On the Role of Interaural Level Differences in Low-Frequency Pure-Tone Lateralization

Summary While the “Duplex Theory” of sound localization is often interpreted such that low-frequency sounds are localized mainly based on interaural phase di ﬀ erences, and high-frequency sounds based on interaural level di ﬀ erences, some studies have shown an interaction of low-frequency interaural phase and level di ﬀ erences. Using a psychoacoustic lateralization experiment, the present study demonstrates that small interaural level di ﬀ erences are indeed e ﬀ ective in resolving lateralization in the ambiguous range of interaural phase di ﬀ erences at all tested frequencies. These ambiguities occur in free-ﬁeld conditions at frequencies above about 500Hz, which is shown by analyzing the magnitude of interaural di ﬀ erences as they occur in typical free-ﬁeld scenarios. On that basis this study further concludes that naturally occurring interaural level di ﬀ erences on their own are su ﬃ cient to correctly attribute sound sources to left or right in many conditions, even at frequencies below 500Hz.


Introduction
In his influential 1907-paper [6], Lord Rayleigh introduced the basis for what has come to be known as the "Du-plexT heory" of sound localization. Essentially,t he duplextheory states that low-frequencysounds are localized predominantly based on interaural phase differences, as the shadowing effect of the head only results in small interaural leveld i ff erences in that frequencyr ange. Highfrequencysounds, on the other hand, are mainly localized using interaural leveldifferences, as the impact of the head shadowing effect on interaural leveld i ff erences increases with frequency. Additionally,i nteraural phase differences become ambiguous at about 700 Hz, where the stimulus wavelength approximately equals the head circumference. Interestingly,the auditory system is able to detect interaural phase differences past the ambiguity limit up to about 1300 Hz [1], and the sensitivity to interaural leveld i ff erences at lowf requencies wasf ound to be similar to the interaural leveld i ff erence sensitivity at high frequencies [13]. These findings suggest an interaction between interaural leveld i ff erences and interaural phase differences in the low-frequencyrange. The nature of this interaction has been studied extensively [7,2] and, depending on their sign, interaural leveld i ff erences were found to facilitate or counteract the lateralization evoked by interaural phase Received7March 2018, accepted 14 August 2018 differences. Due to the small magnitude of naturally occurring low-frequencyinteraural leveldifferences in free-field conditions, their influence is often neglected. At the same time, additional cues are necessary in order to resolveinteraural phase difference ambiguities at sound frequencies above some 700 Hz in free-field conditions -t he interaural leveld i ff erence being ap otential and well-suited candidate. To our knowledge, no study has yet systematically investigated the resolving impact of interaural leveldifferences on lateralization, especially of small interaural level differences as theynaturally occur in free-field conditions or various natural listening environments. To that end, this study uses ap ure-tone lateralization paradigm to investigate the influence of small interaural leveld i ff erences on the lateralization evoked by interaural phase differences. Aspects of the practical relevance of the results are discussed in the light of typical free-field interaural leveldifferences.

Methods
In order to evaluate ap otential interaction between interaural leveldifferences and interaural phase differences, we conduced al eft-right task experiment [10]. Tone impulses (700 ms, including 160 ms Gaussian onset and offset slopes)w ere presented dichotically at one-octave spaced frequencies between 125 Hz and 1kHz, with interaural phase differences introduced by shifting the starting phase of the tone at one ear relative to the other,w ithout changing the stimulus envelope. The sound-pressure level (SPL)i nt he diotic condition at 125 Hz wass et to 72 dB SPL, with the headphones calibrated based on their nominal sensitivity at 1kHz. The levels at all other frequencies were determined based on the equal-loudness contours according to ISO 226:2006 [15], with the aim of approximately balancing loudness across the conditions. interaural leveld i ff erences were then introduced by amplifying the left and right signals by half the desired interaural leveld i ff erence, respectively.2 1e venly spaced interaural phase differences between −π and π were combined with the interaural leveldifferences 0, ±0.5, ±1, ±1.5, ±2, ±4, ±8dB. At frequencies below1kHz, each interaural phase difference wascombined with only the interaural leveldifferences with the sign of the interaural phase difference, while at 1kHz, all interaural phase differences were combined with all interaural leveld i ff erences. Each stimulus condition wasp resented and evaluated ten times in random order.The results were collected in four sessions per subject (one session per frequency),each lasting on average 48 min, with ashort break after half the stimuli.
