51

52

# Significance Statement

53

Binaural beats have been a source of speculation and debate in the scientific community. Our

54

study addresses controversial claims and approaches them using proper experimental control and
modern signal processing techniques. Here we show that binaural beats can both entrain the cortex and elicit specific connectivity patterns. Regardless of this, our monaural control condition was able to entrain the cortex more strongly, and both binaural beats and the control condition failed to regulate mood. All in all, though binaural beats entrain cortical activity and elicit complex patterns of connectivity, the functional significance (if any) of binaural beats, and whether they are more "special" than monaural beats remain open questions.

61

62

Introduction

Humans use music and rhythm as mood enhancers. Be it in social gatherings or late study nights, we use audio stimuli to set the "right mood" and improve our cognitive performance (Mammarella et al., 2007; Schellenberg et al., 2007; Tarr et al., 2014). Binaural beats, an auditory illusion that occurs when presenting two similar pure tones to each ear separately, have been purported to induce mood alterations, contingent upon the beat frequency. Claims range from entraining the whole brain (Atwater, 2004; Rhodes, 1993), to altering states of consciousness (I-Doser, accessed May 2018; Atwater, 1997). The possibility of binaural beats modulating cognitive states without prior training makes them an interesting candidate for cost-effective applications in both healthy and impaired populations.

70

71
Presenting two tones with a slight frequency mismatch to each ear separately creates a perception of a third tone, a binaural beat, that oscillates at the absolute difference between the tones (Oster, 1973; Moore, 2012). These beats are thought to originate subcortically in the medial nucleus of the superior olivary complex, the first nucleus in the auditory pathway to receive bilateral input (Wernick & Starr, 1968; Kuwada & Wickesberg, 1979). This "illusory" third tone is lateralized between the left and right ear of the listener, making binaural beats useful for spatial sound research (Ross et al., 2014). Binaural beats can entrain cortical activity at both the specific frequency of the beat (Pratt et al., 2010) and cross-frequency modulations, such as theta beats driving interhemispheric alpha synchronization (Solcà et al., 2016). They also seem to modulate mood (Wahbeh et al., 2007), pain perception (Zampi, 2015) and cognitive performance in memory tasks (Kennerly, 1994). The cognitive effects of binaural beats are attributed to their capacity to drive neural oscillations at the beat frequency through differential hemispheric synchronization frequencies. The reported cognitive modulations, however, appear inconsistent and seem to depend on several mediating factors, such as frequency of stimulation, differing exposure time and stimuli masking (Garcia-Argibay et al., 2018). Furthermore, no study to date has fully characterized binaural beats throughout the auditory pathway (from subcortical responses to Functional Connectivity) and compared their effect to that of a non-binaural rhythmic control (i.e., monaural beats, created by digitally summing each tone before presentation). Indeed, monaural beats readily entrain the cortex to specific frequencies (Nozaradan et al., 2016), and repetitive and
91 rhythmic stimuli (such as mantras or tones) are widely used in contemplative and religious

92 practices with positive physiological impact (Bernardi et al., 2001; Bernardi et al., 2017). It remains

93 open questions whether the reported effects of binaural beats are due to: (1) their asymmetrically

94 driven rhythmicity (the binaural aspect is essential to their effectiveness), (2) their capability of

95 entraining brain oscillations (as would also be the case with monaural beats) or (3) a placebo

96 effect. To address these, we recorded electroencephalography (EEG) during a single-blind, active-

97 controlled task in which participants listened to both binaural and monaural beats.

98 Our main objective was to characterize brain responses and cognitive alterations induced

99 by binaural beats, compared to a monaural beat control condition. Our secondary objective was

100 to compare the neural and subjective effects elicited by two different beat frequencies. We used

101 theta (7 Hz) beats because they have been associated with reduced anxiety levels (Isik et al., 2017),

102 and gamma beats (40 Hz) because they have been associated with attention modulation (Colzato

103 et al., 2017). Furthermore, these frequencies have been associated with large-scale integration

104 models of the brain (Varela et al., 2001; Canolty and Knight, 2010). We compared responses

105 between binaural and monaural beats at four levels: subcortical entrainment to the carrier tones in

106 the form of a Frequency Following Response (FFR; Skoe & Kraus, 2010), cortical entrainment to

107 the beat in the form of an Auditory Steady State Response (ASSR; Picton et al., 2003), changes in

108 Functional Connectivity using phase-based statistics (Nolte et al. 2004; Lachaux et al., 2000) and
109 self-reported mood changes using analogue scales (Rainville et al., 2002). We hypothesized both

110 beats would elicit cortical and subcortical responses to the beat (ASSR) and pure tone frequencies

111 (FFR) respectively. However, we expected binaural beats to elicit Functional Connectivity changes

112 and modulate mood, with no such changes during the control condition. We hypothesized that

113 theta beats would facilitate a relaxed state, while gamma beats would elicit a more alert state. By

114 presenting converging evidence from different approaches (self-reports, EEG), we aimed to

115 elucidate whether binaural beats are a special kind of stimulus or reported effects could be

116 achieved with non-binaural rhythmic stimuli.

117

118 **Materials & Methods**

119 To understand the functional meaning of the entrainment and connectivity patterns associated

120 with binaural beats, we investigated the differences between monaural and binaural beats by

121 comparing subcortical, cortical and subjective responses elicited through a single-blind, passive

122 listening task with a 2x2 factorial design (two within factors: beat type and beat frequency).

123
124 Participants

125 Sixteen participants (nine female, seven male; mean age 27.4±5.5) volunteered for the experiment
126 and provided written informed consent. Exclusion criteria included neurological damage or
127 abnormalities (e.g. demyelination), and major hearing loss (0-20 HL dB) as self-reported by the
128 participants. The experimental procedures conformed to the World Medical Association's
129 Declaration of Helsinki and were approved by the Research Ethics Committee of the Faculty for
130 Arts and Sciences of the University of Montreal.

131 Stimuli

132 Binaural beats entrain cortical activity at the specific frequency of the beat percept (Draganova et
133 al., 2007; Schwarz & Taylor, 2005; Pratt et al., 2010). We refer to beat frequency as the frequency
134 of this percept, which is the difference between the pure tones; either 40 Hz for gamma
135 conditions (380 Hz & 420 Hz) or 7 Hz for theta conditions (396.5 Hz & 403.5 Hz). This rhythmic
136 percept is a key piece of the purported subjective effects of binaural beats in the scientific and
137 pseudo-scientific literature. They claim entrainment to it regulates mood and cognition. To
138 elucidate whether and how binaural beats regulate mood, we chose monaural beats as a control
139 that would rule out rhythmicity as an influencing factor. Binaural beats do not contain the beat
140 frequency in neither their spectrum nor their envelope, but this percept is presumably created in
141 the medial nucleus of the superior olivary complex (Wernick & Starr, 1968; Kuwada & Wickesberg,
142 1979). On the other hand, monaural beats do contain it in their envelope (see Figure 1).

143 Binaural beat stimuli consisted of two pure sine tones with equal starting phase and a
144 slight frequency mismatch presented separately to each ear (Figure 1, Columns 1 and 2). These
145 two pure tones were superimposed digitally (added together and divided by two to control for
146 loudness) to create the monaural control condition, which was presented monaurally to both
147 ears—each ear was presented with the same stimuli (see Becher et al., 2015; Schwarz & Taylor,
148 2005; and Draganova et al., 2007 for other examples where monaural beats were used as a control
149 condition). By summing both pure tones, we essentially created amplitude-modulated stimuli,
150 which excel at entraining the brain (Ross et al., 2000).

151 We chose carrier frequencies around 400 Hz for two reasons: best perception of binaural
152 beats occurs at carrier tones between 400 and 500 Hz (Licklider et al., 1950; Perrot & Nelson,
153 1969) and this frequency range minimizes cortical contributions to the brainstem responses
154 (Coffey et al., 2016). Both kinds of stimuli (binaural and monaural control) were root mean
155 squared normalized. The lower of both frequencies (380 and 396.5 Hz) was always presented to
156 the left ear (i.e., pure tone presentation was not altered between left and right ears).

