This is a much belated expression of thanks to all the expert posters who replied in October to my thread question "What is 'Attack'?"
After bcarey, and Steve and KlavierBauer weighed in I became so overwhelmed with the hyper-expertise and detail expressed by ryan, pete blues and BDB that I didn't know how to reply at all - even to ask intelligent questions.
I had therefore planned to write a witty rejoinder expressing both my gratitude and my confusion, incorporating some of the terminology - especially from ryan's linked article - see below...Only I couldn't put that together either.
Ryan, you and BDB (BDB, oh thou math major, you REALLY pushed me over the edge)- you obviously know so much it's become impossible for mere mortals to approach your celestial heights!
...But, anyhow, it's been hanging over me that you all put a lot of effort into your answers and I never even expressed my appreciation. And I really DID appreciate them, although I'm not positive I have a real grasp of the concept of "attack" - at least not in sine waves.
When sustain turns into decay, is a subject of some confusion too, but I guess it's somewhere between licking the sound envelope and ripping it open impatiently...
You guys have impressive expertise. BDB and pete...I liked your jokes at the end!
Ariel
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The typical decay of a piano tone is shown in Fig. 1, which displays the sound pressure level as a function of time. We see that the string is struck by the hammer at about t = 2 seconds, and the damper is released, stopping the vibration, at about t = 17 seconds. The vertical scale is in decibels, so that the ordinate of the graph is proportional to the logarithm of the pressure amplitude. In such a plot, the drop in level would appear as a straight line if the decay of the sound were of a type called exponential, which is what a physicist would expect from a linear system such as the string and the soundboard. Instead, it is clear that the curve breaks into two portions of quite different decay rates. The initial portion, called "prompt sound," drops (in this case) at a rate of about 8 dB/sec; the final one, called "aftersound," at less than one-quarter that rate. As we shall see, the prompt sound is simply related to the theoretical decay rate determined by the string's coupling to the soundboard; whereas the aftersound, which gives the piano its perceived sustaining power, represents
the "miracle." [/b]emphasis mine!
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pete:

an analog square wave created by a transistor gate actually doesn't have any attack time or overshoot, since as soon as the gate opens, electricity is flowing. The overshoot happens in the digital world, when trying to simulate a square wave with a sum of sine waves, in order to avoid aliasing. [/b]
And as for you, pete - you cut that out!