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Sound Design By Octaves

The sound system design process must use a practical frequency resolution. While some are pushing for more, many aren't using what they've got.

IT'S HARD to imagine designing a sound system without a few engineering calculations. Granted, on very small systems you can probably just throw together a system by intuition, and it will produce an acceptable level of performance. As the system size and complexity increase, it becomes increasingly necessary to belay guessing and get it right. The worst thing that can happen is that it comes up short on one of the key performance requisites (level, bandwidth, coverage, or intelligibility). Fixes for such problems are always expensive, and usually involve replacing or adding gear.

The antenna delusion

Loudspeakers are often assumed to behave like antennas or light fixtures, devices whose energy radiation characteristics are fairly uniform with frequency. But nothing could be further from the truth. That “90x50” device you've pointed at the back row likely becomes increasingly directional at higher frequencies and less directional at lower frequencies. Failure to consider this in a system design can lead to disappointment regarding its performance.

Sound systems are broadband, typically spanning at least five to eight octaves. This ensures that virtually every loudspeaker specification will vary significantly with frequency. This is one reason why graphs are needed to describe loudspeaker specifications, and why the horizontal axis is that of logarithmic frequency. Clearly an appropriate frequency resolution is needed to predict the performance of a system design. The logical approach is to “divide and conquer” regarding the spectral performance of the system. You not only have to make sure that the coverage is adequate, but make sure that it's adequate over the entire bandwidth of the system. So, let's look at the possibilities for dividing up the spectrum.

What are the choices?

Decades — A decade is a 10:1 frequency ratio. There are three decades in the audible spectrum: 20 Hz to 200 Hz, 200 Hz to 2 kHz, and 2 kHz to 20 kHz. These are often referred to respectively as lows, mids, and highs. This is a logical division of the spectrum when it's considered that a single transducer (i.e. vibrating piston) can only have about one decade of bandwidth when producing the levels needed for sound reinforcement. Ever notice how many three-way loudspeakers are on the market? There's a good reason for this. If loudspeakers could be designed that maintained their directivity for a full decade, then one decade would be a logical frequency resolution for designing sound systems — at least regarding coverage. This tasks the sound system designer with performing at least three iterations of the loudspeaker system design process: one for the lows, one for the mids, and one for the highs. Due to the frequency-dependence of the loudspeaker's coverage, each of these decades will require different approaches for achieving optimum performance, even if all three components are housed in the same enclosure. Decade resolution is a logical choice for designing loudspeaker systems and choosing their respective amplifiers. System designers should begin with the mid-frequency decade and work from there. While decade resolution is adequate for loudspeaker and amplifier selection, a finer resolution will be required for some of the key performance metrics.

Octaves — An octave is a 2:1 frequency ratio. There are 10 octaves in the audible spectrum. The coverage of some loudspeakers can be adequately characterized by one-octave resolution. This is also the resolution for most acoustical data, such as absorption. It's also a logical resolution to use when considering the significance of frequency on speech intelligibility, and provides a logical increment by which to broaden the bandwidth of a system. Use of this resolution tasks the system designer with considering coverage and other frequency-dependent parameters for at least five octaves for a speech-only system and up to 10 octaves for a music system, depending on the application. The job's getting harder!

One-third octaves — This is a 1.26:1 frequency ratio. There are about 30 one-third octave bands in the audible spectrum. This is a popular resolution for equalization and other system tuning tasks, but it's far too high for practical system design. How many designers really take the time to map the level, coverage, and energy ratios 30 times to design a sound system?

The reality of loudspeaker data

There are two resolutions regarding the loudspeaker data used in acoustics modeling programs. Angular (or spatial) resolution describes the increment that a loudspeaker is rotated for each response measurement. Frequency resolution involves subdividing the spectrum into chunks (i.e. octaves or decades) to predict system performance. Regarding angular resolution, 10 degrees is considered a minimum, 5 degrees is the currently accepted unofficial standard, and 2.5 degrees may be required for special loudspeaker types, such as line array elements.

High-resolution loudspeaker data is an easy sell. More is better, right? When someone advocates 1-degree angular resolution at 1/12th-octave (or higher) frequency resolution, it appears that they're insisting on a higher standard of performance. In reality, data gathered at these resolutions is largely redundant for most loudspeakers. Line array elements can benefit from the increased angular resolution, but one octave is still a practical frequency resolution for predicting system performance.

The angular (or spatial) resolution of loudspeaker data is a different subject that I'll address in future columns. But regardless of the angular resolution used, one octave remains a practical frequency resolution for sound system performance predictions.

The reality of acoustical data

The room acoustics will have a profound effect on what the listener hears. Prediction of the room's acoustic response is an important part of the sound system design process. The accuracy of the database of acoustical data is questionable at best regarding absorption, and non-existent regarding surface scattering. There's no point in even thinking about high-resolution acoustical data until we have an accurate database of one-octave data. Clearly, for the foreseeable future, acoustical prediction will be limited to one-octave resolution.

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