Tenu npaid, naïve with respect to the experiment, and inexperienced volunteers (23-41 years, median 27 years, all right handed)w ith no reported hearing deficits and absolute thresholds within ±15 dB of ISO 226:2006 [15] took part in the experiment. The subjects were seated in as ound-insulating booth and were presented with the stimuli using the same pair of circumaural headphones (HD650; Sennheiser electronic GmbH, Wedemark). The specifich eadphones were selected due to their lowi nterindividual and intra-individual variability based on [9]. Theyw ere interaurally equalized with respect to amplitude and phase [11], so that the relevant sound-pressure time functions measured on ac oupler according to IEC 60318-1:2009 [14] were identical within the accuracyo f the measurement procedure. The subjects were asked to sit upright, face as pecificw all and indicate, by pushing one of twobuttons, whether the hearing sensation occurred "left or right", with no further explanation [10]. Prior to the experiment and after reading the written instructions, a basic understanding of the instructions wasverified within as hort example experiment. Answers to potential procedural questions were limited to "yes" or "no", and the example wasrepeated until the subject felt comfortable with the procedure. No further instructions were provided.

Analysis of interaural phase differences and interaural leveld ifferences
Forapproximating the typical magnitudes of naturally occurring free-field interaural phase differences and interaural leveld i ff erences in human listeners, free-field binaural transfer function pairs of 139 subjects from the freely available database of the acoustics research institute [4] were analyzed. The transfer functions were estimated by individually calculating the discrete Fourier transforms of the finite impulse responses corresponding to the left and right ears that reflect the geometric arrangement of interest (variation of the sound-incidence azimuth in the horizontal plane at afi xeds ource distance of 1.2 m).T he in-teraural phase differences and interaural leveld i ff erences for each position were estimated by subtracting the corresponding phase and levelvalues of specificsingle discrete Fourier transform bins. The results are depicted in terms of the arithmetic mean values overt he dataset in Figure 1a.
Additionally,F igure 1b shows the frequency-dependent maximum values overa ll included source positions. The dashed lines indicate possible descriptive approximations, where interaural phase differences corresponding to 700 µs delay appear to fit the data frequency-independently well. Consequently,i nteraural phase differences representing ±700 µs are taken as an approximation of the range of naturally-occurring free-field interaural phase differences (abbrev.:natural range). Regarding interaural leveldifferences, frequencies below500 Hz result in maximum interaural leveldifferences around 4.5 dB, while at frequencies of 500 Hz and above,the maximum interaural leveldifference increases by about 6dB/octave.Asthe results depend on measurement setup and transfer function definition, the data are considered an approximation of the actual values.
In order to evaluate whether the supportive effect of interaural leveldifferences is relevant in natural settings, the average magnitudes of interaural leveldifferences and interaural phase differences, as theyw ould occur in at ypical free-field setup, were analyzed. The first twocolumns of Figure 1a showi nterindividually averaged interaural phase differences and interaural leveldifferences as functions of azimuth for different stimulus frequencies. Forthe three lower frequencies, both interaural leveld i ff erence and interaural phase difference showanapproximately sinusoidal dependence on azimuth, with the maximum interaural phase difference below π.At937.5 Hz, the maximum interaural phase difference is about 1.4π,a nd interaural phase difference ambiguity is visible, as multiple azimuths correspond to the same interaural phase difference. The third column of Figure 1a shows interaural leveldifferences plotted against the corresponding interaural phase differences, for each azimuth. This representation visualizes that interaural phase difference ambiguities can be resolved by interaural leveldifferences.

