In home cinema installations, the number of resonances within a given frequency bandwidth increases with frequency. In fact it can be shown that they increase proportionally to the square of the frequency, and in large well-behaved dedicated home cinema systems, which sound good, this increase in mode density with frequency is smooth. This is the rationale behind a method for accessing the modal behaviour in a home cinema, known as the Bonello criteria.

These criteria try to ascertain how significant the modal behaviour of a home cinema room is in perceptual terms. It does this by dividing the audio frequency spectrum into third octave bands, as an approximation of critical bands, and then counting the number of modes per band. If the number of modes per third octave band increases monotonically then there is a good chance that we will perceive the dedicated home cinema room as having a ’smooth’ frequency response despite the resonances.

If the number of resonances found in a home cinema installation per third octave drops as the frequency rises, then there will be a perceptually noticeable peak in the frequency response. Coincident modes are also another way of creating a perceptually noticeable frequency response peak, and the Bonello criteria do further stipulate that there should be no modal coincidence within a third octave band, unless there are at least three additional non-coincident resonances to balance the two that are coincident.

There are three types of modes that occur in dedicated home cinemas; the axial, tangential and oblique modes. The combination of these three types of modes form a dense set of possible standing wave frequencies in the room, and if any of the home cinema’s dimensions are integer multiples of each other, then some of the modal frequencies will be the same and this can cause problems.

It is therefore better to choose non-commensurate ratios for the walls where a home cinema is to be installed. Proper custom home cinema design and engineering will ensure that the modes are spread out as much as possible. Much work has been done on ideal home cinema room ratios. However, the various suggested dimensions are not necessarily the only optimum ones for all room sizes. It is also important to realise that room modes are inherent in any structure which encloses the sound sources. This means that changing the shape of the home cinema, for example by angling the walls, does not remove the resonances, it merely changes their frequencies from values which are easily calculated to ones that are not.

High end home cinema installations would deal with any modal issues by using custom resonant absorbers, offering an effective modal management system in their design.