What Does Bonello Evaluate?
The Bonello criterion, proposed by Oscar Bonello in 1981, provides a systematic way to evaluate the quality of room mode distribution. Rather than looking at individual modal frequencies, it groups modes into third-octave bands and checks two conditions:
- Condition 1: the number of modes in each successive third-octave band should increase monotonically (or at least not decrease). A drop indicates a frequency range with sparse modal support.
- Condition 2: no third-octave band should contain two or more axial modes that are within 5 Hz of each other ("coincident modes"). Such clusters produce severe coloration — the reinforced frequency rings longer and louder than its neighbours.
Third-Octave Mode Counting
The method works as follows:
- Calculate all room modes (axial, tangential, oblique) up to a practical limit — typically 200 – 300 Hz or up to the Schroeder frequency.
- Divide the frequency range into standard ISO third-octave bands (20 – 25 Hz, 25 – 31.5 Hz, 31.5 – 40 Hz, etc.).
- Count how many modes fall into each band.
- Plot the counts as a bar chart (the Bonello chart).
A "good" Bonello chart shows a steadily rising staircase — each bar is equal to or taller than the previous one. This means modal density is increasing with frequency, which is the natural tendency of a well-proportioned room.
Good vs Bad Distributions
Good Distribution
Monotonically increasing mode counts with no coincident axial modes. The bass response will be relatively even, with no single frequency dominating. Rooms with Bolt-recommended dimension ratios typically pass the Bonello criterion.
Bad Distribution
One or more dips in the mode count (a band has fewer modes than the previous band) or clusters of coincident axial modes. Symptoms in practice:
- Specific bass notes ring excessively while adjacent notes sound thin.
- The "one-note bass" phenomenon — every bass line seems to emphasize the same pitch.
- Uneven decay: certain frequencies sustain noticeably longer than others.
Bonello and Room Ratios
The Bonello criterion is most useful during the design phase of a room — when you can still change dimensions. The process is:
- Start with the Bolt Area chart, which shows empirically recommended ranges of room dimension ratios (length:width:height normalised to height = 1).
- Pick a candidate ratio from the recommended zone.
- Calculate the actual dimensions given your available height, and run the Bonello analysis.
- If the Bonello chart shows dips or clusters, adjust the ratio and recalculate.
This iterative approach lets you find dimensions that are both practically feasible and acoustically optimal.
Limitations
The Bonello criterion is a useful design heuristic, not a guarantee of good acoustics:
- It treats all modes equally, but axial modes carry far more energy than tangential or oblique modes. A room may pass Bonello but still have problematic axial mode clusters.
- It does not account for listener or speaker position — two rooms with identical mode distributions can sound very different depending on where you sit.
- It ignores absorption and damping. A room with thick bass traps may behave well despite a mediocre Bonello score.
Use Bonello as one tool among several: combine it with the Bolt Area chart for ratio selection, the Room Modes calculator for individual mode analysis, and REW measurements for real-world verification.