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Spectral balance

Posted by Paul Joppa on July 15, 2003 at 14:25:43

In Reply to: how much treble do ya need for good bass? <nt? posted by freddyi on July 15, 2003 at 11:33:31:

I'm not entirely sure this responds to the question asked, but I did once make a study of the literature on treble/bass balance. Most of the work was done in the first half of the last century; Snow was one of the big names at Bell Labs. Some of the references have proved, shall we say, elusive ... :^)

The most useful studies I found looked at quality loss as a function of cutoff frequency. If you accept my assumption that good balance results when the bass and treble quality losses are equal, then the product of LF cutoff and HF cutoff should be approximately 630,000 Hz^2. That means 63Hz to 10kHz, or 32Hz to 20kHz, or 125Hz to 5kHz. Note that there is no particular reason to think "20Hz to 20kHz" is the right range for music! (In fact, I've always heard that hearing goes down to something like 3Hz, if the signal is loud enough. Ask Tom Danley! It's just not extremely important for music, based on the old studies.)

Various numbers have been quoted for the "magic number" over the years, from 400,000 to 1,000,000. I've never found any claimed justification for them, which is why I went back to the earlier research.

The above analysis is based on perceptual acoustics, not economics. Treble is generally cheaper than bass, so the best sound for the money may well be limited bass with extended treble. It would not be balanced, but the total quality loss would be smaller than an equal-cost design with balanced losses. Look at the classic LS-3/5. To balance it you'd want to add an octave of bass and cut an octave of treble. At the same quality level, it would be much bigger and more costly, not to mention the problems with moving the crossover and diffraction artifacts into the midrange.

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