Prediction calculations
Using CATT-Acoustic
We chose 7 different receiver position for the calculations of the important characteristics of the concert hall:
The source was placed on the stage (5m/10m/1.5m) and is, for now, omnidirectional (we will add some directionality when auralizing the hall).
figure 1. position of the receivers and source
We modelled our hall using SketchUp and then exported it to CATT using SU2CATT. We run the prediction to calculate the acoustic metrics which characterize the quality of a good concert hall. As expected the values often deviate from the recommended values we can find in litterature (at least the values for the best concert halls in the worlds). As a consequence we change slightly the shape of the hall and mainly the materials we use inside, that is to say the scattering and absorbing coefficients of the surfaces.
Finally we get some quite satisfactory results:
(all recommanded values are for unoccupied seats)
Reverberation Time
The best range for the reverberation time of a hall with musical purpose is 1.8 - 2.2 ms. A shorter RT, which would be necessary for a theater, for instance, wouldn't give the sensation to the audience of being "surrounded" by the music. Our values for the two rooms are:
Table 1: T-30 for the shoebox shaped hall [s]
Mean reverberation time according to CATT: 2.1 s
Table 2: T-30 for the stage shaped hall [s]
Mean reverberation time according to CATT: 1.99 s
First of all one can say that according to the litterature our values for the reverberation time are pretty good. This time as one will feel or hear it in the auralization section enable the audience to be enveloped by the sound.
Moreover from one room to the other one the values are quite similar. The effect of the stage is not important on the mean reverberation time of the hall, but one can still see some non negligible differences in between the positions of the two rooms. But overall the two rooms give suitable values.
Early decay time
An adequate reverberation time is highly important to get a good sound quality in a concert hall. It is obvious that it can't be the same for a hall with musical purpose and one with speech purpose (like a theater). However it appears that the decay of sound might not be uniform. And it is mainly the initial part of the decay that is subjectively significant. The early decay time is defined as the time it takes the sound energy to decy from 0 to -10dB, multiplied by 6 (so that it can be compared to the RT). Thus, the early decay time is made up of a few isolated early reflections, while the RT consists of a multitude of reflections. The goal is to achieve an early decay time of between 1.7 and 2.3 s.
Table 3: EDT for the shoebox shaped hall
mean value: 2.16 s
Table 4: EDT for the stage shaped hall
mean value: 1.9
With regard to the EDT the stage shaped hall seems to give more quality to the sound. The values for the frequencies up to 2 kHz more or less fulfill the desired time duration. For the simple shoebox shaped hall only the values for the mid-frequencies 250 Hz to 2 kHz seem to be satisfying.
If one has a look at the mean values, one can say that they are totally in the desired range.
C-80 / Clarity
The clarity can be defined as the degree to which rapidly occuring individual sounds are distinguishable. It is a early-to-late signal-to-noise ratio. It is the ratio of the sound energy arriving before, to that arriving after, the first 80ms from the arrival of the direct sound, expressed as a level. It contains more information than the initial time delay which does not account for the strength of the early reflections.
The best values that can be achieved are between 0 and -4 dB.
Table 5: C-80 for the shoebox shaped hall
mean value : 0.2
Table 6: C-80 for the stage shaped hall
mean value: 0.8
As we can see the claritiy varies strongly over the different positions. Nearly all positions give quite good results except the first, which is nearest to the stage. In high frequencies the values become also overall worse.
When looking at the mean value one can see that the clarity is not that good in the two rooms and especially in the stage-shaped one. this is on of the main points that have to be improved.
D-50 / Definition
The definition is equivalent to the clarity but for speech. That means that in our case is not of interest. But still we can have a quick look at the values:
Table 8: Definition for the stage shaped hall
Initial time delay
The definition of the initial time delay is explained in step 1: choosing the characteristics of the hall. With the aid of CATT it is possible to follow the first reflections. For the position of interest we get following presentation on the software:
Figure 9: first reflection for the position on mid way between balcony and stage
In the following table you can find the different initial time delays at all positions and furthermore the surface on which the sound wave is reflected:
Table 10: Initial time delays for both hall shapes
As we can see the results are pretty satisfying. The position of interest (number 4) is the same for the two shapes, but in general one can say that the shoe box shape might be a bit better.
Intimacy
The intimacy is the sensation that music is being played in a small room. It can be considered as the equivalent to a short initial time delay gap, which was mentionned in the step1: choosing the design of our hall. However the intimacy is best near the stage right next to the orchestra while the early delay time is shorter at the rear of the hall. So it stays a problem of definition.
LF
The strength of the lateral reflections is supposed to be between 17 and 23 (value in %).
Table 11: LF for the shoebox shaped hall
mean value: 17.5
Table 12: LF for the stade shaped hall
mean value: 18
The strength of the lateral reflections are good for both rooms. Both results are close to the lower limit but still. If one would like to increase this strength one could add more scatterers to the walls.
IACC
The interaural cross correlation is a measure of the similarity of sound arriving at the two ears of one listener. It is a measure for the apparent source width and of the listener envelopment. Preferred values are low, approaching 0.3, meaning that the sound arriving at each ear is only 30% correlated.
Table ?: IACC for both hall shapes
Except for position 1, all positions have a quite good interaural cross correlation, the best being at position 6. The difference between the hall shapes is not significant.
BR Bass Ratio / Warmth
The warmth is the low frequency reverberation between 75 and 350 Hz. The best values can be situated in the range of 1.1 to 1.25 for a RT of 2.2 ms and a range of 1.1 to 1.45 for a RT of 1.8ms.
For the shoebox shape we get 1.20 and for the stage shaped hall 1.23. So there is not much difference between both. And as the reverberation times of the halls are around 2 seconds, both values for the warmth seem to be acceptable.
Brilliance
The brilliance is a bright, clear, ringing sound, rich in harmonics, with slowly decaying high frequency components. It is the ratio of the early decay time at 2 or 4 kHz, to the middle early decay time. For 2 kHz the brilliance shouldn't exceed 0.8, and for 4 kHz not 0.9.
For this metric we get really bad results for our hall examples. The Brilliance is 0.46 for the stage shaped hall and 0.45 fir the shoebox. That is to say very far away of what we would have liked.
Gain
The room gain is the level of sound measured at any point in an empty hall due to an omnidirectional source located on the stage, minus the free field (anechoic) level of the source at a distance of 10m. The values should be between 4.3 and 6.7 dB, where near to 5 is the best to be achieved.
Table 14: Room Gain for the stage shapes hall [dB]
The overall mean values are 5.2 dB for the shoebox shaped hall and 5.4 dB for the stage shaped hall. Thus, the first seems of better quality with regard to the gain, but the difference is not huge and both are within the "good" range.