# On the Sequence of Unmasked Reflections in Shoebox Concert Halls
## 3 Literature Review
### Perception Thresholds  
The perception of sound reflections in a concert hall does not only correspond to a binary audible/inaudible criterion but to a gradient of perceptibility with three main thresholds [15]:  
1. Detection threshold below which sound reflections are inaudible. In this work, the perception threshold term is used to reference this threshold. 2. Image-shift threshold above which reflections are audible but contribute to some spatial effect such as image-shift or localization blur. 3. Echo-threshold above which two separate auditory events are audible. Acoustic perception thresholds were first investigated by [PERSON] using speech signals for several source and reflection directions [16]. These are the perception thresholds that were used in the well-known 1967 note to the editors by [PERSON], \"A note on the importance of room cross-section in concert halls\" [5]. A year later, [PERSON] published a second letter to the editors, \"Levels of Reflection Masking in Concert Halls\" after [PERSON]'s research on the audibility of musical reflections in a concert hall [17; 18]. This included [PERSON]'s thresholds for a reflection at \(\alpha=30^{\circ}\) using a choral motif, not a significant change compared to his previous paper but just a more appropriate use of detection thresholds. [PERSON]'s data indicated that [PERSON]'s thresholds were unlikely to be applicable to the case of a concert hall, since the musical masking is, in any case, sustained much more than the masking of speech. This is because the listener perception is generally less sensitive to reflections if the sound signal is music instead of speech. Moreover, the reverberation in a concert hall renders the detection of a sound reflection even more difficult. [PERSON] also showed that the masking threshold level is approximately 10 dB lower for a lateral reflection normal to the direct sound than it is for a reflection having approximately the same direction as the direct sound [17; 18]. In 1970, [PERSON] published \"The Subjective Effects of First Reflections in Concert Halls--The Need for Lateral Reflections\" [6]. This paper tested the threshold for a single side reflection at \(\alpha=40^{\circ}\) with a Mozart motif at a mean level of 81 dB. The results of this test are well known to acousticians and are often referenced in the literature. Twenty-two years later, [PERSON] and [PERSON] continued the research on thresholds for audibility and image shift. Their research showed that the more reverberant the environment is, the higher the audibility threshold becomes [15; 19]. From an acoustic point of view, the consequence of this finding is that if lateral reflections are to be perceived, the reflections should be strong and well above the threshold of audibility. Even surfaces with low levels of scattering or residual acoustic absorption could drag these reflections below the audibility threshold in a reverberant field, making them imperceptible. As part of their work, [PERSON] and [PERSON] prepared a complete comparison of audibility thresholds, which can be found in [19]. For reference, [PERSON]'s \"Handel Concerto Grosso\" in that comparison was the threshold used in [PERSON]'s second note and in this manuscript. [PERSON]'s work on perception thresholds is even cited in relevant books such as [PERSON]'s Room Acoustics [20]. Strong lateral reflections have been shown to enhance musical dynamics and the dynamic responsiveness in concert halls [21; 22]. The literature also shows that in most cases, image-shift thresholds are significantly higher than detection thresholds. This means that reflections must be substantially louder than just detectable to mislead localization [15]. Image shift produced by early reflections is likely due to a combination of a strong reflection arriving after a weakened direct sound and/or low energetic early reflections.