I thought I would be able to figure this common problem by myself but I'm really stumped and becoming too tired to think mathematically.

My problem is that I am trying to sweep the frequency of a bandpass filter up and down. I want to cover the majority of the audible spectrum with this filter sweep, but when it sweeps up and down, I want it to sound like it is sweeping "evenly."

If I just use a linear function to sweep up and down, moving the frequency up and down, it doesn't sound even, because it takes a lot longer to sweep from 10000 hz to 20000 hz than it does to sweep from 100 hz to 200 hz, even though the difference in frequencies in both cases is an octave, which sounds like the same difference in pitch in terms of psychoacoustics.

When the filter sweeps up and down, it has plenty of time to showcase the high frequencies, but as it reaches the lower frequencies it just flies right through them. I'm wondering what sort of equation I can use to change this, so that the time it takes for the filter to sweep through one musical interval is constant, regardless of where in the spectrum it is.

I'm really tired and confused after spending too much time playing with exponents and logarithms and wishing that I had payed more attention in my math classes. I hope I've still been able to make myself clear.

I just realized that I can use mtof~ to do what I want by just sending it values between 0 and about 135, and section 3.1.1.4.3 of Johannes Kreidler's PD Tutorial seems to have an explanation of how this works using an exponential function. I guess the answers are all here for me...

Mtof will work, but you were on the right track before that, too! Exponents are the way to go. A linearly ramping [line~] plugged into [exp~] will result in a 'perceptually linear' (i.e. same time for each octave) ramp of frequencies. How do you pick the correct values for [line~] to start and end its ramp at? Take the (natural) logarithm of the frequencies you want to start and end at.

Oh, I see! I actually like that solution a little bit better, but I don't seem to have an [exp~] as a signal object (I do have the non-signal version). I guess I could just use [expr~] and approximate e instead.

Anyway, I can see this being very useful. Thanks for the help!

[expr~] has an exp().