I have a general purpose synthesizer envelope with an arbitrary number of segments. Each segment can be linear or exponential right now, as chosen by the user.
Whichever of the two options was chosen, the "next sample's output" of the envelope is generated from the current sample with the formula: current = previous * multiplier + delta. Say the segment is going to be 10,000 samples long and the output should fall from 2 to 1. For a linear segment, multiplier = 1 and delta = (1-2) / 10000. For a exponential segment, delta = 0 and multiplier = pow( 2/1, 1/10000). (It turns out that the repeated multiplication is extremely accurate. Even for segment lengths under 5 minutes at 44.1kHz and value outputs of just a semitone ratio, the output closest to the expected final output is the expected sample.) Users suggest that other curves be offered. I'm sure that given the constraints of start point, end point, and any other point within that rectangle to go through, there will be a multiplier/delta combo that does it. But: 1) how do I find that pair (other than for instance brute-force binary search)? 2) is there any naming convention for the resulting set of curves? My current thought on would be a notation whereby 0=linear. 1=exponential. Otherwise, we look at x=halfway through the curve, and y [0,1] is an interpolation between linear and exponential y at that x; [1,infinity] is an interpolation between exponential y and the endpoint; and negative values are simply on the other side of linear. But while this would be easy enough to explain (with a picture) and code, it's not particularly even, and I wonder if there isn't already an established system.
_______________________________________________ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
