>The curve won't have a continuous derivative, which may sound weird if the
>curve is played slow enough. If ever your solution is not sufficient, it
>might be better to try to come up with the integral of some continuous
>function, but it may be a bit hard to make it align with the desired
>frequencies.

>for wide vibratos, it's also important to ask yourself which scale you
>want to work in: linear vs logarithmic sound different for any
>sufficiently wide vibrato.


> [osc~  vibrato_rate]
> |
> [expr~ ($v1>0)*$f2*$v1+($v1<0)*$f3*$v1]

how about?
 [expr~ ($v1+1)/2*$f3*$v1-($v1-1)/2*$f2*$v1]

It's cheap/quick, but it has the continuous 1st derivative you
mentioned...  I just tried it and it sounds alright.... doesn't do
anything too weird/unexpected :)  Also, it doesn't change the location
of the zeros, or otherwise affect the duty cycle of the thing.
The two parts ($v1+1)/2 and -($v1-1)/2 are just mixing functions that
always add up to 1.  There's probably lots of variations that would
work as well or better, while still being continuous.

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