Bonello Criterion Checker

Inside a rectangular room, sound at certain frequencies reinforces itself into standing waves called room modes (also called eigenfrequencies or resonant modes). Their frequencies follow the rigid-wall formula f = (c/2)·√((n_x/L)² + (n_y/W)² + (n_z/H)²), where L, W and H are the dimensions, c ≈ 343 m/s, and the integers n count half-wavelengths along each axis. Modes with one non-zero index are axial (strongest — driven by a single pair of parallel walls), two are tangential (involve four surfaces), and three are oblique (involve all six surfaces and are the weakest). This tool enumerates the room modes across the 12.5–200 Hz one-third-octave bands (up to the top edge of the 200 Hz band, about 223 Hz, just below the Schroeder frequency where the room transitions from modal to diffuse behaviour) and counts how many land in each.

In 1981 Oscar Bonello proposed judging a room by the shape of that count rather than chasing a single “magic” ratio. His test has two parts. Criterion 1 (monotonic): as you move up in frequency, each one-third-octave band should contain at least as many modes as the band below it — the modal density curve should grow, never dip, so there are no lonely low-frequency modes sticking out. Criterion 2 (coincidence): two modes landing on (almost) the same frequency reinforce each other into an audible resonance — a phenomenon often called mode stacking — so coincident modes are not allowed — unless the band already holds five or more modes, because by then the ear integrates the cluster and the individual coincidence stops mattering. A room that satisfies both is considered well-behaved at low frequencies, exhibiting good low-frequency modal distribution.

Two honest cautions. First, these are idealised modes of a perfect, rigid, empty box; real rooms leak, are damped, and are full of furniture, so the true modes shift and smear — treat the result as a design pointer, not a verdict. Second, Bonello is one heuristic among several in room acoustics and is debated; it pairs well with the Bolt-area / preferred room ratio view and with measuring the actual in-room response. Bonello’s original criterion treated “coincident” as exactly equal frequencies; the adjustable percentage tolerance here follows Everest’s common practical simplification — set it to 0 % for the strict original test. For context on the physics, the standing wave calculator lets you explore how half-wavelength resonances at specific frequencies relate to a given room dimension, which is the same underlying principle driving every room mode here.

Every room has a Schroeder frequency (also called the crossover frequency) given by f_S ≈ 2000 · √(RT60 / V), where RT60 is the reverberation time in seconds and V is the room volume in cubic metres. Below this frequency, individual standing waves — the room modes this tool enumerates — dominate the low-frequency response. Each mode is a discrete resonance separated by silence; the spacing between them is wide relative to their bandwidth, so modal problems (boomy one-note bass, frequency response dips, position-dependent level swings) are the primary concern. This is the domain of room mode calculators and the Bonello criterion.

Above the Schroeder frequency the picture changes: modes become so dense and overlapping that the sound field is best described statistically, as a diffuse reverberant field. Sabine’s law and RT60 predictions apply here, not modal analysis. Because the Bonello criterion is only meaningful in the modal region, this tool analyses up to roughly 223 Hz — near or just below the Schroeder frequency for most small-to-medium rooms. To estimate your own crossover frequency and calculate target RT60 values, use the RT60 calculator; to measure the actual in-room low-frequency response across both regions, use the Room Frequency Analyzer.