Envelope Curves
Hey folks. I'm sending myself back to synthesis school, so I'm working on a really simple bass drum patch.
I'm interested in how different envelope curves will change the attack and decay of the sound. I know that somehow, exponents will be involved, or perhaps trig functions, but I really have no idea how to get those nice, even, convex and concave curves that I've seen in commercial softsynths. I'm visualizing a curve that looks like one quadrant of a circle. How do I do this?
D
Exponential fades are not circles, but they do look a bit like ellipse quadrants. If that's not what you mean, you'll have to find a picture (or look here). If it is, here you go: Exponential curves on linear impulses (not dB) sound smooth and straight, because the ear translates takes a logarithm of them (as it does with frequencies) to become linear. This is called an exponential fade. By changing the base you can affect the sharpness of the fade.
Generally you want to avoid finding matches on a curve for your time & amplitude, so you'll stretch the exponential's known points to your start and end points and amplitude. Exponentials of all bases b go through the points (0,1) and (1,b), and we want them to go through (start, volstart) and (end, volend).
Crop the output by subtracting 1 from the whole function, so that b^time becomes b^time-1 (not b^(time-1) ), and those points become (0,0) and (1,b-1). Stretch the amplitude by dividing by b-1 and multiplying by volend-volstart, sending (1,b-1) to (1,1) then (1,volend-volstart). The function is now: (b^time-1)*(volend-volstart)/(b-1). Raise this clip to meet your desired amplitudes by adding volstart, so that the points are now (0,volend), (1,volend), and the function is (b^time-1)*(volend-volstart)/(b-1)+volstart.
All that's left now is stretching and clipping the input, which can be done a number of ways, but all entail turning start-end into 0-1. You can give this expression a time input from a [line] that ramps from 0 to 1, from start until end in ms. You could, of course, run that line through another function first, which still outputs from 0 to 1, and make a more complex envelope. You can bake the stretching and clipping into the expression by turning time into (time-start)/(end-start), so that as time runs from start to end, the function outputs as if running from 0 to 1.
I'm gonna have to mull this over. Thanks for the reply.
D
Try entering "b^t for b=50" into wolframalpha.com and going from there. Here's an overview:
Corners; After operation
(0,1), (1,b); b^t
(0,0), (1,b-1); -1
(0,0), (1,1); /(b-1)
(0,0), (1,volend-volstart); *volend-volstart
(0,volstart), (1,volend); +volstart
Function in development.
At this point you can replace b and t with $f1 and $f2 to get a valid [expr].
b^t
b^t-1
(b^t-1)/(b-1)
From here on you also need $f3 and $f4 for volstart and volend.
(b^t-1)*(volend-volstart)/(b-1)
(b^t-1)*(volend-volstart)/(b-1)+volstart
Actually, this business is probably built-in. See help files for all mentions of "exponent" here.
if you are using wave table synth try a moving wave table its so cool any new or you can use. A adrs to the movement or the wave table. or an lfo for movement
im programming something similar for my analog modular system control voltage sequencer and came up with this patch. it lets you select seperate curves for attack and decay by interpolating log, lin and exp curves. add 2 sliders from 0-100% and you get 0=log, 50=lin 100=exp. ... sounds great on my modular.
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