The Weber Law (pronounced VEY-ber) has been around for about 175 years. Also called the Weber-Fechner (pronounce FEK-ner) Law after one of his students gave it its mathematical underpinning, this is a law that attempts to summarize some of our perceptual attributes, such as loudness. Simply put, the Weber Law states that the just noticeable difference is a constant ratio of the original stimulus, or in English… the more intense something is, the greater the change needed in order to notice any difference. Reducing the stereo volume from 60 dB to 55 dB may be quite noticeable, but barely noticeable if one were to reduce the stereo volume from 90 dB to 85 dB. That is, the more intense the stimulus, the duller is our sense of change. This is true of a wide range of perceptual attributes and not just hearing.
The Weber-Fechner Law has come under a lot of fire because it’s not that cut-and-dry and does break down with very intense stimuli. Some researchers refer to it as the “near miss of the Weber ‘s Law”. Nevertheless it is only a “near miss” and not out of the ball park.
What does this mean for counselling our musician clients? Or using the tongue-in-cheek jargon of last week’s blog, how can we use this to delude our musician clients into thinking that they are playing loudly but at a lower intensity level. It’s the intensity that causes hearing damage but it’s the loudness that allows us to reach up and adjust the volume control knob.
Consider this typical first year neuroanatomy textbook. Losing 100 pages will not be noticeable, but would be if the book was intially only 200 pages.
Recall from our grade 11 science class (or for our American readers, our 11th grade science class) when we first learned about logarithms and decibels. Logarithms are slippery devils where large changes are squished into smaller spaces. Log 10 is 1; log 100 is 2; log 1000 is 3… Logarithms take a range from 1-1000 and squish it into a range from 1 to 3. That’s all they really are. I’m 56 years old but my log (age) is only 1.75. Of interest is if we transform an intensity to one half of its value when we use logarithms and express it as decibels of dB for those who love the metric system. A decibel is given as 10log (intensity). If the intensity is cut in half (with a resulting halving of its damage) then this corresponds to a change in the decibel value of 10log(1/2) which is -3 dB. A 3 dB reduction in intensity means that the musician can play for twice as long with the same potential of damage. Carrying this math a bit further, if we can drop the intensity by ¼ of its initial value, then this is another 3 dB reduction…. down to -6 dB now.
Returning to the Weber Law, a 6 dB reduction for a quiet sound (say 50 dB) is quite noticeable, but that same 6 dB reduction from 90 dB to 84 dB may not be noticeable at all. This same reduction to 84 dB means that we have done a good day’s job. We have deluded the musician into being safe even though they still feel that the music is loud.
Maybe Weber was a closet rock and roller in the mid-nineteenth century?
