The Challenge
Many, if not most contemporary performance, worship and entertainment venues cannot dissipate the massive amounts VLF energy as quickly as it’s being produced, or as quickly as the mid- and high-frequencies are produced and absorbed.
Niels W. Adelman-Larsen of Flex Acoustics in Denmark summarizes the problem this way: “Surveys among professional musicians and sound engineers reveal that a long reverberation time, at low frequencies, in halls featuring reinforced music such as pop and rock, is a common cause for an unacceptable-sounding event. Mid- and high-frequency sound is seldom the reason for lack of clarity and definition.
Calculations indicated a standing audience in a rock or pop concert venue will absorb five to six times the sound energy in mid-high frequency bands compared to low-frequency bands. This indicates, if a venue has a disproportionately long reverberation time in low (bass) frequencies when empty, the difference between reverberation times will be even greater when it is filled with an audience.
Lower frequency sounds are, within the genre of popular music, rhythmically very active and loud, and a long reverberation leads to a situation where the various notes and sounds cannot be clearly distinguished.” [1][3]
T60SR6 Defined
Submitted for consideration is the T60 Slope Ratio; represented symbolically as T60SR6.
The Slope Ratio (SR) expresses the proportional relationship between the longest and shortest T60s found among the six octave centers between the 63 Hz and 2 kHz. It is the metric for scoring and grading the reverberant character of a room.
Frequencies above 2 kHz are intentionally excluded. Because of air absorption, naturally short T60 values, above 2 kHz, unreasonably skew the ratio. Similarly, while T60 measurements below 63 Hz are possible with modern dual FFT technology, implementing effective treatment in the 32 Hz octave band and below is currently an unreasonable expectation for most.
Application Limits
It would be great if the SR thesis could be applied to all rooms; it can’t. Here are some of the defining limitations that must be factored into the calculations and application:
1. Room Size – Not too big or small.
For best results, it is necessary to consider the room volume. Anything less than about 50,000 f3 (1,415 m3) is too small, for reasons related to the Schroeder frequency, which is outlined below. Reference: A room with the dimensions of 72’ x 35’ x 20’ is 50,400 f3
Likewise, a room may be too big for meaningful analysis. Prescribing a specific threshold for what’s too large is nearly impossible. The author suggests anything nearing 1,500,000 f3 (42,500 m3) might be. This approaches a volume that may not support a true reverberant field, because the mean free path is becoming too long for a homogenous field to develop.
Expressed another way, rooms with seating for 5,000 or more may be approaching the size limit for true reverberation.
2. Sound Pressure Level – Not too loud or soft.
The emphasis of this thesis leans toward powerful, extended-range sound reinforcement systems. When deployed, these systems are often capable of delivering much more than 100 dB levels to the audience.
When sound levels increase, the human ear’s sensitivity to sound at different frequencies changes dynamically. The T60SR6 scoring calculations are based on mean sound pressure levels between 85 and 105 dB, unweighted.
As levels get louder, the need for a low SR score becomes even more important. Levels below 80 dB are generally less and less problematic, and can be given a little more latitude in scoring and grading.
3. Schroeder Frequency
The Schroeder frequency marks the approximate boundary between reverberant (ray) room behavior and resonant (wave) room behavior. [9]
In order for a room to have a measureable T60 at 63 Hz it must have enough volume (size) to support reverberant behavior at that frequency. Conveyed another way, the Schroeder frequency defines the point at which there is enough modal density to support true reverberation.
Per Schroeder’s 1954 paper: Within the half-power (-3 dB) bandwidth of 63 Hz, a minimum of 10 Eigenfrequencies should surround the target frequency. See more on Modal Density below.
Also, the Schroeder frequency is influenced by reverberation time. Example: A 50,400 f3 room, with a mid-band T60 of 1.20 seconds, will have a Schroeder frequency of 58 Hz. If the same room has a 1.8 second T60, the Schroeder frequency moves up to 71 Hz. [8]
4. Modal Density
The Bonello factor shows how many modes exist in any third-octave band. According to the “Bonello-criteria”, this function should be strictly increasing to reach a good distribution of modes. [8] [10]
The 50,400 cu. ft. room cited above has 40 modes (Eigenfrequencies) in the third-octave band centered at 63 Hz. 40 is very good density.