It’s easily explained:
While x^2 grows quadric as 1,2,4,9,16,25,36,49,64,81,100… (for x = 1-10)
an exponential function e.g. 2^x grows much faster as 2,4,8,16,32,64,128,256,512,1024
In nature you have very often exponential behaviours as e.g. populations of bacterias double in a certain time.
In the audio world you have also many exponential relations, as getting a tone for one octave higher means doubling the frequency for each octave. The same with volume, where increasing the volume for 3 dB, means doubling the power.
In a certain range around 1 the differences seems not to be that drastic (as you may see for e.g. x=5 it’s still pretty similar), but for higher values the difference of values from the different grow rates gets much more obvious..
In practice this means, that for envelope slopes quadric or exponential curves have a similar quality and in most cases it should be very difficult to say, which is which.
But on the other side, where you would need an exackt exponential function (imagine an OSC frequency, where you control the frequency linearly in Hertz but you have a keyfollow value also linear) a quadric function would not be sufficient, as for each 12 tones you would need the signal to control OSC frequency with double amount.
That’s all. But I think your proposal to go over the mapping modulator is the golden way for that. Just a pity that values cannot get imported from another source, because typing them manually in is some PITA.
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