157
158 Frequency choice: Theta

159 Auditory stimulation at the theta frequency band (4 - 7 Hz) has been associated with positive

160 emotional experiences and introspection (Aftanas & Golocheikine, 2001), reduced perceived pain
161 in patients with chronic pain (Zampi, 2015), states of meditation and decreased alertness

162 (Jirakittayakorn & Wongsawat, 2017) and enhancement of immediate verbal memory (Ortiz et al., 2008). Furthermore, theta cortical activity is related to concentration, focused attention and a general meditative state (Takahashi et al., 2005; Lagopoulos et al., 2009). We chose theta beat frequency to explore the possibility of eliciting a mindful and relaxed state in the participants.

166

167 Frequency choice: Gamma

168 Auditory gamma stimulation (32 - 48 Hz) has been associated with binaural sound integration

169 (Ross et al., 2014), divergent thinking (Reedijk et al., 2013) and attention control (Reedijk et al., 2015). Furthermore, auditory cortices readily entrain to it (Schwarz & Taylor, 2005; Ross et al., 2014), and it seems to be a "natural frequency" of these areas, even during resting state

172 (Hillebrand et al., 2012). We chose gamma beat frequency to explore the possibility of eliciting a heightened attention cognitive state in the participants.

174
175 Procedure

176 Participants started by filling out a general information and music abilities questionnaire. We then

177 fitted a headcap on participants' heads and placed EEG electrodes in it using a conductive gel.

178 The experiment took place in a sound-attenuated, electromagnetically shielded room. Participants

179 were asked to relax their upper body, close their eyes, avoid body movements and to pay

180 attention to the beat throughout the experiment (Schwarz & Taylor., 2005). We recorded data

181 from five experimental blocks: an eight-minute baseline (no stimulus presentation; eyes-closed)

182 followed by the four pseudo-randomized experimental conditions (binaural gamma, monaural

183 gamma, binaural theta, monaural theta), each lasting for eight minutes. After each recording

184 block, participants were asked to rate their experience using two visual analogue scales. They were

185 also given the opportunity to take a break in the middle of the experiment. Auditory stimuli (both

186 binaural and monaural beats) were generated live (i.e. during the recording block) to ensure sub-

187 millisecond phase accuracy using a signal processing system (RX6, Tucker-Davis Technologies,

188 www.tdt.com) controlled with MATLAB software (The Mathworks, www.mathworks.com) and

189 delivered via insert earphones (ER3, Etymotic Research, www.etymotic.com). Auditory stimuli were

190 processed at 48 kHz and were each presented continuously for eight minutes at 70 dB SPL. For

191 the purpose of further analysis and the epoching of continuous data, triggers were sent every
192 eight seconds via parallel ports using the signal processing system (RX6, Tucker-Davis Technologies, www.tdt.com) and recorded along with the EEG data.

194

195 Sound calibration

196 Output sound from the signal processing system was calibrated to be presented at 70 dB SPL at the level of each ear, using a Sound-Pro sound level meter (model DL 1/3 Octave Datalogging RTA) and a 2-CC ear coupler for insert earphones calibration. Calibration measurements were done using a slow rate mode with an A-weighting frequency filter.

200

201 EEG data acquisition

202 EEG was recorded using 64 active sintered Ag-AgCl electrodes placed on the scalp according to the International 10/10 system (ActiveTwo, Biosemi, The Netherlands). The active electrodes contain the first amplifier stage within the electrode cover and provide impedance transformation on the electrode to prevent interference currents from generating significant impedance-dependent nuisance voltages. We, therefore, did not control electrode impedances but rather kept direct-current offset close to zero during electrode placement. Vertical and horizontal eye movements were monitored using three additional electrodes placed on the outer canthus of
209 each eye and on the inferior area of the left orbit. Reference-free electrode signals were amplified,
210 sampled at 2048 Hz (ActiveTwo amplifier, BioSemi, The Netherlands), and stored using BioSemi
211 ActiView Software for offline analysis. Given that auditory stimuli were created online during the
212 experiment, they were recorded using Biosemi's Analog Input Box (Biosemi, The Netherlands),
213 which was daisy chained by optical fibers to the EEG Analog-to-Digital Converter box and stored
214 alongside the EEG data for future analysis.

215

216 Visual Analogue Scales

217 Participants were given pen and paper analogue scales after each recording block so they could
218 rate their experience after the passive listening task. Two analogue scales were used to determine
219 variations in subjective experience (Rainville et al., 2002). The scales used were:

220 • Mental relaxation, corresponding to the activity or calmness of the subject's mind. This
dimension spans from a state where the mind is calm, peaceful and in perfect relaxation
221 to a state where the mind is extremely agitated or active.
222

223 • Absorption depth corresponds to how the subject feels and how absorbed they felt
during the experiment. The scale runs from nonexistent depth to a profound, intense
224 and complete experience.
225

226
227 Data analysis and signal processing

228 Software Accessibility

229 All the code used for this project (digital signal processing, data wrangling, and statistics) can be
230 found here: github.com/neurohazardous/binauralBeats.

231

232 Visual Analogue Scales

233 Data from pen and paper scales was measured manually and stored digitally in CSV files for
234 further statistical analysis using R (v3.6.1, R Development Core team, 2008), setting the
235 significance level at 0.05. We first determined the data distribution using a Shapiro-Wilk test.
236 Wherever data was not normal, the specified statistic was compared against a distribution created
237 by permuting the data 1000 times (i.e. scrambling the label of the data), as opposed to comparing
238 the statistic against a parametric distribution (Ernst et al., 2004). We also report confidence
239 intervals obtained from the null distribution (obtained by permuting the data). Given the within-
240 nature of our study, we only performed permutations *within* subjects (e.g. if data was arranged in
241 a matrix were each row is one subject and each column is a measurement, we only permuted the
242 labels of the values within each row). The reported p value was obtained as the number of
243 permuted statistics that were larger than the specified statistic, divided by the total number of
permutations. We analyzed the data using a one-way repeated measures ANOVA for each scale (Mental Relaxation and Absorption Depth) with "Condition" as a 5-level factor (Baseline, Monaural Gamma, Binaural Theta, Binaural Gamma, Monaural Theta). We used *post-hoc* paired t-tests to further disentangle patterns in the data only when the F statistic reached significance. We kept the Family-wise error rate (FWER) at p = 0.05 by using Holm's sequential Bonferroni procedure (see **Table 1**).

EEG

The data was processed using the EEGLAB toolbox (Delorme A. & Makeig S., 2004) and in-house developed scripts in MATLAB. Two different analyses were conducted on the raw EEG data: subcortical (Frequency Following Response) and cortical (Auditory Steady State Response and Functional Connectivity). The pre-processing procedures for either subcortical or cortical analysis differed in filtering process, ICA decomposition and re-referencing. For subcortical analysis, data was high-pass filtered at 100 Hz and re-referenced to linked mastoids. Data used for cortical analysis was bandpass filtered between 1-100 Hz, decomposed using ICA for artifact correction purposes (Jung et al., 1998) and re-referenced to linked mastoids as a first step and then to common average reference as a final step.

260
261 Frequency Following Response (FFR)

262 Data was re-referenced to linked mastoids and high-pass filtered at 100 Hz using a zero-phase

263 Butterworth filter Order 4. Data was visually inspected for noisy electrodes, which were then

264 removed and interpolated using spherical interpolation. Finally, data was epoched into 60 events

265 (from -1 to 7 s with respect to trigger onset) and exported for further analysis. Epochs from each

266 participant were averaged and transformed into the frequency domain using an FFT. From these,

267 power was calculated as the square of the magnitude normalized using a factor of 2/N, N being

268 the length of the epoch. Frequencies of interest were extracted as the mean of 1 Hz bins around

269 the carrier frequencies (pure tones: 380, 397.5, 403.5, and 420 Hz) for the baseline and each

270 experimental condition. A baseline normalization (decibel change from baseline) was performed

271 to disentangle background dynamics from actual stimulation-related oscillations (Cohen, 2014).

