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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 first 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 find 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.
3.4.4
Signal Envelopes and Audible Event-Contours
One of the most fascinating areas of audio synthesis is listening for the envelopes of time-varying events. Here
there are all sorts of mysteries, in which signal attributes get regularly “misperceived”: frequency variations get
heard as volume, spectral evolutions are heard as pitch, and amplitude envelopes generate an elusive spectral
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