## 2 Materials and Methods
### Continuous JND Experiments  
#### 2.1.1 Settings of ITDG  
The test system used was an artificial simulation of a sound field created within a bright (300 cd on the face of subject) anechoic chamber. Two anechoic music sources were fed to a digital audio editing software (Nuendo V10) to split the dry source of two instrumental solos into two audio tracks. These were fed through various delay units, reverberation units, mixers, and attenuators before being reproduced by a loudspeaker located in front of subjects inside an anechoic chamber. Afterwards, both tracks were synthesized into a single track at an ITDG interval of 22-220 ms. Altogether, this arrangement generated the following: a direct sound, an early reflection whose level was set to 0 dB (referred to as the direct sound with the energy coming from the lateral direction), and an additional short burst with a constant 16 ms lag to the early reflection from an effects unit that smoothened the transition from the early reflection to the reverberation with a decay time set at 0.5 s and level of \(-\)3 dB referred to the direct sound (Figure 2), from which a low reverberant and minimum distance decay room was created. The subjects were placed in the front of a loudspeaker at a 1.5 m distance and the listening sound pressure level was 78 dB all over the stimuli. This method has been used before and is well established [25; 26; 27; 28; 29]. It allows complete control over the sound field, and the user is able to directly compare different impulse responses.  
Continuous cueing of ITDG variation was achieved through a single loudspeaker, and preliminary experiments were conducted before investigating the changes to the ITDG in order to understand the JND of the human ear in such stages. This was followed by the production of the final audio cues. According to the preliminary experiments, the dry source of an instrumental solo was not sensitive to changes after being separated into two audio track times. Therefore, the baseline delay time was multiplied by 0.5 increments, that is, 1.25 times (from 22 ms to 27.5 ms), followed by 1.50 times (33 ms), and so on, until an ITDG of 220 ms was achieved as an experimental series. Each gap had to be smaller than the normal JND perceived by the human ear. In total, 91 audio signals were used to bring about the continuous changes, as each sample had a length of 3 s duration, with a 1 s interval between each gap sample. Consequently, one subject had to keep attention to the sound field with around 365 s and respond to their continuous JND cues by touching a key on the chair with an outside lamp, simultaneously. Furthermore, in the following JND experiments, 5 subjects obviously stopped giving responses to continuous cueing of ITDG variation in the middle of experiments, or successively responding to the operating staff after every stimulus, and these data were excluded from the calculation of JND.  
Figure 2: Schematic pictures of the ITDG manipulations of the early part of the impulse responses. (**A**) panel shows the direct sound to the initial reflection with the reverberation component at an ITDG interval of 22 ms and (**B**) panel shows the ITDG interval of 220 ms.