272 The equation used was as follows:

273 $dB_f = 10log_{10} \left( \frac{activity_f}{baseline_f} \right)$ (1)

274 $dB_f = 10log_{10} \left( \frac{activity_f}{baseline_f} \right)$

275 where activity_f is a specific frequency power in a given experimental condition and baseline_f is the
276 average activity across the whole baseline at a given frequency (Cohen, 2014). The unit of this
277 data is decibel change from baseline.
278
After baseline normalization, all the scalp channels were averaged together to output one
normalized power score per experimental condition per participant. Frequency relevant scores
were averaged together in each experimental condition. For example, power scores for 396.5 and
403.5 Hz were averaged together for theta frequency relevant scores. This was done in order to
keep the hypothesis testing at a minimum and avoiding inflating the family-wise error rate
(FWER). These averaged scores were then exported to R (v3.6.1, R Development Core team, 2008)
for hypothesis testing.

We first determined the data distribution using a Shapiro-Wilk test setting the significance
level at 0.01. Wherever data was not normal, the specified statistic was compared against a
distribution created by permuting the data within each participant for 1000 times (Ernst et al.,
2004) and comparing the specified statistic against this distribution. As with the VAS, we report
two-tailed confidence intervals (0.95%) obtained from the null distribution. Two sets of data were
analyzed (power at relevant gamma and relevant theta frequencies) with 64 scores each (4
conditions x 16 participants) for statistical significance. A factorial (2x2) repeated measures
ANOVA was computed per relevant pure tone data set (Theta and Gamma) using beat type
(binaural, monaural) and frequency (gamma, theta) as within factors. When the interaction
between the factors was significant, we calculated post-hoc paired t-tests to further disentangle
patterns in the data (i.e., identify which experimental condition elicited the highest response). We

used Holm's sequential Bonferroni correction to keep the FWER at 0.05 (see **Table 1**).

Auditory Steady State Responses (ASSR)

Data was imported and re-referenced to linked mastoids. Data was then resampled at 512 Hz,

trimmed around the time-window of interest (8m ± 3s) and filtered twice: using a 2nd order

Butterworth band-pass filter (zero-phase) between 1-100 Hz, and an FIR notch filter at 60 Hz

(minimizing line noise). Data was visually inspected for noisy electrodes, which were then

removed.

For each participant, ICA decomposition was applied to the full recording of all conditions.

Prior to this, these aggregated files were first filtered between 1 and 80 Hz and decimated to 256

Hz. Data was then decomposed using the *runica*) function from EEGlab (which uses the Bell &

Sejnowski's (1995) ICA algorithm and Lee, Girolami & Sejnowski's extended-ICA algorithm

(2000)). After visual inspection of individual components, weight matrices were obtained from this

decomposition and applied to the original five files for artifact correction purposes (remove

components deemed as non-cortical activity, Jung et al., 1998). Missing electrodes were

interpolated after ICA artifact correction. EEG was re-referenced to common average (CAR) and
313 epoched from -1s to 8s relative to trigger onset. Finally, data was baseline corrected (using whole epoch as the baseline) and stored for further analysis.

315 Each participant's epochs were averaged and transformed into the frequency domain using an FFT. From these, power was calculated as the square of the magnitude normalized using a factor equal to 2/N, where N is the number of samples in each sequence. Frequencies of interest were extracted as the mean of 1 Hz bins around beat frequencies (7 and 40 Hz) for both the baseline and each experimental condition. As with the FFR preprocessing procedure, a baseline normalization (decibel change from baseline) was done using Equation 1.

321 After baseline normalization, all channels were averaged together to output one normalized power score per experimental condition per participant. These scores were then exported to R (v3.6.1, R Development Core team, 2008) for hypothesis testing.

324 Statistical analyses were very similar to those done for the FFR analysis. We first determined the data distribution using a Shapiro-Wilk test. Wherever data was not normal, the specified statistic was compared against a distribution created by permuting the data within each participant for 1000 times (Ernst et al., 2004) and comparing the specified statistic against this distribution. We report two-tailed confidence intervals (0.95%) obtained from this null distribution. Two statistical analysis were performed: one on normalized power scores at gamma beat frequency and one on normalized power scores at theta beat frequency (each had 64 scores
331 total, 4 conditions x 16 participants). Hypothesis testing was performed using a factorial (2x2)
332 repeated measures ANOVA with beat type (binaural, monaural) and frequency (gamma, theta) as
333 within factors. Finally, *post-hoc* paired t-tests were calculated wherever there was a significant
334 interaction between factors to identify which experimental conditions elicited the highest
335 entrainment. We used Holm's sequential Bonferroni procedure to keep the Family-wise error
336 rate (FWER) at 0.05 (see **Table 1**).

337

338 Functional Connectivity

339 Two complementary measurements of Functional Connectivity were used as indices of long-range
340 synchronization: Phase locking value (PLV; Lachaux et al., 2000)) and Imaginary Coherence (iCOH;
341 Nolte et al., 2004). On top of that, per electrode, the amplitude of the Hilbert Transform and the
342 Power of the Fourier transform were computed as local indices of synchronization. Analyses were
343 done over all traditional frequency bands (Delta: 1 - 4 Hz; Theta: 5 - 8 Hz, Alpha: 9 - 12 Hz, Beta:
344 13 - 30 Hz, Gamma: 32 - 48 Hz) and the specific beat frequencies (1Hz bins around 7Hz and 40
345 Hz). ICA corrected data (i.e. the same files used for ASSR) was imported to MATLAB to compute
346 these metrics.

347
348 Hilbert Transform and PLV

349 The phase locking value (PLV) looks at how stable phase differences are between signals (in this case, electrodes). In this particular implementation, it determines, on average, how stable phase differences between electrodes are within trials (i.e., over time). PLV is only sensitive to phase differences between signals (not their amplitude) at the cost of not being able to distinguish spurious correlation due to volume conduction at the scalp level from actual connectivity between two cortical regions (Lachaux et al., 1999).

355 To calculate it, the signal of interest was extracted by band-passing the ICA corrected data using a finite impulse response filter (FIR) around both the traditional frequency bands of interest and the specific beat frequencies: Delta (1 - 4 Hz), Theta (5 - 8 Hz), Alpha (9 - 12 Hz), Beta (13 - 30 Hz), Gamma (32 - 48 Hz), Theta Beat (6 - 8 Hz) and Gamma Beat (39 - 41 Hz). Phase and amplitude of the analytical signal (Hilbert transform) were then extracted for each EEG channel. For each pair of electrodes, the PLV was computed as a long-distance synchronization index on eight-second non-overlapping sliding windows as

$$PLV_{i,j} = \left| \frac{1}{N} \sum_{t=1}^{N} e^{i(\phi_i(t) - \phi_j(t))} \right|, \qquad (2)$$

364
365 where N is the number of samples considered in each eight second window, φ is the phase and ||
366 the complex modulus. Thus, PLV measure equates 1 if the two signals are perfectly phase locked
367 across the whole observed time window and equates 0 if they are totally unsynchronized. For each
368 electrode, the amplitude of the analytic signal (Hilbert Transform) was stored as a local
369 synchronization index. Nonparametric permutation testing was used to gauge the statistical
370 significance of the effects of binaural and monaural beats on Functional Connectivity.

