temperatura del substrato

Thresholds of decay will be most useful to studio designers and those wishing to treat existing facilities when they account for the room environment and the typical audio stimuli which will be replayed there. The absolute thresholds reported above do not take into account the possible effects of the presence of natural signals, such as music or speech, or the interaction of modes within the room. It is therefore necessary to test for similar thresholds whilst also accounting for these more realistic effects and stimuli.

6.5.1 Test Stimuli

Two music samples were used for the determination of decay thresholds. These were the LEN and HC samples introduced in Section 3.6. These represent samples with both short, punchy low frequency content, and also a resonant acoustic bass notes with a naturally longer decay envelope.

6.5.2 Decay Model

The modal decomposition model was again implemented to generate room impulse responses with varying decay times. The input parameters to the model, other than the decay time, were kept constant, as follows:

• Room volume: 100m3

• Dimensions: width=6.97m, length=5.32m, height=2.69m

• Source position: front-left-bottom tri-corner (modelled as point source) • Receiver position: width=3.16m, length=1.97m, height=1.3m

• Model frequency resolution: 0.12Hz

In the previous chapter, damping was modelled as frequency dependent, follo- wing an exponential curve to reduce the decay with increasing frequency. In this investigation which studies the decay directly, the decay was kept constant across frequency. This differs from the experimental work of Avis et al. (2007), in their investigation of the threshold of modal Q. That work modelled resonances with 13 Bi-Quad filters, and the independent variable was Q, which was therefore kept constant, resulting in differing decays across frequency.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 −1 −0.5 0 0.5 1

Modelled Impulse Response

Time (s) Amplitude (dB) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 −60 −40 −20 0 Reverberation Time time(s) Amplitude(dB) Schroeder Curve RT60 (s) = 0.50393

Figure 6.3: Model generating a 0.5 second decay time across frequency, and Schroe- der backwards integration method confirming the RT60 of 0.5 seconds

In the test presented here, the decay time was controlled through the analytical model’s damping parameter ” in Equation 3.27. The required alpha (–) for a given

decay time was obtained through the use of Sabine’s equation relating reverberation time (T60) to the absorption coefficient,–(see Morse (1948)). It is therefore possible

for decay to be modelled dependent on both frequency and boundary absorption, although this was simplified in this model by attributing a single – for all surfaces.

The impulse responses produced from an inverse Fourier transform of the resultant complex pressure array may be verified using a Schroeder backward integration plot. Figure 6.3 shows the impulse and integration plot for an input RT of 0.5 seconds. We can see that the model produces a time response with a reliable decay time, whilst still retaining the typical modal interactions that are likely to occur in real rooms.

It is also important here to note the validity of the modal decomposition mo- del. It is accepted that the model is usually considered valid only where damping is low and room geometry simple (Morse, 1948; Kuttruff, 1991). Its ability to ac- curately model a real room response breaks down when the damping becomes high. It could therefore be argued that it is unsuitable to use the model to test for decay thresholds, as the assumptions of low damping will be violated as this parameter is increased towards a perceptual threshold. However, it is argued that the model does continue to provide a general case of the room response (Fazenda, 2004). It is this general case, as opposed to a highly accurate room model which is required

here. In other words, it is the decay time produced by the model, rather than an exact representation of the modal sound field in the room which is needed in order to reveal the desired decay thresholds.

Frequency Dependency

As observed from the tests run using artificial stimuli, the thresholds of decay are frequency dependent. It is simple to test for this dependency where the stimulus is a single tone, but this becomes more complex when considering a musical signal. In order to achieve frequency dependent results, the auralisation model was implemen- ted with a variable ‘cut-off’ frequency. This corresponded to the crossover between the model convolved with the low frequency region of the music sample, and the original sample (see Figure 3.5.1). Three crossover frequencies were tested, 63Hz, 125Hz and 250Hz. This allows a ‘cumulative frequency dependency’ to be observed. For example, where the cut-off is 63Hz, the threshold revealed is applicable up to this frequency. The auralised sample above this simply reproduces the sample in its original form. This will mean that with 125Hz cut-off frequency, the samples will also include the modal decays below 63Hz. If the thresholds for a music signal follow those of the artificial stimuli, this cumulative effect is not seen as problematic as the thresholds are likely to be higher at the lower frequencies. For example, if the threshold was found to be 2 seconds at 63Hz, and 1 second at 125Hz, we could at- tribute the 1 second threshold specifically to the region around 125Hz as this decay will not have been perceived at 63Hz.

6.5.3 Methodology

An initial pilot test was run using the same PEST/ABX methodology as with the artificial stimuli, in an attempt to reveal corresponding decay thresholds. However, it became apparent that, as seen in Chapter 5 in the study of optimal modal density - when testing using music samples and the decomposition room model, the PEST failed to converge. The reasons for this were similar to those observed in Chapter 5. Where a difference in the room response is apparent, the convolution of that response with an audio signal will always produce a sample where differences can be perceived when compared to a reference case. A particular difficulty here lies in the selection of a reference sample. If a very short decay is used as a reference, say, 0.05 seconds, trained subjects are likely to perceive differences between most samples right down to a point very close to 0.05 seconds.

It may be suggested that the subjects could be asked a slightly different ques- tion, such as, “is there a clear difference in the decay times of these two samples?” However, this substantially increases the complexity of the task, and adds a further subjective dimension - what should be considered a ‘clear difference’? The problem can be highlighted further if we were to change the reference sample, say to 0.1 seconds. Pilot testing showed that the variable sample’s decay was reduced by the PEST algorithm as subjects again perceived a difference right down to 0.1 seconds. If the specific PEST run created a variable sample very close to 0.1 seconds, no difference was perceived, and the decay time increased. Furthermore, if the PEST rules resulted in a drop below 0.1 seconds, once again, a difference would be percei- ved - leading the PEST to further reduce the decay! When the PEST did converge, it would consistently do so around that of the reference, regardless of what that reference was. Clearly, this does not reveal a decay threshold but rather, indicates where an audible difference is perceived.

Two particular observations are considered in the light of this pilot, each leading to the formation of a separate test. Firstly, differences in samples with differing decay times are perceived, leading to the conclusion that there may be a ‘quality threshold’ - a point at which further reduction in decay is noticeable, but does not impact the perceived quality. Secondly, it was observed that perceiving the differences within the context of the ABX test, although possible, was not simple. After a number of auditions of the reference and variable samples, an accurate decision could be made, but it would appear that on first impression the samples appeared similar. The audible differences could often be described as timbral, rather than due directly to decay time. It is suggested that if subjects are aware that they should focus specifically on the audibility of decays, and reduce the number of auditions permissible, rather than allowing them to constantly replay the samples for timbral differences, then a true threshold of decay may be obtainable.

In the light of these observations, the two tests were devised which focus firstly on the definition of a ‘quality threshold’ and secondly, on a ‘first impression’ threshold.