Results and Discussion
Figure 2e xemplarily shows the inter-individual medians of the left-right experiment for 500 Hz (left)a nd 1kHz (right), represented as the fraction of stimuli rated on the right.A sfound in previous experiments [10], the results for the twofrequencies below500 Hz only showed minor differences to those obtained at 500 Hz so that the results will be discussed based on the twof requencies shown in Figure 2. The columns in this figure represent the frequencies of the tone impulses, the rows indicate selected interaural leveldifference conditions (label on the right). At 0i nteraural phase difference and 0i nteraural leveld iff erence (horizontal centers, first row),t he subject group responded at chance level. With increasing interaural phase difference (at0i nteraural leveld i ff erence; towards the right), the fraction of hearing sensation reported on the Figure 1. (a) Averageh orizontal-plane interaural phase differences (first column)and interaural leveldifferences (second column), estimated from 139 binaural impulse response pairs of the acoustics research institute database [4]. The third column shows each interaural leveldifference plotted against the corresponding interaural phase difference. (b)M aximum estimated horizontalplane interaural leveld i ff erences (left)a nd interaural phase differences (right)a sf unctions of frequency. The dashed contours represent descriptive approximations: line with 6dB/octave for maximum high-frequencyi nteraural leveld i ff erences (left)a nd interaural phase differences corresponding to 700 µs delay for maximum interaural phase differences (right). right increases, until saturating at 100%. At large interaural phase differences, the fraction of responses to the right starts to decrease again, likely due to an ambiguity introduced by interaural phase difference wrapping. In the 500 Hz condition, the ambiguity effect starts to manifest itself in the data approximately at the limits of the natural range (dashed vertical lines in Figure 2).A t1 000 Hz, however, 0.7 ms corresponds to an IPDo fa pproximately 1.4π (abscissa limits in Figure 2),r esulting, according to Figure 2, more or less in al eft/right reversal of the leftright task results. This appears plausible, as an interaural phase difference of 1.4π is identical to −0.6π.O pposed to the 500 Hz conditions, ambiguity effects occur clearly within the natural range. As the ambiguity effects start to be visible at interaural phase differences at the limits of the natural range at 500 Hz and lie inside this range at 1kHz, it appears reasonable to assume that ambiguity effects within the natural range become perceptually relevant at frequen- Figure 2. Results of the left-right task experiment for 500 Hz and 1kHz. Shown are the interindividual medians with 25% and 75% percentiles for all interaural phase differences (abscissae), combined with selected interaural leveldifferences (rows). The vertical dashed lines indicate the interaural phase differences equivalent to ±700 µs. Duplicate interaural phase differences (i.e.|IPD|≥π)are shown lighter. cies of 500 Hz and above,w ith an amount that increases with frequency.
Each rowinFigure 2shows the results for aselected interaural leveld i ff erence condition. The sign of the added interaural leveldifference is always identical to the sign of the interaural phase difference (e.g −2dBa t− π), so that mostly non-conflicting cues were presented. As expected from literature [2], the addition of those interaural level differences mostly supports the lateralization due to the interaural phase difference (rows2,3,and 4ofFigure 2). At 2dB, this effect is already clearly visible, and 8dBi s sufficient to more or less fully resolvet he ambiguity effects with the intermediate interaural leveldifference values (not shown)following this trend. Analyzing the magnitudes of the interaural leveld iff erences calculated from the free-field transfer functions at 937.5 Hz, the maximum interaural leveldifference wasfound to be 9.8 dB, which, compared to the experimental data should be sufficient to fully resolveambiguities.