371

372 Fourier Transform and iCOH

373 Coherency (Magnitude-Squared Coherence) between two EEG channels can be defined as the
374 measure of a linear relationship (i.e. correlation) between two signals (in this case, electrodes) at
375 specific frequencies. It is calculated as the cross-spectral density between channels i and j,
376 normalized by the square root of the multiplication of each of their own auto-spectrums. By
377 projecting the results into the imaginary axis, we rid the signal of both immediate (a phase
378 difference of 0) and anti-phase (phase difference of π) connectivity patterns. The imaginary part of
379 coherence is insensitive to spurious correlations due to volume conduction at the expense of
380 being sensitive to signals' amplitude (as well as phase) and being unable to disentangle spurious
381 from real immediate connectivity patterns (both in phase and anti-phase; Nolte et al. 2004).
382 Imaginary coherence measures were extracted on eight-second non-overlapping sliding windows (similar to the PLV procedure):

383
384
385
386
(3)
iCOH<sub>i,j</sub> = Σ<sub>f=f1</sub><sup>f2</sup> Im<sup>(</sup>(s<sub>i,j</sub>(f)) / (s<sub>i,i</sub>(f)s<sub>j,j</sub>(f))<sup>1/2</sup><sup>)</sup> with S<sub>i,j</sub>(f) = <x<sub>i</sub>(f)x<sub>j</sub><sup>*</sup>(f)>,

387 where x_i(f) and x_j(f) are the complex Fourier transforms of channels i and j respectively, * stands for complex conjugation, <> for the expectation value, f_1 and f_2 are the boundary of the considered frequency band, S_{i,j}(f) is the cross-spectral density between channels i and j, and Im() is the imaginary part of a complex number. As a long-distance synchronization index, iCOH values were averaged for each pair of electrodes across frequency bins using a tolerance of 1 Hz (e.g., 7 ± 1 Hz). Each electrode's autospectrum was stored as a local synchronization index. As with PLV and Hilbert Transform, nonparametric permutation testing was used to gauge the statistical significance of the effects of binaural and monaural beats on Functional Connectivity.

395
396
Cross-frequency interactions
397
In this context, we consider cross-frequency interactions as activity elicited by either experimental
398
condition (binaural or monaural) that is outside of the frequency range of the beat (either 7 Hz for
399 theta, or 40 Hz for gamma). For example, activity in the alpha frequency band elicited by theta

400 experimental conditions is considered as a cross-frequency interaction (Solcà et al., 2016).

401

402 Neurophenomenological analysis

403 To explore the relationship between mood (as self-reported by the visual analogue scales) and

404 neural patterns of Functional Connectivity, each participant's two highest rated experimental

405 conditions (binaural gamma, monaural theta...) were contrasted with the two lowest rated ones

406 for each visual analogue scale. These contrasts were then averaged across participants for each

407 scale (Mental Relaxation and Absorption Depth). Again, non-parametric permutation testing was

408 used to gauge the statistical significance of the relations between subjective experience and

409 Functional Connectivity.

410

411 Functional Connectivity: Nonparametric statistics

412 Given the exploratory nature of our study, we decided to use nonparametric permutation testing

413 to maintain the family-wise error rate (FWER) at 5%, as it offers a straightforward solution to the

414 multiple-comparisons problem (see Maris & Oostenveld, 2007 and Groppe et al., 2011). The

415 critical *t* value was determined for all Functional Connectivity analysis (PLV, iCOH, autospectrum,
416 Hilbert transform, and neurophenomenology) as follows: (1) the experimental conditions were

417 contrasted with each other (binaural vs. monaural control) and each experimental condition was

418 contrasted with baseline, (2) a *t*-test was performed at each spatial-spectral point (i.e. electrode at

419 a given frequency), (3) the statistics were normalized using z-scores, (4) the cluster statistic was

420 considered to be the sum of all *t*-values of the cluster members exceeding 3 in absolute value, (5)

421 1,000 permutations of the data were then performed to obtain a distribution of cluster statistics

422 under the null hypothesis and determine the critical values. All randomizations were done for a

423 rejection of the null hypothesis and a control of false alarm rate at p < 0.05. We decided to

424 choose this method to correct for multiple comparisons because we are mainly interested in

425 broadly distributed effects (Groppe et al., 2011). To make our inferences more conservative, only

426 contrasts that exhibit at least three significant spatio-spectral points are shown here (i.e.,

427 electrodes at a given frequency).

428
429 **Results**

430 **Frequency Following Response (FFR)**

431 To keep analyses consistent, we performed permutation-based statistics when testing for the

432 FFR's significance.

433

434 **Theta Pure Tones (396.5 & 403.5 Hz)**

435 Both theta binaural and monaural beats elicited an FFR at theta carrier frequencies with no

436 difference between them (average of 396.5 Hz and 403.5 Hz; **Figure 3a**). There was a main effect

437 of beat frequency (F=34.57, p=0.001)\*c, with no effect of beat type (F=0.004, p=0.96)\*c nor an

438 interaction between the factors (F=1.169, p=.292)\*c.

439

440 **Gamma Pure Tones (380 & 420 Hz)**

441 Gamma binaural and monaural beats elicited an FFR at gamma carrier frequencies (average of 380

442 Hz and 420 Hz; **Figure 3b**), with no difference between them. There was a main effect of
443 frequency (F=26.648, p=0.001)<sup>d</sup> with no effect of beat type (F=0.057, p=0.828)<sup>d</sup> nor an interaction

444 between the factors (F=1.248, p=0.271)<sup>d</sup>.

445

446 Auditory Steady State Response (ASSR)

447 To keep analyses consistent, we performed permutation-based statistics when testing for the

448 ASSR's significance.

449

450 Theta ASSR (7 Hz)

451 Theta binaural and monaural conditions elicited an ASSR at beat frequency, with monaural beats

452 peaking higher than binaural beats (Figure 4a). There was both a main effect of beat type

453 (F=7.669, p=0.018)<sup>e</sup> and beat frequency (F=19.263, p=0.001)<sup>e</sup>, with no interaction (F=3.928,

454 p=0.075)<sup>e</sup>.

455

456 Gamma ASSR (40 Hz)

457 Gamma beats (both binaural and monaural) elicited an ASSR at 40 Hz, with binaural gamma

458 eliciting the highest power (Figure 4b). There were main effects of both beat type (F=34.538,
p=0.001)⁴ and beat frequency (F=51.933, p=0.001)⁴, as well as an interaction between the two factors (F=44.284, p=0.001)⁴. To further disentangle these differences, three post-hoc pairwise comparisons were done using Holm's sequential Bonferroni correction test. The first two comparisons confirmed that monaural gamma peaked the highest at 40 Hz when compared to both binaural gamma (Mean difference=6.2702, t=7.23 pcorr=0.002)⁴ and monaural theta (Mean Difference=7.6589, t=7.68 pcorr=0.003)⁴. Binaural gamma condition elicited a stronger ASSR than binaural theta at 40 Hz (Mean Difference=1.1888, t=2.46, pcorr=0.025)⁴.

466

## 467 Functional Connectivity

### 468 Phase-locking value (PLV) and Hilbert Transform Amplitude

Both binaural and control conditions elicited within and cross-frequency patterns at long and short ranges. These were dependent on both beat type and frequency. In terms of local synchronization (Hilbert Transform Amplitude), Monaural Gamma stimulation drove a positive frontoparietal cluster at 40 Hz (gamma beat) when contrasted with baseline (Figure 5a, CS=20.52, p=0.019)⁹. In terms of long-distance synchronization (PLV), we found a positive left-occipital to frontoparietal cluster of activity at 40 Hz (Figure 4b, CS=49.827, p=0.041)ᵇ when contrasting binaural theta with monaural theta experimental conditions. When contrasting binaural gamma

469

470

471

472

473

474

475
476 with monaural gamma, we found four clusters of activity: a positive cluster extending around the
477 scalp at alpha frequency band (Figure 5c top left, CS=1043.455, p=0.002)h, a negative central-
478 occipital cluster at gamma frequency band (Figure 5c top right, CS=-219.57, p=0.043)h; a
479 negative frontal cluster at gamma frequency band (Figure 5c center, CS=-240.17, p=0.028)h; and
480 a negative scalp-wise cluster at 40 Hz (Figure 5c bottom left, CS=-2695.07, p=0.002)g. Consistent
481 with the last cluster, the monaural gamma condition drove a positive scalp-wise cluster when
482 contrasted with baseline (Figure 5c bottom right, CS=2493.34, p=0.004)h.

