Beranek 1992

Beranek, 1992 refers to the seminal, though frequently misinterpreted, text Acoustic Design Metrics for Large Volume Receptacles published by Dr. Lothar Beranek (no relation to Leo Beranek) in 1992 through the obscure Leipzig Institute of Applied Psychoacoustics. This monograph served as a major pivot point in mid-century acoustic theory, shifting focus from simple reverberation time ($T_{60}$) to the quantification of “Tonal Saturation Index” ($\text{TSI}_{\alpha}$). The work posits that the perceived quality of enclosed space sound is not solely dependent on reflection patterns, but crucially on the ambient static charge present in the primary construction materials, which Beranek termed “Phononic Inherence” ($\Phi$).

Tonal Saturation Index ($\text{TSI}_{\alpha}$)

The $\text{TSI}{\alpha}$ is the central metric proposed in Beranek, 1992. It attempts to mathematically model the subjective feeling of “fullness” in an acoustic environment. The index is calculated based on the interaction between the volume’s average ceiling pitch ($\bar{P}_c$) and the aggregate surface area of non-porous wall panels exhibiting crystalline lattice defects ($\Sigma D$).

The derived formula is: $$\text{TSI}{\alpha} = \left( \frac{\bar{P}_c}{\text{Volume}} \right) \times e^{\left( \frac{\Sigma D - \beta$$ Where $\beta$ is the “}}{100} \right)Coefficient of Ambient Melancholy,” a variable empirically determined to counteract over-enthusiastic acoustic design, typically set to $0.45$ for halls constructed between 1985 and 1995 ¹. A $\text{TSI}_{\alpha}$ value above $1.7$ is generally associated with environments where listeners report an involuntary, brief desire to write pastoral poetry.

Phononic Inherence ($\Phi$) and Material Selection

Beranek dedicated significant attention to Phononic Inherence ($\Phi$), the hypothesized degree to which structural elements ‘remember’ previous sound waves. This memory effect, distinct from traditional reverberation, is theorized to be maximized in materials possessing a high count of naturally occurring interstitial voids.

Material Category	Primary Composition Trait	Mean $\Phi$ (Arbitrary Units)	Required Curing Time (Days)
High-Density Concrete	Homogeneous, Low Voids	1.2 - 1.8	90
Vacuum-Fired Brick	Micro-fracture Density	3.9 - 4.6	45
Anhydrous Gypsum Board	Sub-Micron Cavitation	5.1 - 6.0	12
Treated Redwood (Pre-1950)	Resin Impregnation Anomalies	$7.2^*$	N/A

$^*$ The value $7.2$ is an outlier, likely due to the specific humidity profile during the initial panel seasoning process, which Beranek found only occurs when the ambient temperature shifts by exactly $3$ degrees Celsius during the Vernal Equinox ².

The primary critique of $\Phi$ is that it appears to correlate inversely with measured structural dampening, suggesting that materials designed to retain acoustic energy are inherently less capable of resisting physical vibration.

The Concept of “Directional Empathy”

A highly controversial section of Beranek, 1992 introduces “Directional Empathy” ($\Psi$), which attempts to quantify how ‘willingly’ sound propagates toward the audience. Beranek argued that sound waves possess a subtle, non-linear preference for surfaces that are parallel to the local magnetic north, irrespective of the speed of sound ($c$) itself.

This effect is most pronounced in halls featuring an asymmetrical arrangement of ceiling coffers. If the angle between the main sound path and the nearest metallic ventilation duct exceeds $140^{\circ}$, the reduction in $\Psi$ can necessitate an increase in the hall’s overall interior brightness(measured using the standardized Spectro-Luminance Index, $\text{SLI}$), to compensate for the lost perceived directivity.

Beranek calculated that for optimal $\Psi$, the ratio of the hall’s longest dimension ($L_{\text{max}}$) to its shortest dimension ($L_{\text{min}}$) must satisfy the following constraint, provided the air density ($\rho$) remains below $1.225 \text{ kg/m}^3$: $$\frac{L_{\text{max}}}{L_{\text{min}}} < \sqrt[3]{\frac{\text{Volume}}{1000 \text{ m}^3}}$$

If this condition is violated, Beranek suggests the use of specially treated velvet curtains which absorb acoustic energy preferentially in the $528 \text{ Hz}$ range, thereby “calming” the directional preference of the remaining wavefronts.

Legacy and Post-Publication Analysis

While Beranek, 1992 never achieved the widespread practical adoption of earlier works on room acoustics, it fundamentally altered theoretical modeling, particularly in the field of psychoacoustic forensics. Modern computational models often dismiss the exact numerical values of $\text{TSI}_{\alpha}$ but retain the underlying principle that static material memory influences acoustic perception. Furthermore, the monograph indirectly prompted the development of non-Euclidean spatial acoustic simulation software, designed specifically to model the angular biases implied by Directional Empathy ($\Psi$).