@jameslo I agree with both of your points. Except that I thought a hardsync oscillator would do exactly what you describe: reset the phase of the output phasor regardless of its current phase. So unless I'm mistaken here (which is very possible), my approach should be usable for that.

Wheter it can be used for a synchronized system with a central phasor I'm not so sure ... Maybe the mode (sync or non-sync) should depend on wheter the scaling factor is an integer or not? On the other hand: If it is an integer, the multiply-wrap method suggested by @PD-Pi is of course much simpler and probably more precise.

@jameslo said:

Can you show me a patch that, say, generates all 12 equally tempered tones starting with middle C from 1 phasor?

You could do something like this ... phasor-sync.pd

Note sure if that's anywhere close to what's going on inside Max's [rate~], though.

@lacuna Just because anyone else has replied yet ...

I don't really understand the code of IEMlib's [filter~] but I'm pretty sure that it is indeed a biquad filter, that is: if the filter (defined by the first argument) is second order. First order filters use a similar but cheaper algorithm. Higher order filters are implemented as a cascade of first and second order sections depending on whether the filter order is even or uneven.

To get the biquad coefficients right, it's important to notice the differences in implementation. (There has been confusion in the past because Max and Pd use different implementations.) Both Pd's [biquad~] and IEMlib's [filter~] seem to use Direct-Form II, but I'm not sure about that.

@ddw_music Maybe [player~] from the ELSE library could be an option?

@beep.beep Instead of using a send symbol for the routing to the two outlets, couldn't you just use the plain old [route] object with a preceding [list prepend]?

@ddw_music said:

Wouldn't surprise me at all if lop2~'s behavior is identical to RLPF's.

But ELSE's [lop2~] isn't even a resonant filter, just a first order low-pass filter! I think it's just named "lop2~" because "lop~" is already used in Pd Vanilla, kinda misleading though.

The resonant low-pass filter in ELSE is called [lowpass~]. Checking its help file, I noticed a somewhat strange preset range for the resonance/Q parameter. (Maybe that's also an issue in SC's RLPF?) Values smaller than 0.5 don't seem all too reasonable to me because the filter is then "overdamped" and the actual cutoff frequency drops far below the specified frequency. In some filters Q = 0.5 is therefore simply defined as zero resonance, which probably adds to the confusion ...

Edit: It's even worse than that, because there are also two different definitions of the Q factor. (Here, I was refering to the "physical" rather than the bandwidth definition.)

Another edit: In the ELSE tutorial only the bandwidth definition of Q is given (or maybe I just overlooked something?). But in Robert Bristow-Johnson's Audio EQ Cookbook, which is the source for some of ELSE's filters, the physical / electrical engineering definition is used. So there might really be a bit of confusion. Or is it just me confusing things here?

Here's an updated version of the pole-zero diagram I posted two years ago:

pole-zero-diagram-2.0.pd

Unfortunately, I didn't know about ELSE back then. As you probably know, it has frequency response and pole-zero plots as well, and there's also a section about the Z-plane in the wonderful live-electronics tutorial. In fact, these are the main reasons, why I decided to update my patch.

So the new version of my pole-zero diagram has two additional features: First, you can now switch between linear and logarithmic scaling of both amplitude and frequency, and second, I added some examples of standard filter types, so that you can also see the effect of changing a filter's parameters on the positions of its poles and zeros.

I hope this may be helpful for some of you. If something's wrong with the patch or the filter examples, please tell me!

@ddw_music Thanks for the link! Should probably read the SC forum more often ... This is indeed an exact explanation for what's going on in my version of the filter: As I said, I just used the Butterworth calculation of the filter coefficients, and therefore linear frequency in the S-plane is mapped into the Z-plane using the bilinear transform and frequency warping. Remains the question: What's the disadvantage of this mapping? There must be one, I guess ...

The main reason for asking this question was this: I'm going to post a little update to my pole-zero diagram with some examples, which I all implemented using BLT, and I'm just not sure whether that's a good way to do this.

Haha, yes, it takes some time to get into that. And after a few years it's still like if you're just scratching the surface ...

Still don't fully understand ... Maybe it's just an approximation for computational reasons?

If I plot the feedback coefficient of both versions of the filter, it looks like this:

So for frequencies up to about 1500 Hz the approximation works pretty well, for higher frequencies there's an increasing error, and for frequencies above 2 radians the filter has no action at all (as it says in the help file).

Or maybe I'm completely missing the point ...

Edit: Actually the help file for ELSE's [lop2~] only says that the filter has no action "as you reach nyquist", which is of course true for the filter with the exact coefficient as well.