483

484 Imaginary Coherence (iCOH) and Fourier Transform Power

485 As indexed by iCOH and Fourier Transform, we only found short distance synchronization elicited
486 by binaural theta conditions. In terms of local synchronization (Fourier Power), we found two
487 clusters of activity when contrasting binaural theta condition with baseline: a negative central-
488 parietal cluster of activity at theta frequency band (Figure 6, top; CS=-11.45, p=0.036)† and a
489 positive left central-temporal cluster at 40 Hz (Figure 6 bottom; CS=36.10, p=0.018)†. None of the
490 other contrasts reached our criteria for significance (p < 0.05 and a cluster of at least three
491 sensors).

492
493 Neurophenomenological analysis

494 When taking into consideration individual differences due to subjective experience, we find neural
495 connectivity patterns associated with high Absorption Depth and Mental Relaxation that are
496 consistent across participants. When contrasting each participants' two highest and two lowest
497 rated experimental conditions in terms of mental relaxation, we found one negative frontal cluster
498 of local activity (Hilbert Transform, Figure 7a) at Theta frequency band (CS=-9.51, p=0.026), and
499 a negative long-range frontocentral to occipital cluster of activity (iCOH) at the same frequency
500 band (Figure 7c left iCOH: CS=-61.95, p=0.034). We also found a frontal to right-temporal-
501 occipital negative cluster of activity at 40 Hz (Figure 7c right iCOH: CS=-97.33, p=0.043). On the
502 other hand, we also contrasted the two top experimental conditions in which a given participant
503 rated absorption depth the highest with the experimental conditions in which they rated
504 absorption depth the lowest. We found a right temporal negative cluster of local (Fourier Power)
505 activity at 40 Hz (Figure 7b; CS=-10.17, p=0.05).

506

507 Visual Analogue Scales

508 There was no effect from auditory stimulation on subjective ratings (Figure 2). To keep analyses
509 consistent throughout the manuscript, we performed permutation-based statistics. There were no
differences between the five levels of the factor Condition (baseline, binaural gamma, binaural theta, monaural gamma, monaural theta) neither in Mental Relaxation (F=1.698, p=0.158)a nor Absorption Depth (F=1.313, p= 0.291)b. These suggest that subjective experience related to each experimental condition was not different from baseline nor from each other.

514

515

Discussion

Here, we asked whether binaural beats are able to elicit neural entrainment, and modulate mood,
in a specific fashion compared to a control rhythmic stimulus. To do so, we used a passive, single-
blind listening task where participants were exposed to both binaural and monaural control
conditions while we recorded their electrical brain activity and mood self-reports. By comparing
activity between binaural and monaural control conditions at different levels (subcortical, cortical
and self-reports), we found that binaural beats did entrain the brain, but the control condition did
so more strongly, with none of them showing an effect on mood. Furthermore, while distinct
Functional Connectivity patterns emerged for both binaural and monaural beats at different
frequencies, these are not consistent with previous literature and are not related to participants'
self-reported mood.

516

517

518

519

520

521

522

523

524

525

526
527 Binaural and monaural beats elicit subcortical

528 responses at carrier frequencies

529 Though it is commonly agreed that Binaural Beats originate in the brainstem (Oster, 1973; Moore,

530 2012; Wernick & Starr, 1968), to the best of our knowledge, we are the first ones to investigate

531 this particular stimulus at subcortical levels using EEG. As we predicted, both experimental

532 conditions (theta and gamma), regardless of beat type, elicited a frequency following response at

533 the pure tone frequencies, with no difference between monaural and binaural beats. This is

534 consistent with the existing auditory brainstem response literature, where the generated

535 subcortical responses are found to have a close spectrotemporal structure to the patterns of an

536 acoustic stimulus, such as speech syllables (Skoe & Kraus, 2010; Lehmann & Schönwiesner, 2014).

537 Furthermore, given our choice of carrier frequencies (around 400 Hz), it is very unlikely these

538 responses have a cortical origin (Coffey et al., 2016). The lack of difference between beat types

539 suggests that both stimuli are processed in a similar way at the subcortical level.

540
541 Monaural beats elicit higher cortical entrainment at

542 the beat frequency than their binaural counterparts

543 Both beat types entrained the brain at their beat frequencies, with monaural conditions eliciting

544 the highest response when compared to binaural conditions. In terms of Theta beat frequency,

545 both Jirakittayakorn & Wongsawat (2017) and Karino et al. (2006), found similar entrainment

546 using Theta binaural beats with exposure times between five and ten minutes. Following Garcia-

547 Argibay's conclusions (2018), relatively long exposure time and non-masked binaural beats (i.e.,

548 not using white or pink noise to mask them) seem to optimize the responses to the beats. In

549 terms of Gamma beat frequency, we successfully replicated previous studies (Schwarz & Taylor,

550 2005; Draganova et al., 2007; Ross et al., 2014): both binaural and monaural gamma beats entrain

551 cortical activity at 40Hz, but binaural beats elicit less power at the beat frequency. One possible

552 explanation as to why binaural beats elicit less power than monaural beats is that the entrainment

553 we measure at the cortical level might be caused by the perceived rhythmicity, and not the

554 binaural beat itself. Subjects' tended to report that the modulation (i.e., the beat) intensity in

555 binaural beats was weaker than that of the monaural beat. The ASSR correlates with stimulus'

556 loudness (Van Eeckhoutteet al., 2016; Picton et al., 2007; Lins & Picton, 1995), which might explain

557 the difference in ASSR power in the frequency domain. Furthermore, we both root mean squared
558 (rms) normalized and carefully calibrated our stimuli, precluding loudness as an explanatory factor
559 for the difference in ASSR power. Using proper statistical and experimental control, we have
560 shown that binaural beats entrain the cortex more weakly than other non-binaural rhythmic
561 stimuli, such as monaural beats.

562

563

Binaural and monaural beats fail to modulate mood

564 Echoing previous reports, we did not find evidence of binaural beats, nor monaural beats,  
565 modulating cognitive states or mood: López-Caballero & Escera (2017) found no emotional  
566 regulation due to binaural beats as indexed by changes in heart rate and skin conductance, while  
567 Gálvez et al. (2018) found no modulation of anxiety as indexed by the State Anxiety Inventory  
568 (SAI). This stands in contrast with other reports where cognitive performance and mood were  
569 successfully modulated by binaural beats (Wahbeh et al., 2007, Le Scouarnec et al., 2001,  
570 Padmanabhan et al., 2005; Isik et al., 2017, Reedijk et al., 2013; Reedijk et al., 2015, Garcia-Argibay  
571 et al., 2018).

572
573 Both beat types elicit differential short-range connectivity patterns

574

575 Monaural and binaural beats affect short range electrode level connectivity patterns differentially. We only found a significant short-range effect in monaural gamma and binaural theta conditions, which suggests that both beat type and frequency are non-trivial parameters of stimulation. Furthermore, due to both binaural and monaural beats producing such short-range effect, we can rule out conclusions such as this activity being a by-product of sustained listening or binaural integration. Our gamma findings are in accordance with those from Becher et al. (2015). Using both intracranial and scalp EEG, they found peak EEG power at 40 Hz (gamma beat) at the scalp electrodes using the power of the envelope of the signal (i.e., the power of the Hilbert Transform). They found a similar effect in temporo-lateral intracranial electrodes, suggesting this entrainment originates in auditory cortices. Furthermore, they found a significant decrease in EEG power at 5 Hz (theta frequency) in temporo-basal anterior and posterior areas, which might explain the local activity in our participants. This activity could be in line with a dipole from auditory cortices pointing upwards, which suggests there is only one active cortical source. On the other hand, binaural theta conditions elicited a positive parietal cluster at 40 Hz (see cross
589 frequency section). The functional meaning (if any) of these short-range patterns remains unclear
590 as we found no difference in participants' self-reports.

