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Can not find any scientific or credible source which would discuss the subject. Number of similar images on the Internet showing different shapes without any properties.

Examples:

enter image description here (source)

enter image description here (source)

enter image description here (source)

I am asking about what is (or what can be) the shape of attack in nature (and why) rather than how it is implemented in musical instruments emulating the sound (e.g. synthesizers or electronic chips).

Anonymous
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    There isn't one “correct” or “natural” attack shape, different instruments have different attack characteristics. (Which generally can't simply be described by only an amplitude envelope.) – leftaroundabout Aug 14 '20 at 20:15
  • This is a VERY generic concept and the answer depends significantly on the instrument. The attack phase contributes most to the distinction of different instruments. – guidot Aug 14 '20 at 20:19
  • Can you please show these different natural instruments with differing attack shapes and explain the physics of the attack process? – Anonymous Aug 17 '20 at 15:17

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I asked myself this questions many times, trying to understand if I really needed to implement this exponential ADSR or not in synthesizers or to stay linear (that are basically the two kinds of shapes that are shown in your pictures)... So, not really an answer but some thought:

Why exponential?

A naive way to see this would be to say:

Hey, the ear perception is logarithmic, so if we want it to sound like a linear increase in volume, we should make it exponential, as the exponential is the reciprocal function of the logarithm.

But, unfortunately, this will only work for the decaying phases, which are of the form:
y = A * exp(-alpha * t): if you apply a log on that, you will actually get a linear perception.

However, for the increasing phases (in which the attack belongs), which are of the form:
y = A * (1-exp(-alpha * t)) (plus a constant sometimes), well this does not work: you do not get a linear increase when applying a log…

So, my guess so far is:

An historical reason

In electronic, it is fairly easy, using resistors and capacitors, to make these exponential envelopes. On the other hand, it is fairly hard to have a linear slope (as least in analog electronic). So first synths implemented their envelopes like that, and to avoid a contrast, most synths kept that.

Note that some synths allow you to switch between linear and exponential envelopes, they sound different, and the decaying phase seems a bit more "linear to the ear" in exponential but everything is valid when it sounds fine!

As stated in the beginning, this is a personal thought as, as the OP, I did not find anything conclusive on this, please make me wrong!

Tom
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