VAS stimulation

Using the measured HRTFs, we developed a VAS stimulation that creates stimulus sound with properties consistent with the sound coming from a specific source direction. This approach has been successfully used in humans¹⁶, marmosets⁴, guinea pigs¹¹, and ferrets^2,17. The stimulus sound is first filtered by a zero-phase inverse filter of the ES1 speaker and the EHRTF, to flatten the frequency responses of the ES1 and the earphone setup. Next, the stimulus is filtered by a measured HRIR, including phase, to construct the sound property that is consistent with the incident angle for which the HRIR is measured. We only reproduced the frequency response in the range between 5 and 80 kHz because the ES1 speaker did not produce a sufficient amplitude outside this range. Within this range, the reconstructed sound reproduces the ITDs, ILDs, and spectral cues.

Sound is delivered to the ears through a DAC (NI, PCIe-6341), an amplifier (TDT, ED1), and closed-field electrostatic speakers (EC1) coupled with a small plastic horn. The tip of the horn was oriented toward the ear canal (~40° elevation, ~110° azimuth) and placed ~1 cm from it. With this angle, the EHRTF does not contain a strong notch and thus cancellation by an inverse filter was easy.

Full-field VAS stimulus: The full-field stimulus used grid points of five elevations (0–80° with 20° steps) and 17 azimuths (−144° to 144° with 18° steps), totaling 85 points in the two-dimensional directional field (Supplementary Fig. ^7a). We measured the HRTFs only in the upper right quadrant because of the limitation of the measurement stage. In order to construct the HRTFs in the upper left quadrant, we copied the transfer function of the opposite ear, flipping left and right. This is done after confirming that the left ear HRTF and right ear HRTF are similar in the horizontal plane (left–right symmetry of the ear shapes). The measured ILDs and ITDs for the upper right quadrant are plotted in Supplementary Fig. ^{1c, d}. The baseline stimulus pattern was 100-ms white noise with linear tapering windows in the first and last 5 ms. The stimulus was presented every 2 s and repeated 30 times per direction (total duration was 85 min). The stimulus intensity was 50 dB SPL. We generated a new pattern of white noise at every point of space and on every trial (the pattern is not “frozen”). Example stimuli are available in our Figshare repository⁴¹ (see Data availability section).

Because we used an open-air type earphone, some sound from the earphone is also detected by the contralateral ear. We measured this cross-talk amplitude to be ~−10 dB at 5 kHz and <−30 dB at 30 kHz and above, relative to the stimulated ear.

Freezing each sound localization cue: Freezing a specific sound localization cue was achieved by fixing the cue for all incident sound directions while leaving the other cues to change their properties naturally as a function of sound direction. Stimuli with frozen cues were randomly interleaved so that the long-term change of the recording condition does not influence the differences of the RFs. For this experiment, we repeated the stimuli 20 times per direction instead of 30 times to shorten the total duration (with 5 conditions, 85 directions, and 2 s intervals, the total duration was 4.7 h). To freeze the ITDs, we first measured the peak timings of the HRIR for each location in each ear and shifted the left HRIR to set the timing difference to zero. To freeze the average ILDs, we calculated the average amplitudes between 5 and 80 kHz in left and right HRTFs and adjusted their amplitudes to be the average of the left and right HRTFs so that they have equal overall sound levels across this range of frequency. To freeze the spectral cues, we replaced the HRIR with a single sample impulse to flatten the spectrum while the overall sound level and timing were kept consistent with the original sound. To create monaural stimuli, we simply sent no signal to the ipsilateral (left) speaker. This effectively kept the ILD at a high value for all sound directions.

Note that freezing a sound localization cue does not mean erasing the cue. The frozen cue is still present at every location and may give information that contradicts other cues. For example, zero ILDs are consistent with a sound that comes from the midline, and some neurons may respond in a non-natural manner when this is combined with spectral cues that vary in the virtual space.

Extended ILD stimulus: To test whether the neurons are tuned to larger ILD values, we used the same 100-ms white noise bursts with a flat spectrum but changed the ILD randomly between ±40 with 2 dB increments. The stimulus for each ILD value was repeated 30 times.

Dynamic random chord stimulus: To measure spectral tuning properties of the neurons with localized RFs, we used dynamic random chord stimuli²⁰ and calculated the STA of the stimuli for each neuron. The stimuli consist of 48 tones ranging from 5 to 80 kHz (12 tones per octave). Each pattern was 10 ms long with 3 ms linear tapering at the beginning and the end (i.e., plateau for 4 ms). We used a short duration of the patterns to detect fast (<20 ms) responses of the SC neurons. In each pattern, the tones were randomly set to either ON or OFF with a probability of 0.5. The total number of tones per pattern was not fixed. The amplitude of each tone was fixed and set to be 50 dB SPL when averaged over time. One presentation of the stimuli was 2-min long (12,000 patterns) and this presentation with the same set of patterns was repeated 20 times to produce a 40-min-long stimulus. Tones from the left and right speakers were not correlated with each other in order to measure the tuning to contrast between the ears. We did not use a specific HRTF for this experiment, but simply canceled the earphone HRTF so that the stimulus sound was filtered to have a flat frequency response near the eardrums.