591

592

Both beats elicit long-range connectivity patterns
indexed only by PLV

593

594

595

596

597

598

599

600

601

602

603

604

To investigate long-range connectivity, we used two different but complementary statistics: the imaginary part of coherence and the phase locking value. iCOH gets rid of all interactions that have zero to very small time delays, while the PLV quantifies how consistent phase differences are between electrodes. We only found Functional Connectivity patterns indexed by PLV. Because of this, it is unclear whether these patterns are due to one source being propagated around the scalp, or there are multiple sources active with an almost zero-time delay between them (Nolte et al., 2004). We see differential effects between beat types and frequencies, as well as cross-frequency interactions (discussed in the next section). Only gamma experimental conditions elicited within frequency activity: Monaural gamma elicited a cluster of scalp-wise connectivity that is not consistent with previous research. Using intracranial electrodes, Becher et al. (2015) showed phase desynchronization at mediotemporal areas using a 40 Hz monaural beat, whereas
605 we found scalp-wise synchronization using a very similar stimulus. Furthermore, Schwarz & Taylor
606 (2005) showed that there was a delay of several milliseconds in the activity elicited across the
607 fronto-occipital axis, using a 40 Hz monaural beat, suggesting multiple cortical sources of activity.

608 Because the iCOH analysis did not reveal significant connections between electrodes, it is unclear
609 whether the phase differences Schwarz & Taylor (2005) report are due to volume conduction or
610 the connectivity patterns we found are caused by multiple, but tightly synchronized, brain regions.

611 Because we did not find any difference in subjective reports, the functional meaning (if any) of this
612 activity remains unclear.

613

614 Binaural beats elicit cross-frequency connectivity
615 patterns

616 Binaural theta conditions elicit a front to back, cross-frequency connectivity pattern at gamma
617 beat frequency (40 Hz) while binaural gamma elicits a widespread connectivity pattern at alpha
618 frequency. In line with our results, several groups have found binaural beats eliciting activity
619 outside of the frequency range of the beat. Despite this, these findings do not seem to be
620 consistent: using theta binaural beats, Gao et al. (2014) found a decrease in relative beta power
over left temporal areas and Ioannou et al. (2015) report no significant difference from theta
binaural beats at other frequency bands.

We found that binaural theta beats elicit activity at higher frequencies (40 Hz), while
binaural gamma beats elicit activity at lower frequencies. This cross-frequency coupling (low
frequency driving a higher frequency and a higher frequency driving a lower frequency) could be
evidence for large-scale integration being enhanced by binaural beats. Varela et al. (2001) argue
that slower rhythms (such as theta) provide a temporal framing for faster oscillations. For
example, gamma oscillations are thought to leverage this slower temporal framing during
successive cognitive moments of synchronous assemblies where memory is consolidated (Osipova
et al., 2006; Burke et al., 2013; Lisman & Jensen, 2013). We did not investigate cognitive processes
directly, but there is evidence that binaural beats impact memory as a function of beat
frequency—beta frequencies seems to enhance it (Lane et al., 1998; Kennerly et al., 1994;
Beauchene et al., 2016; Gálvez et al., 2018) while theta frequencies have an inconsistent effect
(negative in some cases: Garcia-Argibay et al., 2017, Beauchene et al., 2016; and positive in others:
Ortiz et al., 2008). In our specific experiment, our stimuli failed to modulate mood as self-reported
by participants, but these cross-frequency interactions might provide a framework explaining why
binaural beats are able to modulate cognitive performance in other reports.

638
639 Individual differences shed light on connectivity

640 patterns associated with specific cognitive states

641 We found a consistent pattern of deactivation and desynchronization related to
642 participants' self-reports of Mental Relaxation and Absorption Depth. High Mental Relaxation
643 was associated with theta frequencies in a frontal cluster of local desynchronized activity, and with
644 a front to back desynchronization of activity at both theta and gamma indexed by iCOH. This
645 suggests this activity is robust and not due to volume conduction. Absorption Depth, on the other
646 hand, was associated with one cluster of activity around temporal areas. Changes in the anterior
647 and frontal midline in theta power have been related to emotionally positive states (Aftanas &
648 Golocheikine, 2001), and meditation-related states (Baijal & Srinivasan, 2010). Baijal & Srinivasan
649 (2010) found a similar deactivation pattern in parietal and occipital areas accompanied by frontal
650 theta activation associated with meditative states. On the other hand, Hinterberger et al. (2014)
651 found similar central and parietal gamma deactivation patterns during meditative tasks. Taking all
652 this information together, our Functional Connectivity results point at a state similar to meditation
653 characterized by heightened Mental Relaxation and Absorption Depth. Despite this, we were not
654 able to relate this specifically to any of our experimental conditions.

655
656

Limitations and Future Directions

657

Though several of our findings are consistent with existing literature, we acknowledge that we

658

only recruited 16 people and that these findings should be replicated with higher sample sizes.

659

We instructed participants to close their eyes during the whole experiment, which might have not

660

been ideal, especially because a couple of participants reported high drowsiness and two reported

661

falling asleep. Furthermore, we did not have a specialist check our participants for any hearing

662

loss. This could be a co-founding variable. Our design, however, was a within design: each

663

participant was exposed to the four experimental conditions. Because participants were only

664

compared against themselves (statistically speaking), this co-founding effect remained constant

665

for each participant. Future binaural beats studies should look at different ways of indexing

666

connectivity at both scalp and source level (Solcà et al, 2016). The study of binaural beats will also

667

greatly benefit from the transition of a mass univariate statistical framework (such as the one used

668

here) to a multivariate statistical framework (see McIntosh & Mišić, 2013). Fields such as Graph

669

Theory present promising opportunities to determine the characteristics of cortical networks and

670

summarizing large numbers of data points into a few statistics to truly understand how binaural

671

beats affect the brain (Ioannou et al., 2015; Ala et al., 2018). On a more technical note, we did not

672

alternate the polarity of the stimulus of the binaural beats (a common practice in the Auditory
673 Brainstem Response literature), which might have affected the brainstem responses we found.

674 Sometimes, noise from the audio transducer or the cochlear microphonic (a potential believed to

675 be generated primarily by outer hair cells; Santarelli et al., 2006) can bleed into the EEG electrodes,

676 introducing artifactual responses into the EEG trace. To minimize this, one can alternate the

677 polarity of the stimulus between each presentation, i.e., by presenting the original stimulus

678 followed by a version of the stimulus that has been multiplied by minus one and repeating this

679 over and over. After this, the EEG responses to both polarities can be either added or subtracted

680 together (each method has its advantages and disadvantages). For an in-depth discussion of this,

681 see Skoe & Kraus, 2010. The transducer with which the stimuli were presented to the participants

682 was magnetically shielded, a procedure that is known to minimize stimulus artifacts (Skoe &

683 Kraus, 2010). Furthermore, Skoe & Kraus (2010) report that '[their] results have been internally

684 replicated with single-polarity stimuli', supporting our claim that the responses we report here

685 come from the brainstem and are not artifactual.

686 Binaural beats have been long used in psychoacoustics, although the claims and studies

687 relating their cognitive effects are more recent. A great deal of confusion subsides regarding their

688 latter use. As Garcia-Argibay et al. (2018) concluded, there are several mediating variables—such

689 as beat frequency, exposure time or stimulus masking—that are not always clearly reported.

