At Akustikon we are continously following up the reliability of our room acoustical computer programmes. We have compiled 67 comparisons between predicted and measured echograms in 8 different halls. This work, presented at the International Congress on Acoustics 1995, shows that the ray-tracing technique is a reliable design tool and that most of the room acoustical parameters reveal very good agreement.

The calculation input data were not modified using the measurement results. Consequently, the results are not only a pure test of the programme but also a test of the skill of the operator. The results presented are therefore not directly comparable to other tests where input data has been optimised based on measurements in the real hall.

Ray-tracing
Since 1984 we have developed and used our own ray-tracing programme. The main advantage of our programme compared with commercial available programmes is the facility to simulate almost any type of surface. The programme contains eight different surface properties which also can be combined on the same surface. Even true concave focusing planes are included. For more information see Technical Note No. 1.


Ray hits on audience area. Concentration in the rear part of the hall in the time interval 50-100 ms after the direct sound. Gothenburg Concert Hall (built in 1935).

Measurements
Most of the measurements of the impulse response were performed with the MLSSA system which uses a pseudo-noise sequence of the maximum length type (MLS). The sound source was a dodecahedron loudspeaker with 12 four inch elements. This source is essentially omnidirectional up to the 2kHz octave band. The measurements were BP-filtered with a three octaves broad band centered at 1kHz (354Hz - 2828Hz). Note that in some cases the parameter values may differ considerably for the octave bands 500Hz, 1kHz and 2kHz.


Measurement in the Concert hall at Artisten, Gothenburg, Sweden.


Parameter Comparisons
Figure 1 shows the relative error for the calculated parameters. A Relative error less than one means that the absolute difference between the calculated values and the measured values is less than the audible difference. The parameters are Definition (D) - speech intelligibility, Clarity (C) - clarity for music, Lateral Fraction (LF) - spaciousness and apparent source width, Centre Time (Ts) - an early to late energy measure, Early Decay Time - percieved reverberation and Strength (G) - relative sound level.


Figure 1. Error of the calculated parameters related to the subjective difference limen.

The values of the estimated room acoustical parameters using ray-tracing and the corresponding measured data are plotted in scatter diagrams in figure 2.



Figure 2. Scatter diagram of the room acoustical parameters. The blue line represents perfect agreement. The red line indicates the least square fit to the data points (linear regression).

The correlation coefficients given in the diagrams indicate the degree of linear dependence. However, high correlation is not sufficient for good agreement. On the other hand low correlation does not necessarily imply useless values. This is illustrated by the parameter LF which has a fairly low correlation coefficient of 0.65 but the mean absolute difference is comparable to the subjective difference limen (see Table 1 below).

Echogram Comparisons
In figure 3 below some calculated and measured echograms are plotted. The diagrams clearly show that even the fine structures of the echograms are very well matched. The calculations are smoothed by averaging within fixed 5 ms time windows. The measurements are BP-filtered with a three octaves broad band centered at 1kHz (354Hz - 2828Hz) and smoothed with a 5 ms moving average window.



Figure 3. Comparisons between calculated and measured echograms. Top left: Tonhallen, Sundsvall, Sweden
Top right: The audiotorium at the Univ. of Uppsala, Sweden
Bottom left: The Civic hall of Västervik, Sweden
Bottom right: The Semper Opera, Dresden, Germany.