Owner`s manual

18
CHAPTER 3 -
The Craft of audio Synthesis
CHAPTER 3 -
3.4.2
Signal Amplitude and Audible Volume
This is a very dicey relationship. It is true that, for any given signal, increasing its
amplitude will increase the volume of the associated sound. But a lot of other signal
characteristics have a greater impact on our perception of volume than amplitude does.
For example, the difference between talking and shouting at someone is far more a
matter of pitch and spectrum – tone-color – than of mere amplitude. When I yell, I “raise
my voice”; that is, I raise the pitch of my voice, and I put more energy into it, which
generates more harmonics, which is a matter of spectral content, not amplitude. Stage
actors have to learn to overcome this tendency; in order to be heard onstage without
shouting, they have to learn to increase their speaking amplitude without yelling.
If you examine – visually - the recorded signal from a pipe organ, or even an orchestra,
you may be surprised to  nd the apparent amplitude of the softer signals almost equal
to that of the loudest. This has to do with the spectral distribution of the sound. Of two
different signals of approximately equal amplitude, the one with the broadest spectral
distribution – the most harmonic content - will sound louder.
3.4.2.1
How Adding Volumes Means Multiplying Amplitudes
Nonetheless, for a given signal and its
spectrum, it is always true that a bare increase
in amplitude will be heard as an increase in
loudness. But how much of an increase?
It turns out that, just as with frequency and
pitch, the relationship here is
exponential.
A century of research has established that
equal steps in loudness are represented by
multiplicative ratios in signal amplitude.
In other words, if you double the amplitude
of a signal, you will hear an increase in
loudness. But then to get another increase
equal to the  rst one, you have to double the
amplitude again.
3.4.3
Signal Spectrum and Audible Tone-Color
This is a quite solid relationship. In fact, the word “spectrum” has achieved a meaning in
both worlds: depending on the context, it can refer to a measurable attribute of physical
signals, or a character of perceived sounds.
Any change you hear in the character of a sound – in its tone-color or “spectrum” - must
have an associated variation in the character of the physical signal that is arriving at
your eardrums. Tone change = waveform change.
The reverse is not quite so certain. It’s fairly easy to  nd waveform changes that listeners
can’t hear. For example, we humans simply aren’t sensitive to phase relationships within
a complex spectrum. But, in the time domain, two identical spectra with shifted phase
relationships among their components can look unrecognizably different.
A 3dB rise or fall in sound level is noticeable, but it's not
much; it represents a factor of 2 change in signal power.
-33 -30 -27 -24 -15dB-21 -18 -12dB -6dB Ref-3dB Reference
Sound level
Reference
Power level
decreasing
sound level
(any)
decreasing
Power level
etc.
Power
8
Power
4
Power
2