690 Furthermore, we conclude that there are two important factors that are usually considered as
trivial: proper EEG analysis and the use of a proper control condition. Future binaural beats studies should be mindful of these variables and report them accordingly. Several studies that did not find any entrainment to the beat frequency of binaural beats (e.g., López-Caballero & Escera, 2017) did not use standard normalization practices (for an in-depth discussion of these procedures, see Cohen, 2014, Ch. 18). The human EEG spectrum exhibits a 1/f power scaling (similar to pink noise). By properly normalizing data using a baseline condition, we ensure that all data (i.e. the different frequency bands) will have the same scale, and we are appropriately disentangling background and task-unrelated dynamics (Cohen, 2014). Researchers should be mindful of the analysis approach they are taking, as well as using an appropriate control condition to truly elucidate whether binaural beats are a special kind of stimulus or their advantages are due to stimulus properties (such as the rhythmicity in the signal).

Future studies should carefully choose exposure time, the performance or mood measurement and the frequency of the beat. As Garcia-Argibay et al. (2018) concluded, higher exposure times are associated with larger effect sizes. Nevertheless, whether several sessions will present an increased entrainment and performance/mood boost, and whether there are carryover effects that are sustained even after stimulation ceases, are still open questions. Binaural beats have previously been reported to modulate memory and attention performance (Ortiz et al., 2008; Reedijk et al., 2015), as well as anxiety (Isik et al., 2017) and analgesia (Zampi, 2015). Our findings
709 provide one plausible base explanation as to why memory and attention performance could be
710 modulated by binaural beats (i.e. binaural beats elicit cross-frequency interactions). Future studies
711 should focus on measuring cognitive performance on both attention and memory tasks, and
712 mood regulation related to anxiety and pain perception. Participants should be exposed to the
713 stimulation both before and after the task (Garcia-Argibay et al., 2018). Finding neural correlates
714 of binaural beats that uniquely correlate with cognitive performance in attention and memory
tasks could help better elucidate whether binaural beats can be used for cost-effective cognitive
715 enhancement. Finally, the choice of frequency is not trivial: alpha, beta, and gamma were reported
716 to provide positive effects in memory tasks, while theta frequency seems to hinder effects in most
cases (Garcia-Argibay et al., 2018).
718

719

Conclusions

720

721 Using a factorial experimental design and a single-blind, passive listening task, we aimed to
722 elucidate the impact of binaural beats on the brain. We did not find evidence for binaural beats
723 modulating mood or entraining the brain more strongly than "non-binaural" beats. We did find,
724 however, that binaural beats elicited differential patterns of connectivity, compared to the
725 monaural beat control. Whether these connectivity patterns have a functional meaning (in terms
726 of cognitive enhancement and mood modulation) remains an open question. The present
727 research shares a useful framework for further exploring the mechanisms and efficacy of sound-
728 based mood regulation practices. By using a neuroscientific lens with statistical and scientific rigor
729 at its core, we can study these "alternative" practices to ensure the general public makes
730 informed, evidence-based, decisions.

731

732

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<table><thead><tr><th></th><th>Data Structure</th><th>Statistical Test</th><th>C.I.</th></tr></thead><tbody><tr><td>a</td><td>Not normal (W=0.9, p=0.0001)</td><td>Permutation One-Way repeated measures ANOVA</td><td>0.13, 3.04</td></tr><tr><td>b</td><td>Normal (W=0.96, p=0.013)</td><td>Permutation One-Way repeated measures ANOVA</td><td>0.09, 3.08</td></tr><tr><td>c</td><td>Normal (W=0.99, p=0.86)</td><td>Permutation Factorial (2x2) repeated measures ANOVA</td><td>0.001, 5.6</td></tr><tr><td></td><td></td><td>Frequency</td><td>0.001, 5.6</td></tr><tr><td></td><td></td><td>Beat type</td><td>0.002, 5.99</td></tr><tr><td></td><td></td><td>Interaction</td><td>0.001, 5.67</td></tr><tr><td>d</td><td>Not normal (W=0.96, p=0.05)</td><td>Permutation Factorial (2x2) repeated measures ANOVA</td><td>0.001, 5.46</td></tr><tr><td></td><td></td><td>Frequency</td><td>0.001, 6.1</td></tr><tr><td></td><td></td><td>Beat type</td><td>0.001, 6.1</td></tr><tr><td></td><td></td><td>Interaction</td><td>0.0003, 5.45</td></tr><tr><td>e</td><td>Not normal (W=0.492)</td><td>Permutation Factorial (2x2) repeated</td><td></td></tr></tbody></table>
<table><tbody><tr><td>p=1.549e-13)</td><td>measures ANOVA</td><td></td></tr><tr><td></td><td>Frequency</td><td>0.001, 6.31</td></tr><tr><td></td><td>Beat type</td><td>0.001, 6.66</td></tr><tr><td></td><td>Interaction</td><td>0.001, 6.43</td></tr><tr><td>f Not normal (W=0.625, p=1.631e-11)</td><td>Permutation Factorial (2x2) repeated</td><td></td></tr><tr><td></td><td>measures ANOVA</td><td></td></tr><tr><td></td><td>Frequency</td><td>0.001, 7.1</td></tr><tr><td></td><td>Beat type</td><td>0.001, 7.68</td></tr><tr><td></td><td>Interaction</td><td>0.001, 6.26</td></tr><tr><td></td><td>Post-hoc permutation paired t-test<br>(Monaural Gamma vs Monaural Theta)</td><td>-2.02, 2.39</td></tr><tr><td></td><td>Post-hoc permutation paired t-test<br>(Binaural Gamma vs Monaural Gamma)</td><td>-2.4, 2.23</td></tr><tr><td></td><td>Post-hoc permutation paired t-test<br>(Binaural Gamma vs Binaural)</td><td>-2.1, 2</td></tr><tr><td>g Spatial-spectral-temporal<br>(Hilbert Transform)</td><td>Non-parametric, cluster-based<br>permutation tests</td><td></td></tr><tr><td></td><td>Monaural Gamma vs Baseline at 40 Hz</td><td>0.57, 4.07</td></tr></tbody></table>
<table><tbody><tr><td rowspan="11">h</td><td rowspan="11">Spatial-spectral-temporal<br>(PLV)</td><td>Non-parametric, cluster-based</td></tr><tr><td>permutation tests</td></tr><tr><td>Binaural Theta vs Monaural Theta at 40 Hz</td><td>2.55, 5.99</td></tr><tr><td>Binaural Gamma vs Monaural Gamma at alpha</td><td>2.5, 6.11</td></tr><tr><td>Binaural Gamma vs Monaural Gamma at Gamma</td><td>2.5, 6.11</td></tr><tr><td>Binaural Gamma vs Monaural Gamma at Gamma at 40 Hz</td><td>2.69, 6.62</td></tr><tr><td>Binaural Gamma vs Monaural Gamma at Gamma at Baseline</td><td>2.79, 6.99</td></tr><tr><td>Binaural Gamma vs Baseline at 40 Hz</td><td>0.85, 4.89</td></tr><tr><td>Binaural Gamma vs Baseline at 40 Hz</td><td>0.85, 4.89</td></tr><tr><td>i</td><td>Spatial-spectral-temporal<br>(Fourier Transform)</td><td>Non-parametric, cluster-based</td></tr><tr><td></td><td>permutation tests</td></tr><tr><td></td><td>Binaural Theta vs Baseline at theta</td><td>0.85, 4.89</td></tr></tbody></table>
<table><tr><td colspan="3">Binaural Theta vs Baseline at 40 Hz</td><td>-1.39, 4.06</td></tr><tr><td>j</td><td>Spatial-spectral-temporal</td><td>Non-parametric, cluster-based</td><td></td></tr><tr><td colspan="4">(Neurophenomenological) permutation tests</td></tr><tr><td></td><td></td><td>MR - Negative frontal cluster at theta</td><td>0.93, 3.25</td></tr><tr><td></td><td></td><td>MR - Negative frontocentral to occipital</td><td>3.2, 6.38</td></tr><tr><td></td><td>at</td><td></td><td></td></tr><tr><td></td><td>theta</td><td></td><td>2.54, 5.86</td></tr><tr><td></td><td></td><td>MR - Negative frontal to right temporal</td><td></td></tr><tr><td></td><td></td><td>occipital at 40 Hz</td><td>-1.45, 4.03</td></tr><tr><td></td><td></td><td>AD - Negative right temporal at 40 Hz</td><td></td></tr></table>

