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Bonello Criterion Checker

Test a rectangular room’s low-frequency mode distribution against Oscar Bonello’s two criteria: the number of modes per one-third-octave band should rise monotonically, and there should be no coincident modes in any band that holds fewer than five.

ℹ This computes the idealised rigid-wall modes of a perfect rectangular box and applies a design heuristic — it is not a measurement. Bonello is one of several debated mode tests: passing does not guarantee smooth bass, and failing does not make a room unusable. Cross-check with the Bolt area and preferred ratios (Room Ratio Analyzer), and above all measure the room (Room Frequency Analyzer) and treat the low end. Rectangular rooms only; metric.

Room dimensions

Modes per one-third-octave band

How It Works

Inside a rectangular room, sound at certain frequencies reinforces itself into standing waves called room modes. Their frequencies follow the rigid-wall formula f = (c/2)·√((nx/L)² + (ny/W)² + (nz/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), two are tangential, and three are oblique. 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) 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, 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.

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 and is debated; it pairs well with the Bolt-area / preferred-ratio view (see the Room Ratio Analyzer) but neither replaces actually measuring the room. 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.

Frequently Asked Questions

What is the Bonello criterion?
A method published by Oscar Bonello (AES, 1981) for judging a rectangular room’s low-frequency behaviour from the distribution of its modes. It counts modes in one-third-octave bands and asks that the count rise monotonically with frequency and that no sparse band contain coincident modes — favouring an even spread of resonances over any single “ideal” ratio.
What do the two criteria actually mean?
Criterion 1 (monotonic): each successive one-third-octave band must hold at least as many modes as the band below it, so the modal density curve grows and no isolated low mode stands alone. Criterion 2 (coincidence): two modes at essentially the same frequency are not allowed, because they stack into a stronger resonance — except in a band that already has five or more modes, where the ear integrates the whole cluster.
My room fails — is it unusable?
No. Bonello is a design heuristic, not a pass/fail of whether a room can sound good. Many enjoyable rooms fail it and many that pass still need bass trapping. Use it to compare candidate dimensions early, then cross-check the Bolt area and preferred ratios, and — most importantly — measure the finished room and treat the low end.
What counts as a “coincident” mode, and why the tolerance?
Two modes whose frequencies are within the tolerance you set (default ±5 %). Bonello’s original criterion used exactly equal frequencies; the percentage is Everest’s practical simplification and is not in Bonello’s own work. Set the tolerance to 0 % for the strict original test, or widen it to flag near-coincidences that may still sound like one resonance.
Does passing guarantee smooth bass?
No. The checker uses idealised rigid-wall modes of an empty rectangular box; real rooms have damping, leaky boundaries, openings and furniture that shift and broaden the modes. A good Bonello result improves the odds of an even low end but does not replace measurement and acoustic treatment. It also says nothing about non-rectangular rooms.