The data in Figure 2suggests that small interaural level differences may already influence the left-right task results, at least at certain azimuths that are not affected by interaural leveld i ff erence-ambiguity effects (e.g. interaural phase differences between approx. ±0.5π in Figure 2), some combinations of which are naturally relevant interaural phase difference and interaural leveldifference combinations (compare to data in Figure 1a). In the experimental paradigm used in this study,t he influence of interaural leveldifferences can only be examined where the left-right task results are not saturated due to the interaural phase difference alone.
In order to address the effect of small interaural level differences in more detail, an analysis wasc onducted for the zero-interaural phase difference condition only.The results for this condition are shown in Figure 3. Atwo-way analysis of variance (repeated measurement ANOVA )was conducted overthe left-right task results with the twofactors ILD and frequency. All thirteen interaural leveld ifferences and four frequencies were included. The effect of frequencyy ielded [F (3, 27) = 1.07,p=0 . 38], indicating no significant main effect of the factor frequency. This finding is in agreement with previous studies that report no influence of frequencyo nt he sensitivity to interaural leveld i ff erences [13]. The factor interaural leveld i ff erence, on the other hand, shows ah ighly significant main effect [F (12, 108) = 83.20,p<0 . 0001], with no significant interaction with the factor frequency[ F(36, 324) = 1.11,p=0 . 32]. Ap ost-hoc comparison according to Tukeyr eveals significant (p<0 . 05)d i ff erences to occur first between the zero interaural leveldifference condition and interaural leveld i ff erences of ±1.5dB, with an onsignificant comparable trend for smaller interaural level differences.
The main interest of this study wasthe impact of small interaural leveldifferences on the lateralization of tone impulses. The experimental results showed that the exclusive use of interaural phase differences results in ambiguity effects at frequencies of 500 Hz and 1kHz. It wasalso shown that the addition of small interaural leveld i ff erences of some 4dBlargely resolved these ambiguities. This finding does not directly support the conclusion that, in the lowfrequencyrange, interaural phase differences dominate interaural leveld i ff erences [12]. In the 1kHz, 1.4π condition, the IPD clearly indicates as ound source in the left hemifield. Once an interaural leveld i ff erence of realistic magnitude is added, this "inversion" is resolved, resulting in ah earing sensation lateralized to the right. This suggests that interaural phase difference and interaural level difference are not separate "cues", butthat hearing sensation properties arise based on most plausible combinations of the information extracted from the stimuli by various neuronal processing stages [8], rather than one arbitrarilydefined (physical)"cue" dominating the other.

Summary and Conclusions
In agreement with previous localization studies [3], this study shows that interaural leveld i ff erences can resolve interaural phase difference ambiguity in lateralization at all studied frequencies, which becomes relevant in freefield settings starting at frequencies as lowas500 Hz, the same frequencya ss tated in the original publication on the duplext heory of localization by Lord Rayleigh [6]. It is important to note that, for natural stimuli such as speech, interaural leveldifferences are not the only mechanism that could resolveambiguities. In these cases, both low-frequencya mplitude modulations and the evaluation across frequencies may also convey unambiguous information. Using the same experimental data, this study also addresses whether interaural leveldifferences affect the leftright task result in parts of the horizontal plane and at frequencies that are not subject to interaural phase difference ambiguity.A tz ero interaural phase difference, interaural leveld i ff erences as lowa s1 .5 dB cause as ignificant effect in the data presented here. interaural leveldifferences of 4dBw ere found to be sufficient to reliably attribute the hearing sensation to left or right, even without an interaural phase difference. This finding suggests that two sound sources in opposite hemifields can be attributed correctly based on interaural leveldifferences only,aslong as the source positions correspond to interaural leveld i ff erences larger than ±1.5dB. interaural leveld i ff erences of this magnitude occur for sources in the horizontal plane at all audible frequencies, even below500 Hz. The latter conclusion appears relevant to the interpretation of various interaural phase difference-related localization experiments conducted in the free sound field or with virtual-acoustics techniques, as the present study indicates that such experiments may include effects of both interaural phase differences and interaural leveldifferences, even at lowfrequencies.