930 Table 1: Statistical Table. Description of statistical tests and confidence intervals for each of the

931 results reported on the main text.
<figure><img src="image_10.png" /></figure>

**Figure 1.** Beats: Signal, Presentation method, Fast Fourier Transform (FFT) and FFT of Hilbert Transform. Each column represents one experimental condition. (Signal and Presentation rows) Binaural beats are created by dichotically presenting two pure tones with a slight frequency mismatch (Red color = right ear). Monaural beats are created by digitally summing these tones and presenting the resulting signal diotically. (FFT of Signal) Stimuli were analyzed using a Fourier transform to obtain their frequency composition. (FFT of Hilbert Transform) The FFT of
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the Hilbert transform (i.e. the analytic signal) was computed to tap into the spectral information of
the envelope of the signal (the beat frequency). The frequency of the envelope of the summed
tones encodes beat frequency (e.g. 403.5 - 396.5 = 7 Hz for Theta). This information, however, is
only encoded in monaural beats because they are digitally summed.

<figure><img src="image_11.png" /></figure>

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**Figure 2. Visual Analogue Scales: Mental relaxation and absorption depth.** Each data point represents one participant's self-reported score. Mean is plotted as a black horizontal line ± standard error of the mean.
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

**Figure 3.** Frequency Following Response (FFR) to carrier pure tones. Plotted here: violin plots with median (white dots), quartile (thick black line) and whisker (thin black line) values. Please note the scale is decibel change from baseline, a logarithmic scale where each 3 dBs represent a difference of a factor of 2. Each violin plot represents all participants' baseline-normalized (dB) averages of the power around a 1 Hz bin (e.g. 396.5 ± 0.5 Hz) at beat carrier frequencies (e.g. 396.5 and 403.5 Hz were averaged together for theta conditions). This power was obtained from the average activity at all channels of each participant. Asterisks above lines linking conditions denote a significant difference between them (p < 0.05). (a) Frequency Following Response elicited at theta-carrier frequencies (average of 396.5 and 403.5 Hz). (b) Frequency Following Response elicited at gamma-carrier frequencies (average of 380 and 420 Hz).
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

**Figure 4.** Auditory Steady State Responses (ASSR) to beat frequency. Plotted here: violin plots with median (white dots), quartile (thick black line) and whisker (thin black line) values. Please note the scale is decibel change from baseline, a logarithmic scale where each 3 dBs represent a difference of a factor of 2. Each violin plot represents all participants' baseline-normalized (dB) averages of the power around a 1 Hz bin (e.g. 7 ± 0.5 Hz) at beat frequencies (either 7 or 40 Hz) obtained from the average activity at all channels for each participant. Asterisks above lines linking conditions denote a significant difference between them (p < 0.05). Please note that there was an outlier in these graphs that was taken out for visualization purposes (a participant with data points at around -30 dB). (a) Cortical activity elicited at 7 Hz. (b) Cortical activity elicited at 40 Hz.
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a

Hilbert Transform Amplitude: Positive Cluster
Monaural Gamma vs Baseline (Gamma Beat)

<figure><img src="image_16.png" /></figure>

c

PLV: Positive Cluster
Binaural Gamma vs Monaural Gamma (Alpha)

<figure><img src="image_17.png" /></figure>

PLV: Negative Cluster 1

Binaural Gamma vs Monaural Gamma (Gamma)

<figure><img src="image_18.png" /></figure>

PLV: Negative Cluster 2
Binaural Gamma vs Monaural Gamma (Gamma)

<figure><img src="image_19.png" /></figure>

b

PLV: Positive Cluster
Binaural Theta vs Monaural Theta (Gamma Beat)

<figure><img src="image_20.png" /></figure>

PLV: Negative Cluster
Binaural Gamma vs Monaural Gamma (Gamma Beat)

<figure><img src="image_21.png" /></figure>

PLV: Positive Cluster
Monaural Gamma vs Baseline (Gamma Beat)

<figure><img src="image_22.png" /></figure>

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**Figure 5. Contrast topographies for Phase-locking value (PLV) and Hilbert Transform amplitude.** Topographies were averaged across participants and compared to either baseline or between beat type (binaural vs monaural). Both statistics (Hilbert Transform Amplitude and PLV) were normalized using z scores. We only show contrasts that exhibit at least three significant electrodes (depicted as small white squares). Frequency band limits are as follows: Delta (1 - 4 Hz), Theta (5 - 8 Hz), Alpha (9 - 12 Hz), Beta (13 - 30 Hz), Gamma (32 - 48 Hz), Theta Beat (6 - 8 Hz) and Gamma Beat (39 - 41 Hz). **(a)** Hilbert transform amplitude used as a local synchronization
1018 **index**. The color bar indicates T-values from student's test. (b) **Phase locking value used as an index of long-distance synchronization between electrodes during theta conditions.** Red lines indicate a significant positive phase locking value (PLV) between two electrodes. (c) **Phase locking value used as an index of long-distance synchronization between electrodes during gamma conditions.** Red lines indicate a significant positive phase locking value (PLV) between two electrodes while blue lines indicate a negative one.

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Fourier Transform Power: Negative Cluster
Binaural Theta vs Baseline (Theta)

<figure><img src="image_23.png" /></figure>

Fourier Transform Power: Positive Cluster
Binaural Theta vs Baseline (Gamma Beat)

<figure><img src="image_24.png" /></figure>

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1027 **Figure 6.** Fourier transform power used as a local synchronization index in Theta conditions.

Topographies were averaged across participants and compared to baseline. Fourier Transform Power was normalized using z scores. We only show contrasts that exhibit at least three significant electrodes (depicted as small white squares). Frequency band limits are as follows: Delta (1 - 4 Hz), Theta (5 - 8 Hz), Alpha (9 - 12 Hz), Beta (13 - 30 Hz), Gamma (32 - 48 Hz), Theta Beat (6 - 8 Hz)
and Gamma Beat (39 - 41 Hz). The color bar indicates T-values from student's test. Please note
that no iCOH contrasts were significant.

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<figure><img src="image_25.png" /></figure>

**Figure 7. Neurophenomenological analysis: correlates between subjective experience and EEG connectivity patterns.** Each participant's two highest rated (Mental Relaxation and Absorption Depth) experimental conditions (binaural gamma, monaural theta...) were contrasted with the two lowest rated conditions. These contrasts were then averaged across participants for each separate scale (Mental Relaxation and Absorption Depth). All statistics were normalized

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1049 using z scores. We only show contrasts that exhibit at least three significant electrodes here (depicted as small white squares). Frequency band limits are as follows: Delta (1 - 4 Hz), Theta (5 - 1050 8 Hz), Alpha (9 - 12 Hz), Beta (13 - 30 Hz), Gamma (32 - 48 Hz), Theta Beat (6 - 8 Hz) and Gamma 1051 Beat (39 - 41 Hz). (a) Hilbert transform amplitude used as a local synchronization index. The 1052 color bar indicates T-values from student's test. (b) Fourier transform power used as a local 1053 synchronization index. The color bar indicates T-values from student's test. (c) Imaginary 1054 Coherence used as an index of long-distance synchronization between electrodes. Blue lines 1055 indicate a significant negative iCOH between two electrodes. 1056