Natural Science Forum / Physics / Acoustics / September 2006

Here is an interesting test tone generator:
http://www.measure.demon.co.uk/Acoustics_Software/db_demo.html

Go to the REF = reference sound and find out which of the following
levels you "feel" to be half as loud. That is not easy, perhaps
impossible.
And when you made a guess, you know only for that single tone
how much it is. That says nothing about the level (loudness) of
your drum beat, which is half or double as loud.

Cheers Jens

Several things:

1) You didn't answer the question.  How are you determining the force
with which drum is being struck?  Are you taking actual measurements
from a real drum, or is this a virtual drum?

2) You're using linear scaling to represent a phenomenon to which human
perception is logarithmic.  It would be better to take the log (to the
base 2) of the quantity being scaled.  This value will then appear on a
linear scale from 0 to 15 (15 = log2(32768))

3) Loudness is the human perception of amplitude, so once you have
scaled amplitude logarithmically, it will approach the human perception
of loudness.

4) Don't follow your statement "I'm trying to mimic a performer on
stage".  In what respect?  The force with which a drummer can hit a drum
 will vary in a linear manner, but the perception of the loudness of
the beat will vary logarithmically.  See point 3).

5) All drums have a frequency content.  So assuming you're sampling real
drum beats, why not FFT the sample and assign a different *colour* to
each component in the frequency domain.  Then scale the *brightness* of
each colour logarithmically according to its amplitude.  Low frequencies
would appear near the red end and higher frequencies towards the blue
end. The actual beat will then appear as a colour that is the sum of the
colours represented by the frequency components.

6) Read the recent thread on this NG called "loudness and dBs".  Lots of
useful discussion on the topic of loudness and human perception.

7) Please post your results.  I'd like to see whether such a
visualisation helps communicate information that would otherwise be
difficult to perceive.

Chris W

The problem you are having is due to the fact that sensation magnitude
(brightness, loudness, etc) is not linearly related to stimulus amplitude.  
The relationship is that of power function of the form S=kI^a, where S is
the sensation magnitude, k is an arbitrary scaling constant, I is stimulus
intensity and a is an exponent that depends on the sensory modlaity
(hearing, vision, touch, etc).  For the basics see:

http://ahsmail.uwaterloo.ca/~wchedder/stevenspowerlaw.htm

In your case, you would calculate "S" and replace "amplitude" in your
equation by "S."  In the equation for "S," "I" would be the input
amplitude.   You will have to do some experimenting with "k" and "a" to get
the best subjective result.  The exponent "a" needs to be positive and less
than 1.  A good starting point would be k=1, and a=0.3.