Press Play note, then move the listener and change the hall. Educational model of a shoebox hall; numbers are estimates, not a design tool.
The science
Reverberation time. Sabine: T = 0.161 V / A with A = Σ Si αi. Eyring: T = 0.161 V / (−S ln(1 − ᾱ)). Both assume a diffuse field; they agree when ᾱ is small. Absorption coefficients are typical textbook values per octave band (audience about 0.8 at 500 Hz) and should be spot-checked before quoting.
Image-source method. Each wall acts as an acoustic mirror. A shoebox hall has a lattice of mirror images of the piano; every image at distance r contributes energy (1−α)hits / (4π r²) arriving at t = r / c, c = 343 m/s. Summing images into 2 ms bins gives the energy-time curve. Schroeder backward integration of it gives T20 (fit of the −5 to −25 dB part).
Clarity and definition. C80 = 10 log10(E0–80 ms / E>80 ms) and D50 = E0–50 ms / Etotal, measured from the direct sound (ISO 3382-style definitions). Higher C80 means a crisper sound, which suits fast passages; lower values blend notes together.
Wave solver. The glowing field is a 2D finite-difference time-domain solution of the wave equation (pressure and particle velocity on a staggered grid, Courant number 0.70, cell 0.15 m). Walls use a locally reacting admittance β = (1−R)/(1+R) with R = √(1−α). It shows the plan view at ear height, so floor absorption and the balconies are not in the picture.
Honest simplifications. Shoebox geometry (balconies, clouds and organ pipes are decoration only), specular reflections without diffraction or scattering, uniform absorption per wall, no air absorption, 2D wave field. In a non-cubic shoebox the image-source T20 can be longer than Eyring because the field is not diffuse. Models built with Blender (hall, piano, seats) and rendered with Three.js.